JPH05159085A - Programarle membership function device and fuzzy inference method/device using it - Google Patents

Abstract

PURPOSE:To obtain the programable membership of variable weight by being given the generating circuit of a weighting signal expressing the maximum value of a membership function and the weighting signal of the generating circuit. CONSTITUTION:A membership function circuit group 12 is provided with many membership function circuits of variable parameters. selects prescribed one or plural numbers of them in accordance with an input signal from a converting circuit 11 and outputs a signal expressing a membership function corresponding to the input signal. On the other hand, a circuit 15 generating one or plural membership functions is provided. The output of the membership function from the circuits 12 and 15 are calculated in accordance with a fuzzy inference and the calculation result is outputted. The output of a fuzzy logicalcircuit network 13 or a defuzification circuit 14 is compared with a reference input. A control/ storing circuit 16 is changed a parameter including the shape and weight of the respective membership functions so as to make the deviation to be zero in accordance with the result of the comparison.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a programmable membership function device and a fuzzy inference method and device using the same.

[0002]

BACKGROUND OF THE INVENTION New Fuzzy Logic Circuits Operating in Mode Fuzzy logic is logic that deals with fuzzyness or "ambiguity." There is ambiguity in human thoughts and actions. Therefore, if such ambiguity can be quantified and theorized, it should be applicable to the design of traffic control, emergency, social systems such as applied medical systems, and robots imitating human beings. LA Za in 1965
Since deh proposed the concept of fuzzy sets, fuzzy logic and fuzzy reasoning have been studied as one means to deal with "ambiguity" from this point of view.

Fuzzy inference is most commonly performed according to so-called If, then rules. The If, then rule is formulated as follows.

If x = A, y = B, then z = C

Here, x and y are input variables and z is an output variable. A, B, and C represent fuzzy sets, and are generally expressed using a membership function.

[0006] Human experience rules, know-how, etc. are described in If, t
It is properly expressed by a set of hen rules (rules). Whether or not the set rules are correct is verified by the fuzzy inference result or the control result of the object based on it.

If the result of the verification is that the rule group is insufficient or erroneous, a more appropriate rule group will be formed by deleting, adding or correcting a part of the rule group. Modification of some of the rules involves modification or adjustment of the membership function, which is achieved by changing the parameters of the membership function. The type of membership function parameter depends on how the membership function is defined, but the value that represents the maximum value of the membership function (the maximum value of the grade) is particularly important. The maximum value of this membership function is also called the weight of the membership function.

[0008]

DISCLOSURE OF THE INVENTION The present invention provides an apparatus for generating a membership function with variable parameters, in particular, a programmable membership function apparatus with variable weight, and a fuzzy inference method and apparatus using the same. It is a thing.

A programmable membership function device according to the present invention is provided with a weight signal generating circuit representing a maximum value of a membership function and a weight signal of the generating circuit, having a predetermined shape, and having a maximum by the weight signal. It is characterized in that it is composed of a membership function circuit which outputs a signal representing a membership function whose value is defined, and the maximum value of the membership function represented by the weight signal of the generating circuit is variable.

A fuzzy inference method according to the present invention uses a membership function according to a set fuzzy rule, and applies an input signal to the membership function to perform a fuzzy inference operation according to the fuzzy rule to obtain a fuzzy inference operation. The inference operation result is compared with the reference value, and the weight of the membership function is changed according to the comparison result.

In the fuzzy reasoning apparatus according to the present invention, the membership function is set according to the set rule, the grade corresponding to the input of the membership function is output, and at least the maximum grade of the membership function is output. Changeable membership function value generating means, means for executing fuzzy inference operation according to the above rule by using the grade output from the membership function value generating means, and the member in the membership function value generating means Means are provided to control the maximum grade of the ship function.

According to the present invention, since the maximum value of the membership function, that is, the weight can be changed, the fuzzy reasoning result or the control result based on it can be compared with human experience rules, know-how, expected values, target values, etc. It is possible to modify the rules by changing the weight of the membership function so that a better fuzzy reasoning result can be obtained upon verification.

[0013]

Embodiments of the present invention will be described in detail below.
Although the following embodiments mainly show a circuit that operates in the current mode, the present invention can be realized not only by an analog circuit architecture including a voltage mode but also by a digital circuit architecture including a computer and software processing. Needless to say.

(1) Concept of Membership Function Circuit and Fuzzy Control System (FIGS. 1 and 2) The fuzzy set A is characterized by the membership function μ _A (x). The membership function μ _A (x) represents the degree to which the variable x belongs to the fuzzy set A, and this degree is represented by continuous values [0, 1] in the interval from 0 to 1. .. An example of the membership function μ _A (x) is shown in Fig. 1 (A).

The membership function circuit is a circuit which outputs a value μ _A (x) representing the degree to which the variable x belongs to the fuzzy set A when the variable x having a certain value is given as an input.

An example of the concept of a fuzzy control system using a fuzzy logic circuit (or device) and a membership function circuit (or device) is shown in FIG.

As an example of the application of fuzzy control, it has been considered to automate the control of a system that has been operated or controlled by humans based on abundant experience and feelings.
The general system of human control is extremely complicated, but if it is simplified, it can be understood as a combination of some or many empirical rules. This empirical rule is that if XX (state etc.) is XX, △△
(State of etc.) can be expressed in a straightforward manner. To make this rule of thumb a little more complicated, "XX is XX
And (or) 〇 × is × 〇, △△ is □
□ Let's develop it, and it becomes more general. In the fuzzy control system, the propositional form of this general empirical rule is called control rule or fuzzy inference rule or If, then rule.

According to the usage of the feedback control system, the output e of the controlled system and its deviation Δe are used as control inputs, and the control output given to the controlled system is Δu.

In FIG. 2, as an example of the control law, control law 1 "If e is a small negative value and Δe is a small positive value, let Δu be a small positive value" is given.
This control rule 1 is expressed as e = NS and Δe = PS → Δu = PS. Here, NS is a negative small value.
ll), PS is a positive small value, an
d means "Katsu", respectively.

As the control law 2, "if e is a small positive value and Δe is a small negative value, then let Δu be a small negative value". This is expressed as follows.

E = PS and Δe = NS → Δu = NS

In addition, some or many control rules are set.

Answer to the question as to how much the given control input e = e ₀ is a small negative value in judging "e is a small negative value" in the control rule 1. Is membership function 1 _A <MS function 1 _A
>>. The membership function 1 _A is obtained from the membership function circuit (not shown), and the control input e
Represents the degree of belonging to the “set of small negative values”. In FIG. 2, as the membership function 1 _A , a triangular function having a peak at a certain negative value of e is given. According to this function 1 _A , a certain control input e = e ₀ =-
The degree (fitness) that 0.2 belongs to this set is 0.8.

Similarly, FIG. 2 shows a membership function 1 _B <MS function 1 _B > representing the degree to which the control input Δe belongs to the “set of small positive values”. This function 1 _B also has a triangular shape that peaks when Δe has a certain positive value. According to this membership function 1 _B output from the membership function circuit (not shown),
The degree to which a control input Δe = Δe ₀ = + 0.1 belongs to this set is 0.6.

The condition "and" of "e is a small negative value and Δe is a small positive value" in the control rule 1 is generally calculated by fuzzy logical product (MIN). This operation MIN specifically selects the smaller of the two variables. Therefore, the membership function 1 above
From the value 0.8 of _A the 1 _B value 0.6 Prefecture, 0.6 is obtained as representing the operation result of MIN.

