JPH0535470B2 - - Google Patents

Description

[Detailed Description of the Invention] Table of Contents (1) Background of the Invention (1.1) Technical Field (1.2) Limitations of Digital Computers and New Fuzzy Logic Circuits Operating in Current Mode (1.3) Concepts of Membership Function Circuits and Fuzzy Control Systems (Figures 1 and 2) (1.4) Concept of fuzzy system with learning function (Figure 3) (2) Summary of the invention (2.1) Purpose of the invention (2.2) Structure and effects of the invention (3) Description of Examples (3.1) Various types of membership functions and their definitions (Figure 4) (3.2) Z-function circuit (Figures 5, 6, 7, 8) (3.3) S-function circuit (9, 10) , 11, 12) (3.4) Arbitrary setting of gradient during use (14th,
(Figure 15) (3.5) Gradient switching control (15th, 16th, 17th,
(Figure 18) (3.6) Programmable multi-membership function circuit (Figures 19, 20, 21) (3.7) MIN circuit and MAX circuit (Figures 22, 23,
24, 25, 26, 27, 28) (3.8) Simplified programmable multi
Membership function circuit (Figures 29 and 30) (3.9) Extended programmable multi-membership function circuit (Figures 31, 32, 33)
(3.10) S function circuit applicable to crisp set (Figures 34 and 35) (3.11) Upgradient function circuit applicable to crisp set (Figures 36 and 37) (3.12) Applicable to crisp set Programmable multi-membership function circuit (38th
(1) Background of the Invention (1.1) Technical Field The present invention relates to a membership function device useful for constructing a new fuzzy inference or control system.

(1.2) Limitations of digital computers and new fuzzy logic circuits operating in current mode Fuzzy logic is logic that deals with fuzzyness, or "ambiguity." Ambiguity is inherent in human thoughts and actions. Therefore, if we can quantify and theorize such ambiguity,
It should be possible to apply it to the design of social systems such as traffic control, emergency, and applied medical systems, as well as robots created to imitate humans. Since the concept of fuzzy sets was proposed by LAZadeh in 1965, research on fuzzy logic has been conducted as a means of dealing with ``ambiguity'' from this perspective.
However, the current situation is that much of this research is directed toward application to software systems using digital computers. Digital computers perform calculations based on binary logic consisting of 0 and 1, and although the calculation processing is extremely precise, it is necessary to add an A/D conversion circuit to input analog quantities, and this There is a problem in that when trying to process a huge amount of information, it takes a long time to obtain the final result. Furthermore, programs for applying fuzzy logic must be extremely complex, and complex processing requires a large digital computer, which is not economical.

In the first place, fuzzy logic is logic that deals with continuous values (0, 1) in the interval from 0 to 1, so 2
It has the aspect that it is not compatible with digital computers based on value logic. Furthermore, since fuzzy logic deals with ambiguous quantities with a range,
It does not require the same degree of precision as calculations performed by a digital computer. This is why it is desirable to realize new circuits suitable for handling fuzzy logic.

In order to meet these demands, the inventor has already proposed a number of fuzzy logic circuits that operate in current mode (for example, Japanese Patent Application No.
57121 etc.). The fuzzy logic circuits proposed by the inventor include marginal difference circuits, logical complementary circuits, marginal sum circuits, limited product circuits, logical sum (MAX) circuits, logical product (MIN) circuits, absolute difference circuits, implication circuits, and equal circuits. All of these circuits operate in current mode. All the above fuzzy logic circuits are
It is characterized by being constructed by a combination of one or more limit difference circuits and addition (subtraction) circuits. In current mode, addition and subtraction can be realized by simple wire connections (wired sum or wired subtract), so all the above fuzzy logic circuits basically have fuzzy limit difference circuits as their only constituent unit. It can be said that. Therefore, fuzzy logic circuits operating in current mode have many advantages both in circuit design and in IC fabrication.

(1.3) Concept of membership function circuit and fuzzy control system (Figures 1 and 2) Fuzzy set A is characterized by 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 expressed by continuous values [0, 1] in the interval from 0 to 1. It will be done. An example of the membership function μ _A (x) is shown in FIG. 1A.

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

An example of the concept of a fuzzy control system using fuzzy logic circuits and membership function circuits as described above is shown in FIG.

As an example of the application of fuzzy control, it is considered to automate the control of systems that have traditionally been operated or controlled by humans based on their extensive experience and intuition. The control system that humans have used is extremely complex, but if we simplify it, we can understand it as a combination of several or many empirical rules. This rule of thumb can be simply expressed as ``If 〇〇 (state, etc.) is XX, then △△ (state, etc.) should be □□.'' We can make this rule of thumb a little more complicated by saying, “〇〇 is ××,
And (or) If 〇× is ×〇, then △△ should be □□.'' It becomes more general. The propositional form of this general empirical law is called a control law in fuzzy control systems.

In accordance with the usage of the feedback control system, let the output e of the controlled system and its deviation Δe be the control input, and the control output given to the controlled system be Δu.

In FIG. 2, control law 1 is given as an example of a control law: ``If e is a small negative value and Δe is a small positive value, set Δu to a small positive value.'' This control law 1 is expressed as e=NS and Δe=PS→Δu=PS. Here NS is a small negative value (nega−
tive small), PS is a positive small value
small), and and means "and", respectively.

Control law 2 is given as follows: "If e is a small positive value and Δe is a small negative value, then set Δu to a small negative value." This is expressed as follows.

e=PS and Δe=NS→Δu=NS Several or many other control laws are set.

In determining whether ``e is a small negative value'' in control law 1, the answer to the question to what extent can a given control input e = e ₀ be a small negative value is the membership function. _1A ＜MS
The function 1 is given by _A >. The membership function _1A is obtained from a membership function circuit (not shown) and represents the degree to which the control input e belongs to the "set of small negative values." In Figure 2, a triangular function with a peak at _a certain negative value of e is given as the membership function 1 _A.
According to , the degree to which a certain control input e=e ₀ =−0.2 belongs to this set is 0.8.

Similarly, the membership function represents the degree to which the control input Δe belongs to the "set of small positive values"
1 _B <MS function 1 _B > is shown in FIG. This function _1B also has a triangular shape that peaks when Δe is a certain positive value. According to this membership function 1 _B output from a membership function circuit (not shown), a certain control input Δe = Δe ₀ = +
The degree to which 0.1 belongs to this set is 0.6.

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

"Make Δu a small positive value" in control law 1
The command also has membership function < original command 1
> is given. The function representing this original command 1 is also shown as an example of a triangular function that has a peak value of 1 when Δu is a certain positive value. The function representing original command 1 is generated from a membership function generation circuit (not shown).

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

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

Similarly, in control law 2, <command 2> is created by applying control law 2 to given control inputs e and Δe. Other commands may be created as well by application of other control laws.

Generally, a plurality of control laws are set for one controlled system as described above. Each command derived from these control laws is used to finally obtain the control output Δu. Therefore,
A fuzzy logical sum (MAX) calculation is performed for the commands derived from each control law. The graph of <inference results> shown in FIG. 2 shows the MAX calculation results of <command 1> and <command 2>. Among these, the solid line graphs indicate those in which multiplication is used as the "if" condition of each control law, and the broken line graphs indicate those in which MIN calculation is performed as the "if" condition.

Using such inference results, the control output Δu is finally determined. This is called defuzzification. Each of the above-mentioned operations, including the generation of membership functions, is performed in a state that includes "ambiguity" according to fuzzy logic, but at this stage, the
The control output Δu, which has two values, must be determined.

Defagration can be performed, for example, by taking a weighted average of a function representing the <inference result>, that is, by determining the position of the center of gravity. In this embodiment, the control output Δu=Δu ₀ =+0.1 is finally determined. Even when MIN is performed as an “if” operation,
Almost the same results will be obtained.

The differential adjustment may be performed by first determining the position of the center of gravity of <Command 1> and the position of the center of gravity of <Command 2>, and then taking a weighted average of these two positions.

Preferably, the membership functions _1A , _1B, etc. are variable. That is, in the process of continuing to control the controlled system using the control output Δu determined as described above, it is monitored whether the control is being performed appropriately. If optimal control is not being performed, the membership function (its value or graph shape) is changed to find a membership function that allows optimal control. This is generally called the "learning function."