The command "set Δu to a small positive value" in control law 1 is also a membership function <original command 1
> Is given. The function representing this original command 1 is also Δ
A triangular shape having a peak value of 1 when u is a positive value is shown as an example. The function representing the original command 1 is generated from a membership function generating circuit (not shown).

The "if" in control law 1 is executed by, for example, multiplication. The value 0 by the MIN operation described above.
6 is obtained. When the function of original command 1 is multiplied by this 0.6, a triangular function <command 1> with a peak value of 0.6 is created.

The calculation of "if" may be performed by MIN. In this case, a trapezoidal function as shown by the broken line will be obtained as the command 1.

Similarly in the control law 2, the <command 2> is created by applying the control law 2 to the given control inputs e and Δe. The application of other control laws could create other directives as well.

In general, a plurality of control rules are set for one controlled system as described above. The respective commands derived from these control laws are used to finally obtain the control output Δu. Therefore, the fuzzy logical sum (MAX) operation is performed on the commands derived from each control law. The graph of <inference result> shown in FIG. 2 shows the MAX operation result of <command 1> and <command 2>. Among them, the solid line graph shows that multiplication was used as the “if” condition of each control law, and the broken line graph shows that MIN was performed as the “if” condition.

Finally, the control output Δu is determined using such an inference result. This is called defuzzification. The above-mentioned operations including the generation of the membership function are performed in a state in which “ambiguity” is included according to the fuzzy logic. At this stage, however, the control output Δu having one fixed value is set.
Have to decide.

The defuzzification can be performed, for example, by taking the weighted average of the function indicating the <inference result>, that is, by obtaining the position of the center of gravity. In this embodiment, finally the control output Δu =
It has been determined that Δu ₀ = + 0.1. Almost the same result will be obtained when MIN is performed as an operation of “if”.

The position of the center of gravity of <command 1> and the position of the center of gravity of <command 2> may be obtained first, and the weighted average of these two positions may be taken to perform the defuzzification.

Membership functions 1 _A , 1 _B, etc. are preferably variable. That is, it is monitored whether or not the control is properly performed in the process of continuing the control of the controlled system by the control output Δu determined as described above. If the optimal control is not performed, the membership function (its value or the shape of the graph) is changed to pursue the membership function that enables the optimal control. This is generally called "learning function".

(2) Concept of Fuzzy System with Learning Function (FIG. 3) FIG. 3 schematically shows an example of the fuzzy system with the learning function as described above.

Any physical input, such as the above-mentioned control input or key-input data, is normalized by the input conversion circuit 11 as necessary, or converted into a signal of an appropriate form. This conversion circuit 11 may be unnecessary in some cases.

The membership function circuit group 12 is provided with a large number of variable membership function circuits, one of which is predetermined according to the input signal from the conversion circuit 11.
Alternatively, a plurality of signals are selected and a signal representing the membership function corresponding to the input signal is output.

On the other hand, a circuit 15 for generating one or more membership functions is provided. The membership function outputs from these circuits 12 and 15 are input to a fuzzy logic network 13, where an operation according to a predetermined fuzzy logic is performed and the operation result is output. The logic of this network 13 and the parameters of the membership function generating circuit 15 are also preferably changeable as required.

The fuzzy information output from the fuzzy logic circuit network 13 may be output as it is, but in some cases, the defuzzification circuit 14 makes some decision and outputs it.

This output may be displayed or used as the control output Δu described above, and may be used for various purposes.

The output of the fuzzy logic network 13 or the defuzzification circuit 14 is compared with a reference (standard, standard) input. This reference input represents the correct answer for learning, such as experienced expert, digital
It may be given by computer simulation or the like.

The control / memory circuit 16 includes the shape and weight of each membership function of the membership function circuit group 12 and the membership function generation circuit 15 so that the deviation becomes zero according to the comparison result. The parameters and the like are changed, and the type and connection of logic functions in the fuzzy logic network 13 are changed.

In this way, the fuzzy system is adjusted and changed by learning so that the correct output (correct answer) is always generated.

(3) Membership functions of various types and their definitions (FIG. 4) Membership functions are generally represented by curves as shown in FIG. 1 (A). It is often done. However, whether it should be represented by a curve is not essential to the membership function. The more important feature of the membership function is that it takes continuous values from 0 to 1.

On the other hand, from a practical point of view, FIG. 1 (B)
As shown in Fig. 3, it is easier to handle the membership function with a straight broken line, the membership function can be characterized by a small number of parameters, and the design and setting are also easy. Moreover, even if the membership function is represented by a broken line, the above characteristics are not lost.

Therefore, in the following description, all memberships will be represented by straight lines or broken lines thereof.

The membership function shown in FIG. 1B is only an example. There are many other types of membership. The definitions will be described below.

FIG. 4 and FIG. 5 show ten kinds of membership functions.

The first (FIG. 4 (A)) is a function that always takes a value of 0 regardless of the value of the variable x, which is defined as a φ function.

The second (FIG. 4 (B)) is defined as one function that always takes the value of one.

The third one (FIG. 4 (C)) takes a value of 1 in the region where the variable x is small, and when it reaches a certain value Z _B , it decreases with a constant gradient and finally reaches 0, and x becomes zero. It is a function that always takes a value of 0 in a region larger than that. That is, the variable X
It has one down slope on the axis. This is named the Z function. We call x = Z _B a breakpoint. The gradient can take any value. The Z function can be defined by the breakpoint Z _B and the slope. Z _B = 0, Z _B
Even if <0, this is included in the Z function.

The fourth type (FIG. 4 (D)) is an inverted version of the Z function, which is defined as the S function. That is, it has one upward slope on the X axis. The S function is also defined by the breakpoint S _B and the slope.

The fifth one (FIG. 4 (E)) is called the π function and takes a value of 1 when the variable x is in a certain region, and x becomes smaller than the break point S _B2 or When it becomes larger than Z _B2 , it decreases with a constant gradient and finally becomes 0.
Is a function that takes a value of 0 and is always 0 in a region where x is smaller and larger than that. It can also be called a trapezoidal function. The π function has two break points S _B2 and Z _B2.
And gradient.

In a special case, S _B2 = Z _B2 , which is a triangle as shown by the chain line.

The sixth one (FIG. 5 (F)) is defined as a U function which is the inverse of the π function. It can be said that the function has one valley. The U function is defined by two breakpoints Z _B1 , S _B1 and a slope. In a special case, the shape is indicated by a chain line (Z _B1 = S _B1 ).

The form of the membership function becomes more complicated.

The seventh one (FIG. 5 (G)) is a combination of a trapezoidal function (π function) and an up-slope function (S function) in a region where x is larger than that, and N Defined as a function. From a different perspective, this can also be said to be a combination of a function having a valley (U function) with a function of an upslope (S function) in a region where x is smaller than that. In any case, this N-function is defined by three break points S _B2 , Z _B2 , S _B1 and a slope.

The eighth one (FIG. 5 (H)) is the inverse of the N function and is defined as the И function. This is also defined by three break points Z _B1 , S _B2 , Z _B2 and a slope.

The ninth one (FIG. 5 (I)) is called the W function, which can be said to be a combination of two functions having valleys (U functions), or a trapezoidal function ( It can also be said that a function having a downward slope (Z function) and a function having an upward slope (S function) are combined with the π function), and further, a combination of the N function with the Z function or the И function with the S function. It can also be a combination. In any case, the W function has four break points Z _B1 , S _B2 , Z
Defined by _B2 , S _B1 and the slope.