(1.4) Concept of fuzzy system with learning function (Figure 3) Figure 3 schematically shows an example of the fuzzy system with the above-mentioned learning function.

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

The membership function circuit group 12 is provided with a large number of membership function circuits whose parameters are variable, and one or more predetermined ones are selected according to the input signal from the conversion circuit 11, and membership function circuits according to the input signal are selected. A signal representing .

On the other hand, a circuit 15 is provided for generating one or more membership functions. The membership function outputs from these circuits 12 and 15 are input to a fuzzy logic network 13, where calculations are performed according to predetermined fuzzy logic, and the results of the calculations are output. It is preferable that the logic of this circuit network 13 and the parameters of membership function generating circuit 15 can also be changed as necessary.

The fuzzy information output from the fuzzy logic circuit network 13 may be output as is, but in some cases, the fuzzy information may be output from the above-mentioned differential logic circuit 1.
4, some decision is made and this becomes the output.

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

The output of the fuzzy logic circuit 13 or the differential logic circuit 14 is the reference (reference, standard)
compared to the input. This reference input represents the correct answer for learning and may be provided, for example, by a skilled expert, a simulation by a digital computer, or the like.

The control and storage circuit 16 changes the shape of each membership function of the membership function circuit group 12 and the membership function generation circuit 15 by changing the parameters, etc., or by changing the shape of the 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 above comparison result. The type of logic function within the network 13 may change the connection.

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

(2) Summary of the invention (2.1) Object of the invention The object of the invention is to provide a membership function device that is useful in the above-mentioned fuzzy inference system or fuzzy control system and outputs a membership function value corresponding to an input value. It is in.

(2.2) Structure and Effects of the Invention The present invention provides a membership function device that outputs a membership function value corresponding to the value of a given input variable, which sets the position of an inflection point on the input variable axis of the shape of the membership function. gradient setting means for selectively setting the gradient of the membership function on at least one side of the set number of inflections; gradient setting means for selectively setting the gradient of the membership function on at least one side of the set inflection point; The present invention is characterized by comprising crisp set setting means for setting to output 0 or 1, and means for activating either the slope setting means or the crisp set setting means in response to a given command.

In a fuzzy set, whether something belongs to the fuzzy set is expressed by the degree of belonging, that is, a continuous value from 0 to 1. An important feature of the membership function representing this degree is that it takes a continuous value from 0 to 1. Membership functions are generally represented by curves, but it is easier to approximate them by straight broken lines.

On the other hand, in the crisp set, whether something belongs to the crisp set is clearly expressed as 1 or 0. The membership function of the crisp set has a part that changes discontinuously from 1 to 0 or from 0 to 1 (a part with an infinite gradient).

In order to allow the fuzzy inference device to perform appropriate or highly accurate fuzzy inference, it is preferable to be able to set not only a membership function representing a fuzzy set but also a membership function representing a crisp set. Further, in a membership function representing a fuzzy set approximated by a straight line, it is desirable to be able to switch or set the slope of the straight line.

According to this invention, it is possible to selectively output not only the membership function value of the polygonal line approximation representing the fuzzy set but also the membership function value representing the crisp set. When outputting the membership function value of the polygonal line approximation for the fuzzy set, it is possible to selectively set two or more slopes of the polygonal line. Also, when outputting the membership function value for a crisp set, the membership function value is between 0 and 1.
You can specify a position that changes discontinuously from 1 to 0 or from 1 to 0.

In this way, according to the present invention, a more appropriate membership function can be set in a fuzzy inference or control system equipped with the above-mentioned learning function, or even in a general fuzzy system.
It can be expected to achieve more appropriate or more accurate inference or control.

(3) Explanation of Examples (3.1) Various types of membership functions and their definitions (Figure 4) Membership functions are generally as shown in Figure 1A.
It is often expressed as a curve, as shown in the example below. However, whether or not it should be expressed as a curve is not essential for membership functions. A more important feature of the membership function is that it takes on a continuous value from 0 to 1.

On the other hand, from the point of view of circuit design, Figure 1B
As shown in Fig. 1, it is easier to handle the membership function by expressing it as a straight broken line, the membership function can be characterized with a small number of parameters, and the design is also simpler. Moreover, even if the membership function is represented by a broken line, the above characteristics are not lost.