The last one (FIG. 5 (J)) is an inversion of the W function and is defined as the M function. This is also defined by four break points S _B1 , Z _B2 , S _B2 , Z _B1 and a slope.

It can be easily understood that a more complicated membership function can be defined by appropriately combining the above two or more functions.

Although only the positive region of the variable x is shown in FIGS. 4 and 5, it goes without saying that it can be extended to the negative region of x. In this case, the above-mentioned break point can also generally take a negative value.

Although it is possible to take any gradient such as an upslope, a downslope, a trapezoid, a valley, etc.
(Or -1) is the simplest. As will be described later, even if the gradient is 1, an arbitrary gradient can be obtained by changing the range of the vertical axis and the horizontal axis when using the circuit. If the gradient is defined beforehand, the above-mentioned 10 functions can be uniquely defined by only one or a plurality of break points.

(4) Z function circuit (FIGS. 6 to 9) FIG. 6 shows an example of a membership function circuit that outputs a Z function. Here, the input variable is represented by Z, and the Z function is represented by f _Z. In addition, this circuit operates in the current mode, and is a circuit with a suction input and a discharge output. Suction input is a form in which the input current flows into the circuit, and discharge output is a form in which the output current flows out from the circuit.
In the current mode, positive and negative of variables and functions are represented by the direction of current, and their absolute values are represented by current values.

The membership Z-function circuit of FIG. 6 has a current source (which gives the circuit a discharge input current) 23 for supplying a current representing the break point Z _B , and a current mirror (C
M) 25, a current source (providing a sinking input current to the circuit) 26 for giving a current of value 1, and a diode 28. The current mirror 25 is composed of two N-MOS FETs. A graph showing the current flowing through each part of the circuit of FIG. 6 is shown corresponding to the arrow indicating the direction of the current. Further, a graph of the output current f _Z is shown in FIG.

A current representing the value of the input variable Z (Z ≧ 0) flows into the input terminal 21. A current source 23 is connected by a wired OR 24 between the input terminal 21 and the input side of the current mirror 25.
A current of _B (Z _B ≧ 0) flows out. Therefore,
From wired OR24 to current mirror 25 Z and Z _B
The current that represents the difference (Z-Z _B ) from the
Actually, the current mirror 25 acts as a current blocking diode against the reverse current, so that a current having a limit difference (Z <BD> Z _B ) flows (see the graph). Here <BD>
Represents the operation of the fuzzy marginal difference (however, the minus sign is circled according to the usual usage in the drawing), and the marginal difference has the following contents.

[0067]

[Equation 1]

From the output side of the current mirror 25, a sink current of the same value is output. A current source 26 is connected by a wired OR 27 between the output side of the current mirror 25 and the output terminal 22. Therefore, in wired OR27 1-
(Z <BD> Z _B ) is calculated, and the current of this value is about to be discharged or sucked from the output terminal 22 (see the graph). However, wired OR27
Since the diode 28, which is in the forward direction with respect to the discharge output, is connected between the output terminal 22 and the output terminal 22, the sink output current which appears at the terminal 22 becomes zero. This is 1
This is equivalent to the operation of <BD> (Z <BD> Z _B ).

The above operation is summarized as follows.

[0070]

[Equation 2]

FIG. 7 is a graph showing this operation. The down slope of this Z-function is -1.

The diode 28 is a diode-connected MOS.
It can be replaced by FET.

When the input current Z is negative (provided that Z _B ≧
0), the current (Z + Z _B ) tries to flow from the current mirror 25 toward the wired OR 24, but the current mirror 25
Prevents this current from flowing out, so that the current flowing between the current mirror 25 and the wired OR 24 is zero. Therefore, the output current of the current mirror is also 0, and the current of the value 1 of the current source 26 is discharged to the output terminal 22 as it is.

When the break point Z _B is negative (where Z ≧ 0), the current (Z + | Z _B |) flows from the wired OR 24 into the current mirror 24, so that the current mirror 25
Also the suction output current becomes _{(Z + | | Z B)} . Therefore, the output is represented as:

[0075]

[Equation 3]

Expression 3 represents an operation in which the graph of FIG. 7 is left-shifted as it is so that Z _B is on the negative side.

Break point Z _B and input current Z
When both are negative, a current of (| Z _B | <BD> | Z |) flows from the wired OR 24 toward the current mirror 25. Therefore, the suction output current of the current mirror 25 is also given by (| Z _B | <BD> | Z |), and the discharge output current is expressed by the following equation.

[0078]

[Equation 4]

Expression 4 also expresses the state where the graph of FIG. 7 is shifted to the left.

In this way, the circuit of FIG.
Applicable to the values of and Z _B.

FIG. 8 shows a Z-function circuit realized by using a bipolar transistor array (TA78 manufactured by ROHM). Circuits corresponding to the current source, the current mirror and the like in FIG. 6 are given the same reference numerals. In addition, the input terminal 21 of FIG.
The input circuit 21A instead of the output terminal 22 and the output circuit instead of the output terminal 22.
22A is provided. As the diode 28, a diode between the base and emitter of an NPN transistor (one in TA78) is used.

FIG. 9 shows experimental results measured using the circuit of FIG. Experiments were performed on three different Z _B (parameters). The input current Z, the break point current Z _B , the current with a value of 1 and the output current f _Z were measured as the voltage drop of the resistance in each circuit. f _Z = 10 μA corresponds to μ = 1, and f _Z = 0 μA corresponds to μ = 0.

As can be seen from this graph, the circuit of FIG. 8 has a very good linearity and the circuit structure is simple. Such excellent linearity cannot be realized by a simple voltage mode circuit, and this is a major reason why a membership function circuit is realized by a current mode circuit. Further, the circuit of FIG. 8 has a characteristic that it is suitable for integration because it uses a current mirror and thus has good temperature stability and does not use resistors other than the current source.

Further, as can be seen from FIGS. 8 and 9,
The Z function circuit can be realized with extremely high practicality not only by the MOS FET but also by the bipolar element.

(5) S-function circuit (FIGS. 10 to 13) An example of the membership S-function circuit is shown in FIG. The input variable (input current) is shown by S, and the S function output (output current) is shown by f _S. The current S _B representing the break point is provided by the current source 33 and the current representing the value 1 is provided by the current source 36.

The basic difference between the S function circuit and the Z function circuit lies in the direction of the current input to the wired OR 34 (corresponding to the wired OR 24 in FIG. 6). This wired OR
The input current S is supplied to the 34 as a discharge input, and the break point current S _B is supplied to the 34 as a suction input. For this reason, the direction of the sinking input current given to the input terminal 31 is inverted by the current mirror 39. In addition, the break point current source 33 is designed to give a suction input to the circuit (the current source in FIG. 6).
Compare with 23).

The wired OR 34 and the current mirror 35 calculate S _B <BD> S. Furthermore, the calculation of _{1- (S B <BD> S} ) by wired OR37 is performed. Diode-connected MOS acting as a diode
Since current in the output direction suction by FET 38 is prevented, f _S = 1 <BD> as eventually the output current (S _B <BD
A discharge output current representing> S) is obtained. A graph of this output current is shown in FIG.