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

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

Figure 4 shows 10 types of membership functions.

The first one is a function that always takes a value of 0 regardless of the value of the variable x, and this is defined as the φ function.

The second one is defined as a single function that always takes a value of 1.

The third one 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 at a constant slope until it finally reaches 0, and it always has a value of 0 in the region where x is larger than that. It is a function that takes . That is, variable X
It has one downward slope on the axis. This is named the Z function. x=Z _B is called a break point. The gradient can take any value. The Z function can be defined by a break point Z _B and a slope. Even if Z _B =0 and Z _B <0, this is included in the Z function.

The fourth one is an inverted version of the Z function, and is defined as the S function. That is, there is one upward slope on the X axis. The S function is also defined by a break point S _B and a slope.

The fifth one is called the π function, which is the variable x
When x is in a certain region, it takes a value of 1, and when x becomes smaller than the breakpoint S _B2 or larger than Z _B2 , it decreases at a constant slope, and finally takes a value of 0, when x is smaller than that and It is a function that is always 0 in large areas. It can also be called a trapezoidal function. The π function is characterized by two break points S _B2 , Z _B2 and a slope.

In a special case, S _B2 = Z _B2 , resulting in a triangular shape as shown by the chain line.

The sixth one is defined as the U function which is the inverse of the π function. It can also be called a function with one valley. The U function is defined by two break points Z _B1 , S _B1 and a slope. In special cases, it takes the form shown by the chain line (Z _B1 = S _B1 ).

The shape of the membership function becomes even more complex.

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

The eighth one 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 is called the W function, and it can be said to be a combination of two functions with valleys (U functions), or a trapezoidal function (π function) with a downward slope (Z function). It can also be said to be a combination of a function) and a function with an upward slope (S function),
Furthermore, it is also possible to use a combination of the N function and the Z function or the combination of the Θ function and the S function. In any case, the W function has four breaks and
Defined by points Z _B1 , S _B2 , Z _B2 , S _B1 and slope.

The last one is the inverse 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.

Furthermore, it is easy to understand that even more complex membership functions can be defined by appropriately combining two or more of the above functions.

In FIG. 4, only the positive region of the variable x is illustrated, but it goes without saying that it can be extended to the negative region of x. In this case, the above-mentioned breakpoints can also generally take negative values.

Although it is possible to take any slope such as an upward slope, a downward slope, a trapezoid, a valley, etc., it is simplest to set the slope to 1 (or -1) in terms of circuit design.
As will be described later, even if the slope is 1, any slope can be obtained by changing the ranges of the vertical and horizontal axes when using the circuit. By predetermining the gradient, the ten functions described above can be uniquely defined using only one or more break points.

(3.2) Z function circuit (Figures 5, 6, 7,
(FIG. 8) FIG. 5 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 _fZ . Furthermore, this circuit operates in current mode and is a sink input and source output circuit. A sink input is a form in which an input current flows into a circuit, and a source output is a form in which an output current flows out from a circuit. In current mode, the positive and negative values of variables and functions are represented by the direction of the current, and their absolute values are represented by the current value.

The membership _Z function circuit of FIG. a source 26 (providing sink input current to the circuit);
It is composed of a diode 28. The current mirror 25 is composed of two N-MOS FETs. A graph representing the current flowing through each portion of the circuit of FIG. 5 is shown corresponding to the arrows indicating the direction of the current. Also, the graph of the output current f _Z is the sixth
As shown in the figure.

The input terminal 21 has an input variable Z (Z≧0)
A current representing the value of is flowing. Input terminal 21
and the input side of the current mirror 25.
The current source 23 is connected by the OR 24, and a current of value Z _B (where Z _B ≧0) flows out from the wired OR 24. Therefore, wired OR24
The difference between Z and Z _B (Z
-Z _B ) tries to flow, but since the current mirror 25 actually acts as a current blocking diode for reverse current, a current with a limit difference (ZZ _B ) will flow (see graph). Here, the calculation of fuzzy marginal difference is expressed, and the marginal difference has the following contents.