In this S function circuit, it is possible to set the break point S _B to a negative value, but S _B
In the case of <0, the output current f _S always takes the value of 1 in the region of S ≧ 0, and it is not possible to find any special meaning in setting S _B to be negative. It suffices if S _B = 0.

An S-function circuit implemented using bipolar transistors is shown in FIG. Also in this figure, the circuits having the same functions as those shown in FIG. 10 are designated by the same reference numerals. Reference numeral 31A is an input circuit corresponding to the input terminal 31, and reference numeral 32A is an output circuit corresponding to the output terminal 32. The measured characteristics (parameterized by S _B ) of the circuit of FIG. 12 are shown in FIG. It can be seen that this S-function circuit also has an excellent straight line.

(6) Arbitrary Setting of Gradient at Use (FIGS. 14 and 15) As shown in the conversion circuit 11 in FIG. 3, generally in the discussion of the membership function, the input value of the physical quantity is The maximum value (or the allowable value of the circuit) is used for normalization, and the normalized value is used as an input value. For example, when the height H is handled, the maximum value (for example, 2 m) H _max is used to normalize the height input by H / H _max .

As an example, the membership function μ _SH of the set “tall person” is shown in FIG. 14 (A) as the S function, and the membership function μ _ZH of the set “short person” is shown in FIG. 14 (B). Each is shown as a Z-function. The horizontal axis (variable) of these membership functions is S = H / H _max , Z = H / H
Expressed as _max .

Therefore, in the circuit, the maximum value H
Setting the effective slope of the membership function, that is, the upward slope of the S function and the downward slope of the Z function, to arbitrary values depending on how many μA the _max corresponds to and how many μA the grade 1 of the function corresponds to Is possible. In the Z function circuit and the S function circuit using the current mirror described above,
The slope of (output current) / (input current) must be -1 or 1
However, it is possible to obtain an arbitrary gradient depending on how it is used.

An example in which the slope is substantially changed is shown in FIG. 15 using the Z function. Fig. 15 (A) shows that H _max is 100 µ.
In A, the membership function of the set “short person” when grade 1 is made to correspond to 10 μA is shown. For a membership function such as
When it is desired to reduce to 1/2, as shown in Fig. 15 (B), H _max
Should correspond to 50 μA. Further, when it is desired to make the gradient 1/4, H _max should be set to 25 μA as shown in FIG. 15 (C).

As described above, even if the gradient of the membership function generating circuit is fixed to +1 or -1, it is possible to set an arbitrary gradient depending on how it is used.

(7) Gradient switching control (FIGS. 16 to 19) It will be described below that it is also possible to change the gradient of the membership function in the circuit configuration.

FIG. 16 shows a configuration in which the current source 23, the wired OR 24 and the current mirror 25 in the Z function circuit shown in FIG. 6 are taken out and the current mirror 25 is modified to be a current mirror 25A.

The current mirror 25A includes a current mirror 41 having two output drains having the same area and an N-MO for switching the parallel connection of these two output drains.
It consists of S FET 42. The FET 42 is on / off controlled by a control signal V _C given to the control terminal 43.

Output signal Z <BD> of this current mirror 25A
A graph of Z _B is shown in FIG. Control signal V _C to L
When set to level, FET 42 is off, so the current mirror
The output current slope at 25 A is 1. In this case, the current mirror 25A has the same function as the current mirror 25 shown in FIG. When the control signal V _{C is set} to the H level, the FET 42 is turned on, a current flows through the two output drains, and as a result, a double output current flows, so that the gradient is 2
Becomes

Therefore, when such a current mirror 25A is used in place of the current mirror 25 of FIG. 6, a Z function circuit capable of switching the gradient according to the level of the control signal V _C is realized. Entering the Z-function circuit when the gradient becomes 2,
The output characteristic is shown by the broken line in FIG.

It is possible to switch an arbitrary number of gradients without being limited to two types of gradients. FIG. 18 shows a part of the S-function circuit. Here, the current mirror of FIG. 10 is used.
35 is replaced by a current mirror 35A. Current mirror 35
In A, the current mirror 44 has three output drains, these output drains are connected in parallel, and two of them are FEs as switching elements.
T 45 and 46 are connected. The FETs 45 and 46 are on / off controlled by control signals V _C1 and V _C2 applied to their control terminals 47 and 48.

As shown in FIG. 19, when both of the two FETs 45 and 46 are off (V _C1 = V _C2 = L), the slope of the output current is -1, and when either one is on. (V _C1 =
H, V _C2 = L or V _C1 = L, V _C2 = H) The gradient is -2,
When both are on (V _C1 = V _C2 = H) the slope is -3.

(8) Programmable multi-membership function circuit (FIGS. 20 to 22) Of the ten fuzzy membership functions described above, M
A multi-membership function circuit in which nine functions, excluding functions, can be freely programmed (or externally controlled) is shown in FIG. This function circuit includes a multi fan-out circuit 50, a first Z function circuit (No.1) 51, a second Z function circuit.
Z function circuit (No. 2) 52, first S function circuit (No. 1) 5
3, a second S function circuit (No. 2) 54, a MIN (fuzzy logical product) circuit 55 and a MAX (fuzzy logical sum) circuit 56. Variable (input) by x, the finally obtained function (output) is given by f _X.

The multi-fan-out circuit 50 generates a plurality of (in this case, four) currents x having the same value and the same direction from one input current x, and an example of a specific configuration thereof. Are shown in FIG. This circuit is connected to a current mirror 58 for reversing the direction of the input current, and is connected to the output side of this current mirror 58, and generates a plurality of (four) output currents having the same value as the input current but opposite directions. It is composed of a multi-output (multi-drain) current mirror 59.

The four output currents x of the multi fan-out circuit 50 are Z function circuits 51, 52 and S function circuits 53, 54, respectively.
Are typing in. The Z function circuits 51 and 52 are the same as those shown in FIG. 6, and their break points are Z
In _B1, Z _B2, the output current is represented respectively by f _ZX1, f _ZX2. The S function circuits 53 and 54 are the same as those shown in FIG. 10, and their break points are S _B1 and
In S _B2 , the output current is expressed by f _SX1 and f _SX2 , respectively. Therefore, the slope is 1, -1 here.

The output f _ZX2 of the second Z-function circuit 52 and the output f _SX2 of the second S-function circuit 54 are given to the MIN circuit 55. As shown in FIG. 22 (A), these circuits 52,
Assuming that the break point of 54 satisfies the condition of S _B2 ≦ Z _B2 , the MIN operation result of the outputs of these circuits 52 and 54 becomes a trapezoidal function, that is, a π function. This π function (MIN
The output of circuit 55) is represented by f _πx . This is because the MIN operation is an operation for selecting the smallest value (smaller value) of a plurality of input values (here, two input values).

The output f _πx of the MIN circuit 55, the output f _ZX1 of the first Z-function circuit 51 and the output f _SX1 of the first S-function circuit 53 are given to the MAX circuit 56. MAX is an operation that selects the largest of a plurality of input values. The current value corresponding to the grade 1 of the function is I _O. Referring again to FIG. 22 (A), when these break points are selected so as to satisfy the conditions of Z _B1 + 2I _O ≤S _B2 and Z _B2 ≤S _B1 -2I _O , the output of the MAX circuit 56 becomes W Represents a function.

It is possible to replace the current mirror (reference numeral 25 in FIG. 6 and reference numeral 35 in FIG. 10) in these function circuits 51 to 54 with a current mirror whose gradient can be switched (current mirror 25A in FIG. 16 or the like). is there. In this case, the control signals applied to the control terminals are V _Z1 , V _Z2 , V _S1 , V _{S2 in FIG.}
Is given in. By setting the levels of these control signals, it is possible to independently set any of the four gradients of the W function to a value other than 1 as shown in FIG. 22 (B). FIG. 22B shows a state in which V _Z1 = V _S2 = H and V _Z2 = V _S1 = L are set. It goes without saying that the gradient can be switched by any function described below.

Next, it will be shown that the circuit of FIG. 20 can realize nine fuzzy membership functions according to the setting of break point values. Let us proceed with reference to FIGS. 4, 5 and 22 (A).

Further, in the following description, H _I means to be set to a value larger than a value ([maximum input current value] + I _O ) obtained by adding the above-mentioned I _O (for example, 10 μA) to the maximum value of input current. However, L _I means setting to a value equal to or lower than −I _O. DC indicates Don't Care, that is, any value.

The conditions under which the circuit of FIG. 20 realizes each of the nine function circuits are as follows.

[0111] φ function _{Z B1 = L I, S B1} = H I, S B2 = H I, Z B2 = DC _{or, Z B1 = L I, S} B1 = H I, Z B2 = L I, S B2 = DC 1 function Z _B1 = H _I, other (i.e. _{Z B2, S B1, S B2} ) is DC (where Z _B1, as may be larger than the maximum input current value does not increase the types of control signals was Z _B1 = H _I as sufficient conditions to.) or, S _B1 = L _I, others may be at less DC (S _B1 is 0A but, S _B1 in the sense of suppressing the increase in the types of control signals = L _I ) or S _B2 = L _I , Z _B2 = H _I , others DC (same as above, S _B2 should be 0 A or less, Z
_B2 should _just be more than the maximum input current. ) Z function _{S B1 = H I, S B2} = H I, Z B2 = DC ( in this case, Z _B1 becomes breakpoint.) _{Or, S B1 = H I, Z} B2 = L I, S B2 = DC (Again Z _B1 becomes breakpoint.) _{or, S B1 = H I, S} B2 = L I, Z B1 = L I ( in this case, Z _B2 is breakpoint. Further,
S _B2 may be 0 A or less. ) S function _{Z B1 = L I, Z B2} = L I, S B2 = DC ( in this case, S _B1 becomes breakpoint.) _{Or, Z B1 = L I, S} B2 = H I, Z B2 = DC (Again S _B1 becomes breakpoint.) _{or, Z B1 = L I, S} B1 = H I, Z B2 = H I (.S B2 in this case, S _B2 becomes breakpoints if larger values than the maximum input current value may.) [pi function _{Z B1 = L I, S B1} = H I, S B2 ≦ Z B2 ( breakpoint is S _B2 and Z _B2 .S _B2 = Z _B2
In the case of, the shape becomes triangular as shown by the chain line in Fig. 4 (E). ) U function _{S B2 = H I, Z B2} = DC Z B1 + I O ≦ S B1 -I O ( breakpoint is Z _B1 and S _B1 .Z _B1 + I _O
In the case of = S _B1 −I _O, the shape shown by the chain line in FIG. ) Or Z _B2 = L _I , S _B2 = DC Z _B1 + I _O ≦ S _B1 −
I _O N function _{Z B1 = L I, S B2} ≦ Z B2 ≦ S B1 -2I O ( breakpoint is _{S B2, Z B2, S B1} .) И function _{S B1 = H I, Z B1} + 2I O ≦ S _B2 ≦ Z _B2 (breakpoints Z _B1, S _B2, a Z _B2.) W function _{Z B1 + 2I O ≦ S B2} ≦ Z B2 ≦ S B1 -2I O ( as described above.)

In FIG. 20, the circuit indicated by reference numeral 55 is an MA
By replacing the 56 in the X circuit with the MIN circuit, the W function is excluded from the 10 functions in FIGS. 4 and 5.
It can be easily understood that the function can be realized.

(9) MIN circuit and MAX circuit (FIGS. 23 to 29) The MIN (fuzzy AND) circuit used in the programmable multi-membership function circuit of FIG. 20 and
Details of the MAX (fuzzy logical sum) circuit are described in an application filed by the applicant (for example, Japanese Patent Application No. 59-57121), which will be briefly described here.

The MIN operation is defined as

[0115]

[Equation 5]

Here, μ _X and μ _Y represent membership functions, respectively.

Figure 23 shows a circuit that implements the MIN circuit with a MOS FET.
Is shown in. For convenience, the input current is expressed in μ _X and μ _Y , and the output current (MIN calculation result) is given in μ _Z.

The direction of the input current μ _X is inverted by the current mirror 61. The input current μ _Y is input to the multi-fanout circuit consisting of the current mirrors 66 and 67, which produces two currents μ _Y of equal value.

The wired OR 62 has a discharge input current μ
Given the _X and the sinking input current μ _Y , this wired OR 62 is connected to the current mirror 63. Current mirror
63 also functions as a diode, and the wired OR 62 and the current mirror 63 form a fuzzy limit difference circuit. Therefore, the sinking output current of the current mirror 63 is given by the following equation.

[0120]

[Equation 6]

Similarly, the wired OR 64 and the diode 65 form a limit difference circuit, and the discharge output current of this MIN circuit is given by the following equation.

[0122]

[Equation 7]

Equation 7 is the same as Equation 5.

An example in which the MIN circuit is composed of bipolar transistors is shown in FIG. From the comparison with the circuit in Fig. 23, it can be easily understood that the circuit in Fig. 24 performs the MIN operation.

FIG. 25 shows the measurement result of the input / output characteristic of the circuit of FIG. One input μ _Y is used as a parameter. In the circuit of Fig. 24, TA57 was used as the PNP transistor and TA78 was used as the NPN transistor.

In FIG. 20, the MAX circuit 56 has three inputs. Generally, a 2-input MAX circuit can be easily constructed. To configure a 3-input MAX circuit, two-input MAX circuits 56A and 56B may be connected in two stages as shown in FIG.

FIG. 27 shows a 2-input MAX circuit (56A or 56A).
An example in which B) is configured by using a MOS FET is shown. The fuzzy MAX operation is defined by the following equation.

[0128]

[Equation 8]

The input current μ _Y is input to the 2-output current mirror 71, whereby two currents μ _Y whose directions are opposite to those of the input current μ _Y
Is generated, one of them is input to the wired OR 72, and the other is reversed in direction by the current mirror 75, and the wired OR 72 is generated.
Given to 74.

The input current μ _X is also input to the wired OR 72. A limit difference circuit is formed by the wired OR 72 and the diode 73, and a current given by the following equation is output from the diode 73 and flows to the wired OR 74.

[0131]

[Equation 9]

In the wired OR74, this current μ _X
Since the current μ _Y is added to <BD> μ _Y , the output current μ _Z is as follows.

[0133]

[Equation 10]

Expression 10 represents the same contents as Expression 8.

FIG. 28 shows an example in which the MAX circuit is composed of bipolar transistors. In FIG. 28, components corresponding to those shown in FIG. 27 are designated by the same reference numerals with A added. The circuit of FIG. 28 does not entirely correspond to the circuit of FIG. The two current mirrors 71, 75 of FIG. 27 have been replaced in FIG. 28 by three current mirrors 76, 77, 78.