ZZ _B =Z−Z _B 0 Z>Z _B Z≦Z _B (1) The output side of the current mirror 25 outputs a sink current of the same value. A current source 26 is wired between the output side of the current mirror 25 and the output terminal 22.
Connected by OR27. Therefore,
The wired OR 27 performs a calculation of 1-(ZZ _B ), and a current of this value is about to be drained or sucked from the output terminal 22 (see graph). However, since a diode 28 is connected between the wired OR 27 and the output terminal 22 so that the diode 28 is in the forward direction with respect to the drain output, the sink output current that is about to appear at the terminal 22 becomes zero. This is equivalent to the operation of 1 (ZZ _B ).

The above operations can be summarized as follows.

f _Z = 1 1-(Z-Z _B ) 0 (Z≦Z _B ) (Z _B <Z≦Z _B +1) (Z>Z _B +1) ...(2) This behavior is expressed graphically. , FIG. 6. The downward slope of this Z function is -1.

Note that the diode 28 is a diode-connected MOS
It can be replaced with FET.

When the input current Z is negative (however, Z _B > 0),
A current of (Z+Z _B ) tries to flow from the current mirror 25 toward the wired OR 24, but the current mirror 25 blocks this current, so 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 with a value of 1 from the current source 26 is directly discharged to the output terminal 22.

If break point Z _B is negative (however, Z≧
0), from wired OR24 to current mirror 2
Since a current of (Z+|Z _B |) flows into 4, the output current of the current mirror 25 is also (Z+ | Z _B |)
becomes. Therefore, the output can be expressed as:

f _Z =1−(Z+|Z _B |) 0 (1>Z+|Z _B |) (1≦Z+|Z _B |)
...(3) The third equation represents the operation of shifting the graph in Figure 6 to the left so that Z _B is on the negative side.

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

f _Z =1 1−(Z| _B |−|Z|) 0(|Z|≧|Z _B |) (|Z _B |−1<|Z|<|Z _B |) (|Z|<| Z _B |-1) ...(4) Equation (4) also expresses the state in which the graph in FIG. 6 is shifted to the left.

In this way, the circuit of FIG. 5 is applicable to all values of Z and values of Z _B.

FIG. 7 shows a Z-function circuit realized using a bipolar transistor array (TA78 manufactured by ROHM). Circuits corresponding to the current source, current mirror, etc. in FIG. 5 are given the same reference numerals.
In addition, the input circuit 2 can be replaced with the input terminal 21 in FIG.
1A, an output circuit 22A is provided in place of the output terminal 22. As the diode 28,
A diode between the base and emitter of an NPN transistor (one in TA78) is used.

FIG. 8 shows experimental results measured using the circuit shown in FIG. Three different Z _B (parameters)
An experiment was conducted on. The input current Z, the break point current Z _B , the unity value current and the output current f _Z were measured as the voltage drops across the resistors in the respective circuits. f _Z = 10 μA becomes μ = 1, f _Z =
0μA corresponds to μ=0.

As can be seen from this graph, the circuit shown in FIG. 7 has extremely excellent linearity and has a simple circuit configuration. Such excellent linearity cannot be achieved with simple voltage-mode circuits, and this is a major reason why membership function circuits were realized with current-mode circuits. Also,
The circuit shown in FIG. 7 uses a current mirror, so it has good temperature stability, and since no resistors are used except for the current source, it is suitable for integration.

Also, as can be seen from Figures 7 and 8,
A highly practical Z-function circuit can be realized not only with MOS FETs but also with bipolar elements.

(3.3) S-function circuit (Figures 9, 10, 11)
FIG. 12) An example of a membership S function circuit is shown in FIG. The input variable (input current) is indicated by S, and the S function output (output current) is indicated by _fS . The current S _B representing the break point is provided by a current source 33, and the current representing the value 1 is provided by a current source 36.

The basic difference between S function circuit and Z function circuit is
Wired OR34 (wired OR2 in Figure 5)
4)) is in the direction of the input current. The wired OR 34 is supplied with the input current S as a source input and the break point current S _B as a sink input. For this purpose, the direction of the sinking input current applied to the input terminal 31 is reversed by the current mirror 39.
Break point current source 33 also provides a sinking input to the circuit (compare current source 23 in FIG. 5).