When a multi-output current mirror is composed of bipolar transistors having a plurality of collectors, if at least one of the output collectors is opened, saturation occurs in that collector, and the output currents of the other output collectors are increased. Error occurs. In order to prevent saturation of the collector of the multi-output current mirror in any case, it is necessary to secure a certain collector-emitter voltage. In the circuit of FIG. 28, the saturation of the collector is prevented by connecting a circuit having a small input resistance such as the current mirror 78 to the collector of the multi-output current mirror 77.
Regarding measures to avoid saturation of the collector in a multi-output current mirror, the applicant's patent application, Japanese Patent Application No. 59
-263386.

FIG. 29 shows an example of the measurement result of the input / output characteristics with μ _Y of the MAX circuit of FIG. 28 as a parameter.

(10) Simplified programmable multi-membership function circuit (FIGS. 30 and 31) FIG. 30 shows a simplified programmable multi-membership function circuit based on the S function circuit. There is. Here, a P-MOS FET is used. Therefore, the direction of current flow is opposite to that of the S-function circuit shown in FIG. The input current is indicated by x _i and the output current is indicated by Z.

The multi-output current mirror 81 has one input current x _i
To generate three currents x _i having the same value and opposite directions. These currents x _i become the input currents of the three circuits described below.

The first S-function circuit is the wired OR84,
Current mirror 85, wired OR87 and diode connection
It consists of MOS FET 88. Compared with FIG. 10, these elements correspond to the wired OR 34, the current mirror 35, the wired OR 37 and the diode-connected MOS FET 38, respectively. The wired OR 84 is supplied with the discharge input current having a value of x ₁ +1 as a break point. The operation of the first S-function circuit can be easily understood from the comparison with FIG. 10 and the graph shown in FIG. 30 corresponding to the arrow indicating the direction of the current.

The second S-function circuit is a wired OR94,
It is composed of a current mirror 95, a wired OR 97 and a current mirror 98. The current mirror 98 has the function of inverting the direction of the current together with the diode function. The break point is x ₂ , and for convenience of explanation, x ₂ −1 ≧ x ₁ +1
The condition of is satisfied.

Further, the break point x ₃ (x ₃ ≧
x ₂₎ functions with the value of the ascending slope (gradient 1) (hereinafter, this circuit for generating a) of upslope function is provided, this circuit is wired OR92 and diode-connected
It consists of MOS FET 93. Wired OR92
The discharge input current of the value of x ₃ is given to.

The output current of the up-slope function circuit is input to the second S-function circuit in the wired OR96. In this wired OR 96, the output current of the up-slope function circuit is subtracted, and the reverse current is blocked by the current mirror 98, so that the output current of the current mirror 98 represents the π function (break point x ₂ ，
x ₃ ).

The current representing this π function is the wired O
It is input to the first S-function circuit at R86 and is subtracted from the current flowing there. Therefore, the output current Z is as if the π function is subtracted from the S function, which is N
Represents a function.

In the circuit of FIG. 30, diode-connected MOS
FETs 99 and 89 have been added. These FETs work as follows. That is, the current mirror 81 and the diode connection
A threshold voltage between the source and the gate of the current mirror 98 and the diode-connected MOS FET 99 is applied between the source and the drain of the MOSFET 93 to enable normal operation of these. Two diode-connected MOS FETs are connected between the diode-connected MOS FET 99 and the source / drain of the current mirror 98.
The voltage between the source and drain of 88 and 89 (that is, the sum of these thresholds) is added to enable normal operation.

The circuit of FIG. 30 can realize the seven functions excluding the И function, the W function and the M function out of the ten functions described above as follows.

[0147] φ function _{x 1 = H I, x 2} , x 3 = DC (H I , the .I _0, which means that the set to the maximum input current] + I ₀ is the current value corresponding to Grade 1 Φ
In the case of a function, x ₁ ≧ [maximum input current] may be satisfied. ) _{Or, x 2 = L I, x} 3 = H I, x 1 = DC (L 1 may be any x ₂ ≦ 0 in the case of .φ function means to set the -I _0. The x ₃ ≧ may be a Max input current].) 1 function _{x 1 = L I, x 2} = H I, x 3 = DC , _{or, x 1 = L I, x} 3 = L I, x 2 = DC Z function _{x 1 = L I, x 3} = H I (x 3 ≧ [ maximum input current] a long if it .x ₂ -1 becomes breakpoint.) S function _{x 2 = H I, x 3} = DC (x ₁ +1 becomes breakpoint.) _{or, x 1 = L I, x} 2 = L I (x 2 ≦ 0 is long if it .x ₃ +1 becomes breakpoint.) [pi function x ₃ = H _I (x ₃ ≧ may be a maximum input current] .x ₁ + _1, x
₂ -1 break point. ) U function _{x 1 = L I (x 2} , x 3 is breakpoint.) N function above conditions, i.e., _{x 1 + 2 ≦ x 2 ≦} x 3 +2

The circuit of FIG. 30 is based on the S function circuit. A simplified programmable multi-membership function circuit can also be realized by using the Z function circuit as the keynote. That is, a Z function circuit having a value as shown in FIG. 31A and having a break point at x ₁ is provided in place of the first S function circuit described above. Then, if the π function as shown in FIG. 31 (B) is subtracted from this Z function, the И function output is obtained as shown in FIG. 31 (C). However, the condition is x ₂ ≤x ₃ ≤x ₁ -1.

In such a circuit, x ₁ , x ₂ ,
It can be easily understood that by changing the condition of x ₃ , 7 kinds of functions except the И function, W function and M function can be realized among the above 10 functions.

(11) Expanded programmable multi
Membership function circuit (Figs. 32 to 34) Fig. 32 is an expanded version of the membership function circuit of Fig. 30. Expansion has two meanings. One of them is that two grades α and β are provided. In all the circuits described above, the maximum grade (maximum membership function value) was always fixed at 1, but values α and β that are variable between 1 and 0 are prepared as new grade parameters. ing. The other is that, as can be seen from the graph of the output current Z in FIG. 32, with the introduction of new grade parameters, a new membership function form, which should be called M-type deformation, was created.

In FIG. 32, the same elements as those shown in FIG. 30 are designated by the same reference numerals with A added. Only the points different from those shown in FIG. 30 will be described below.

The multi-output current mirror 81A has four input currents x
It is supposed to generate _i .

In the first S-function circuit, the wired O
A discharge input current of value x ₁ is applied to R84A. The wired OR 87A is supplied with a discharge input current having a value of α from a current source (not shown).

Two wired OR of the first S-function circuit
A wired OR 89 is newly provided between 87A and 86A, and the output current of the newly provided upslope function circuit (first upslope function circuit) flows into this. This first upslope function circuit consists of a wired OR 82 and a diode connected MOSFET 83, the break point of which is x ₄ .

Therefore, the first s-function circuit (break
Points x ₁ , x ₄ , grade α) are generated.

In the second S-function circuit, the wired OR94A is supplied with the x ₂ + β discharge input current, and the wired OR97A is supplied with the β discharge input current.

A wired OR 92A of an up-slope function circuit (second up-slope function circuit) attached to this S-function circuit is supplied with a discharge input current of x ₃ -β. The current mirror 99 is for inverting the β output and the input.

It goes without saying that the three input currents of the value β given to the wired ORs 94A, 97A and 92A can be generated by a multi-output current mirror (not shown).

The second S-function circuit and the second up-slope circuit generate a second π-function with break points at x ₂ + β and x ₃ -β and a grade of β.

As a result of subtracting the second π function from the above first π function by the wired OR86A, the maximum grade is α.
At, an M-function with a dent in β is obtained. However, the conditions of α ≧ β, x ₁ ≦ x ₂ , x ₂ + 2β ≦ x ₃ ≦ x ₄ are required.

The circuit shown in FIG. 32 can be controlled so as to generate 9 functions excluding the W function among the 10 functions described above, and in addition, it is possible to make modifications thereof by setting α and β. You can also

As a precaution, sufficient conditions for generating 6 functions except 9 functions and φ functions from 9 functions will be shown.

Z function x ₁ = x ₂ = x ₃ = L _I , α = 1, β = DC (x ₄ becomes a break point) or x ₁ = L _I , α = 1, β = 1 , X ₃ = x ₄ = H
_I (x ₂ becomes breakpoint.) S function _{x 2 = x 3 = x 4} = H I, α = 1, β = DC (x 1 is the breakpoint.) Or, x ₁ = x _{2 = L I, α = β} = 1, x 4 = H I (x 3 becomes breakpoint.) [pi function α = 1, β = 0, x 2, x 3 = DC (x 1, x 4 There the breakpoint.) _{or, x 3 = x 4 = H} I, α = β = 1 (x 1, x 2 is the breakpoint.) _{or, x 1 = x 2 = L} I, α _{= β = 1 (x 3,} x 4 is the breakpoint.) U function x ₁ = L _I, is _{x 4 = H I, α =} β = 1 (x 2, x 3 the breakpoint. ) N function _{x 4 = H I, α =} β = 1 (x 1, x 2, x 3 is the breakpoint.) И function _{x 1 = L I, α =} β = 1 (x 2, x 3 , x ₄ is the break point.) M The number _{α ≦ x 1 ≦ x 2,} x 2 + 2β ≦ x 3 ≦ x 4, α = β = 1 (x 1, x 2, x 3, x 4 is the breakpoint.)

It goes without saying that α and β may be values other than 1 in the above. That is, the membership function can be grade programmable.

The circuit of FIG. 32 is also based on the S function, but it is needless to say that the extended programmable multi-membership function circuit can be realized also by using the Z function as the basis.

FIG. 33 shows a modification of the circuit of FIG. 32 so that the gradient can be switched between 1 and 2. The current mirrors 85A and 95A shown in FIG. 32 are replaced with current mirrors 85B and 95B capable of switching the gradient. These current mirrors 85B and 95B are the same as the current mirror 25A shown in FIG. 16 and the current mirror 35A shown in FIG.

The diode-connected FETs 83, 93A are also replaced by gradient switchable current mirrors 83B, 93B and in front of them to correct the direction of the current.
C and 93C are provided respectively.

The wired ORs 94A and 92A are respectively provided with currents x ₂ and x ₃ for simplification.

The current mirrors 85B, 83B, 95B, 93B are P-
Since it is composed of MOS FETs, the switching FETs are turned on when the control voltage signals V _{C1 to} V _C4 become L level, the gradient becomes 2 or -2, and the output current Z is
It becomes the shape shown by the broken line at 34. Of course, the control voltage V _{C1 to} V
_It goes without saying that _C4 can be adjusted independently of each other.

The value α of the above-mentioned parameters is also called “weight”. By changing this value α, the weight of the membership function in the rule is expressed.

(12) S-function circuit applicable to crisp set (FIG. 35, FIG. 36) The circuit of FIG. 35 is obtained by modifying the S-function circuit (FIG. 10 or FIG. 33) so that it can be applied to crisp set. Is. Further, here, a gradient switching circuit is provided. In comparison with Fig. 10 (or Fig. 33), the wired OR104 is the same.
34 (or 84A), switchable current mirror 105 to current mirror 35 (or 85B), and wired OR107 to 37.
(Or 87A), diode 108 is diode-connected FE
Corresponds to T 38 (or 88) respectively. The gradient is switched by the control signal V _C1 .

Therefore, the P-MOS FET 106 as a switching element connected between the wired OR 104 and the current mirror 105, and the wired OR 107 and the current source (not shown) of the value α were connected in parallel. N-MOS FET 101 and P-MOS FET 102 as switching elements are newly provided. FETs 102 and 106 are control signals V _C2
ON / OFF is controlled by. FET 101 has 10 nodes
Controlled by the potential of 9. The node 109 is provided between the wired OR 104 and a current source (not shown) having a value x ₁ , and its level changes to H or L level depending on the magnitude of the current flowing in or out of the node.

In a fuzzy set, whether or not a certain thing belongs to the fuzzy set is represented by a degree of belonging, that is, a continuous value of 1 to 0. Therefore, the membership function indicating this degree has a sloped portion as described above. On the other hand, in a crisp set, whether one belongs to the crisp set is clearly represented by 1 or 0. The membership function of the crisp set has a portion (infinite gradient portion) which changes discontinuously from 1 to 0 or from 0 to 1.

Now, in FIG. 35, when the control voltage V _C2 is at L level, the two FETs 102 and 106 are on.
Since FET 101 is connected in parallel with FET 102, whether it is on or off, the circuit of FIG. 35 acts as a fuzzy set membership S-function circuit. When the control voltage V _C1 is H, the gradient is 1, and when it is L, the gradient is 2. The input / output characteristics at this time are shown by a solid line and a broken line in FIG. 36, respectively.

When the control voltage V _C2 becomes H level, the FET 10
Both 6 and 102 are turned off. Therefore, when the FET 106 is off, the input current x _i does not flow into the current mirror 105 but flows from the wired OR 104 toward the node 109. Wired O when FET 102 is off
Whether or not the discharge input current α is given to R107 is FE.
Depends on the state of T 101.

When x _i <x ₁ , the potential at the node 109 is at L level and the FET 101 is off. Therefore, the output current Z is O. When x _i ≧ x ₁ , the node 109 becomes H level and the FET 101 is turned on. The current α flows from the wired OR 107 through the FET 101.
Since the output current of the current mirror 105 is 0, the output current Z eventually becomes equal to α. In this way, as shown by the chain line in FIG. 6, the output Z which is inverted from 0 to 1 at x _i = x ₁ is obtained. When the control voltage V _C2 is at H level,
The level of the control voltage V _C1 may be H or L.

The difference between the S-function circuit and the Z-function circuit is only the direction of the current that defines the break point as described above. Therefore, the Z-function circuit applicable to the crisp set can be similarly configured by directly applying the concept of the circuit in FIG. 35 and appropriately selecting the MOS FET as a constituent element to the P type or the N type. ..

(13) Upslope function circuit applicable to the crisp set (FIGS. 37 and 38) The circuit of FIG. 37 is an upslope function circuit (wired OR82, current) having the slope switching function shown in FIG. Mirror 83C
And a circuit composed of a gradient switchable current mirror 83B or a circuit composed of a wired OR 92A, a current mirror 93C and a gradient switchable current mirror 93B) so as to be applicable to a crisp set.