By wired OR34 and current mirror 35
The calculation of _SBS is performed. Additionally, wired
An operation of 1-(S _B S) is performed by OR37. Diode connection that acts as a diode
Since the current in the sink and output direction is blocked by the MOS FET 38, the output current is f _S = 1.
A discharge output current representing (S _B S) is obtained. A graph of this output current is shown in FIG.

In this S function circuit, the break point
It is also possible to set S _B to a negative value, but if S _B <
In the case of 0, the output current f _S always takes a value of 1 in the region where S≧0, so there is no particular meaning in setting S _B to be negative. It is sufficient to set S _B =0.

S achieved using bipolar transistors
The functional circuit is shown in FIG. In this figure as well, circuits having the same functions as those shown in FIG. 9 are given the same reference numerals. code 31
A is an input circuit corresponding to the input terminal 31, and 32A is an output circuit corresponding to the output terminal 32. The measured characteristics of the circuit of FIG. 11 (with S _B as a parameter) are shown in FIG. It can be seen that this S-function circuit also has an excellent straight line.

(3.4) Arbitrary setting of slope during use (No. 13)
(Fig. 14) As shown in the conversion circuit 11 in Fig. 3, in discussions of membership functions, the input value of a physical quantity is normally and the normalized value is used as the input value. For example, height H
When handling, the maximum value (e.g. 2m)
Using H _nax , the height input is normalized by H/H _nax .

As an example, the membership function μ _SH of the set ``tall people'' is shown in Figure 13A as the S function, and the membership function μ <sub>ZH</sub> of the set ``short people'' is shown in Figure 13A.
Each is shown as a Z function in Figure B. The horizontal axis (variable) of these membership functions is S=
It is expressed as H/H _nax and Z=H/H _nax .

Therefore, on the circuit, the effective slope of the membership _function , that is, the upward slope of the S function and Z It is possible to set the downward slope of the function to any value. In the Z function circuit and S function circuit using the current mirror described above, (output current)/(input current)
The gradient of is always -1 or 1, but any gradient can be obtained depending on how it is used.

An example of substantially changing the slope is shown in FIG. 14 using a Z function. Figure 14 A is H _nax
It shows the membership function of the set ``Short People'' when 1 corresponds to 100 μA and Grade 1 corresponds to 10 μA. If you want to reduce the gradient to 1/2 for a membership function like this,
As shown in FIG. 14B, H _nax may be made to correspond to 50 μA. Also, if you want to make the slope 1/4,
As shown in FIG. 14C, H _nax may be made to correspond to 25 μA.

As described above, it can be seen that even if the gradient of the membership function generating circuit described above is fixed to ±1 or -1, any gradient can be set depending on how it is used.

(3.5) Gradient switching control (Fig. 15, 16,
(FIGS. 17 and 18) It will be explained next that it is possible to change the slope of the membership function in the circuit configuration.

FIG. 15 shows a configuration in which the current source 23, wired OR 24, and current mirror 25 in the Z function circuit shown in FIG. 5 are taken out, and the current mirror 25 is modified to form a current mirror 25A.

The current mirror 25A is composed of a current mirror 41 having two output drains having the same area, and an N-MOS FET 42 for switching the parallel connection of these two output drains. The FET 42 is controlled on and off by a control signal V _C applied to a control terminal 43.

A graph of the output signal _ZZB of this current mirror 25A is shown in FIG. Control signal V _C to L
When set to level, FET42 is off, so
The slope of the output current of current mirror 25A is unity.
In this case, current mirror 25A has the same function as current mirror 25 shown in FIG. Control signal
When V _C is set to H level, FET42 turns on,
The current flows through the two output drains, resulting in 2
Since twice as much output current will flow, the slope will be 2.

Therefore, if such a current mirror 25A is used in place of the current mirror 25 of FIG. 5, a Z-function circuit whose slope can be switched depending on the level of the control signal V _C is realized. The input and output characteristics of the Z function circuit when the gradient is 2 are shown by broken lines in FIG.

It is possible to switch between any number of slopes without being limited to two types of slopes. Figure 17 shows S
This shows a part of the function circuit, and here the 9th
Current mirror 35 in the figure has been replaced by current mirror 35A. In the current mirror 35A, the current mirror 44 has three output drains, these output drains are connected in parallel, and two of them are connected as switching elements.
FETs 45 and 46 are connected. FET45,
46 are turned on and off by control signals V _C1 and V _C2 applied to their control terminals 47 and 48, respectively.