In comparison with FIG. 33, the wired OR10
2 is 82 (or 92A), current mirror 103C is 83C
(Or 93C), the gradient switchable current mirror 103B corresponds to the same 83B (or 93B). However,
The connection order of the current mirror 103 C and the gradient switchable current mirror 103 B is opposite to that of the current mirror 83 C (or 93 C) and the gradient switchable current mirror 83 B (or 93 B). Also configure these current mirrors
The FET's P type and N type have been replaced. Thus, the gradient switchable current mirror 103B comprises a current mirror 108 having two output drains and a FET 109 for switching one of the output drains. The FET 109 is on / off controlled by the control signal V _C3 . Also, an N-MOS FET 107 for opening the gate connection drain of the current mirror 108 is newly added. This FET 107 is controlled by the control signal V _C4 .

The configuration of the circuit of FIG. 37 is clearly understood when compared with that of FIG. Only FET 107 and current mirror 103 C are added to the circuit shown in FIG.

When the control signal V _C4 is at the H level, this circuit has the same function as the up-slope circuit for the fuzzy set shown in FIG. That is, when V _C4 is H, the FET 107 is turned on. At this time, the slope of the output current Z is determined by the control signal V _C3 , and the output current Z exhibits the input / output characteristics shown by the solid line and the broken line in FIG.

When the control voltage V _C4 becomes L level, the FET 107
Turns off. By turning off FET 107, FE
T 108 no longer acts as a current mirror, it is just an amplifier.

When x _i <x ₁ , the output current Z is naturally 0 because the current flowing into the gate of the FET 108 is 0.
Is.

X _i ≧ x ₁ and even if the value is small, the FET 108
If there is a current that is about to flow into the FET 108, it will be amplified by the FET 108, and a sharply increasing current will flow to the output side. Therefore, as shown by the chain line in FIG. 38, x _i =
An input / output characteristic of the output current Z that rises almost vertically at x ₁ is obtained.

Since the circuit of FIG. 37 is used in FIG. 39, reference numeral 110 is particularly attached.

(14) Programmable multi-membership function circuit applicable to crisp set (FIG. 39) FIG. 39 is a main part 100 of the S function circuit applicable to the crisp set shown in FIG. 35 and FIG. The upslope function circuit 110 applicable to the crisp set shown in Fig. 33 is applied to the extended programmable multi-membership function circuit shown in Fig. 33 and applied to the crisp set obtained by improving it. Figure 3 shows a possible programmable multi-membership function circuit.

In FIG. 39, the same components as those shown in FIG. 33 are designated by the same reference numerals. Also, since two circuits 100 in FIG. 35 are used, these are shown as 100 A and 100 B,
Similarly, two of the circuits 110 of FIG. 37 are also used, so these are designated 110 A and 110 B.

From the graph shown corresponding to the arrow indicating the current flowing in the circuit, in the circuit of FIG. 39, by changing the parameters x _{1 to} x ₄ , α, β, many types including M function can be obtained. It can be easily understood that the output current Z representing the fuzzy membership function can be obtained. The gradient can be changed by switching the levels of the control voltages V _{C11 to} V _C14 and V _{C21 to} V _C24 , and many types of crisp membership functions can be generated.

[Brief description of drawings]

[Figure 1] (A) shows a general membership function,
(B) shows a practical membership function fitted with a straight line.

FIG. 2 shows the concept of a fuzzy control system.

FIG. 3 is a block diagram showing a concept of a fuzzy system having a learning function.

4 (A) to (E) are graphs showing various types of membership functions.

5 (F)-(J) are graphs showing various types of membership functions.

FIG. 6 is a circuit diagram showing a Z function circuit configured by using a MOS FET.

7 is a graph showing input / output characteristics of the Z-function circuit shown in FIG.

FIG. 8 is a circuit diagram showing a Z-function circuit configured using bipolar transistors for measuring input / output characteristics.

FIG. 9 is a graph showing measured input / output characteristics.

FIG. 10 is a circuit diagram showing an S function circuit configured by using a MOS FET.

FIG. 11 is a graph showing the input / output characteristics of the S function circuit.

FIG. 12 shows an S-function circuit configured with bipolar transistors for measuring input / output characteristics.

FIG. 13 is a graph showing measured input / output characteristics.

14A and 14B are graphs showing a practical example of a membership function.

15 (A) to (C) are graphs showing how the slope can be arbitrarily set depending on how the membership function and its variable are associated with the input / output current of the circuit.

FIG. 16 is a circuit diagram showing a part of a Z-function circuit capable of switching the gradient to two.

17 is a graph showing input / output characteristics of the circuit shown in FIG.

FIG. 18 is a circuit diagram showing a part of an S-function circuit capable of switching the gradient to three.

19 is a graph showing input / output characteristics of the circuit shown in FIG.

FIG. 20 is a block diagram showing an example of a programmable multi-membership function circuit.

FIG. 21 is a circuit diagram showing an example of a multi-fanout circuit.

FIG. 22 (A) shows how the W function is generated by the fuzzy MIN operation and the fuzzy MAX operation of the Z function and the S function, and (B) is a graph showing the W function with the gradient switched. is there.

FIG. 23 is a circuit diagram showing a MIN circuit configured by using a MOS FET.

FIG. 24 is a diagram showing a MIN circuit configured by using a bipolar transistor for input / output characteristic measurement.

FIG. 25 is a graph showing measured input / output characteristics.

FIG. 26 is a block diagram showing a 3-input MAX circuit configured by combining two 2-input MAX circuits.

FIG. 27 is a circuit diagram showing a MAX circuit configured by using a MOS FET.

FIG. 28 shows a MAX circuit configured by using a bipolar transistor for input / output characteristic measurement.

FIG. 29 is a graph showing measured input / output characteristics.

FIG. 30 is a circuit diagram showing an example of a simplified programmable multi-membership function circuit based on an S function circuit.

31A to 31C are graphs showing that a similarly simplified programmable multi-membership function circuit can be created based on a Z function.

FIG. 32 is a circuit diagram showing an extended programmable multi-membership function circuit.

FIG. 33 is a circuit diagram showing an extended programmable multi-membership function circuit having a gradient switching function.

34 is a graph showing input / output characteristics of the circuit shown in FIG. 33.

FIG. 35 is a circuit diagram showing an S-function circuit applicable to a crisp set.

36 is a graph showing input / output characteristics of the circuit shown in FIG. 35.

FIG. 37 is a circuit diagram showing an upslope function circuit applicable to a crisp set.

38 is a graph showing input / output characteristics of the circuit shown in FIG.

FIG. 39 is a programmable program applicable to a crisp set.
It is a circuit diagram which shows a multi-membership function circuit.

[Explanation of symbols]

 12 Membership function circuit group 13 Fuzzy logic circuit network 16 Control and memory circuit

Claims (3)

[Claims] 1. A weight signal generation circuit that represents the maximum value of a membership function, and a membership function that is given a weight signal of the generation circuit and has a predetermined shape and whose maximum value is defined by the weight signal. A programmable membership function device comprising a membership function circuit that outputs a signal representing the maximum value of the membership function represented by the weight signal of the generation circuit. 2. A membership function according to a set fuzzy rule is used, and a fuzzy inference operation according to the fuzzy rule is performed by acting an input signal on the membership function, and the fuzzy inference operation result is used as a reference value. A fuzzy inference method in which the weight of the membership function is changed according to the comparison result. 3. A member having a membership function set according to the set rule, capable of outputting a grade corresponding to the input of the membership function and changing at least the maximum grade of the membership function. Ship function value generating means, means for executing a fuzzy inference operation according to the above rules using the grade output from the membership function value generating means,
And a means for controlling the maximum grade of the membership function in the membership function value generating means, a fuzzy inference apparatus.