As shown in Figure 18, two FET45,4
6 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), the slope of the output current is -1. ,
V _C2 = H) the slope is -2; when both are on (V _C1 = V _C2 = H) the slope is -3.

(3.6) Programmable multi-membership function circuit (Figures 19, 20, 21) Of the 10 fuzzy membership functions mentioned above, 9 functions excluding the M function can be freely programmed (or can be programmed externally). (can be controlled from)
The membership function circuit is shown in FIG. This function circuit includes a multi-fanout circuit 50, a first Z function circuit (No. 1) 51, and a second Z function circuit.
Function circuit (No. 2) 52, first S function circuit (No.
1) 53, second S function circuit (No. 2) 54,
It consists of a MIN (fuzzy logical AND) circuit 55 and a MAX (fuzzy logical sum) circuit 56. The variable (input) is x, and the final function (output) is given by _fX .

The multi-fanout circuit 50 generates multiple (four in this case) currents x having the same value and in the same direction from one input current x,
An example of its specific configuration is shown in FIG. This circuit is connected to a current mirror 58 for reversing the direction of the input current, and to the output side of this current mirror 58, and generates multiple (four) output currents having the same value as the input current but in the opposite direction. It consists of a multi-output (multi-drain) current mirror 59.

The four output currents x of the multi-fanout circuit 50 are input to Z function circuits 51 and 52 and S function circuits 53 and 54, respectively. Z function circuit 51,
52 are respectively the same as shown in FIG.
Their break points are Z _B1 and Z _B2 , and the output currents are represented by f _ZX1 and f _ZX2 , respectively. S
The function circuits 53 and 54 are the same as those shown in FIG. 9, and their break points are
In S _B1 and S _B2 , the output currents are expressed as f _SX1 and f _SX2 , respectively. Therefore, the slope is here 1, −
It is 1.

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. 21A, the break points of these circuits 52, 54 are S _B2
Assuming that the condition ≦Z _B2 is satisfied, the MIN calculation result of the outputs of these circuits 52 and 54 becomes a function on a trapezoid, that is, a π function. This π function (output of the MIN circuit 55) is expressed as f〓 _x . This is because the MIN operation is an operation for selecting the smallest value (smaller value) among a plurality of input values (here, two input values).

The output f〓 _x of the MIN circuit 55, the output f _ZX1 of the first Z function circuit 51, and the first S function circuit 5
3's output _fSX1 is given to the MAX circuit 56.
MAX is an operation that selects the largest value of multiple input values. Let I0 be the current value corresponding to grade 1 of the function. Referring again to Figure 21A, Z _B1 +
If we choose these break points to satisfy the conditions 2I0≦S _B2 , Z _B2 ≦S _B1 −2I0, then
The output of MAX circuit 56 represents the W function.

The current mirrors (numeral 25 in FIG. 5, numeral 35 in FIG. 9) in these function circuits 51 to 54 are
It is possible to replace it with a current mirror whose slope can be switched (such as current mirror 25A in FIG. 15). Control signals given to the control terminals in this case are given as V _Z1 , V _Z2 , V _S1 , and V _S2 in FIG. 19. 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. 21B, for example. Figure 21B shows V _Z1 =
A state in which V _S2 = H and V _Z2 = V _S1 = L is shown. It goes without saying that gradient switching is also possible with any of the functions described below.

Next, it will be shown that the circuit of FIG. 19 can realize nine fuzzy membership functions depending on the setting of break point values. The discussion will proceed with reference to FIG. 44 and FIG. 21A.

In addition, in the following explanation, H _I means to set the value to a value larger than the maximum value of the input current plus the above-mentioned I0 (for example, 10 μA) ([maximum input current value] + I0), and L _I This means setting it to a value less than or equal to -I0. DC means don't care, meaning it can be any value.

The conditions for the circuit shown in FIG. 19 to realize each of the nine function circuits are as follows.

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 , others (i.e. Z _B2 , S _B1 , S _B2 ) are DC (here Z _B1 should be larger than the maximum input current value, but in order to avoid increasing the types of control signals) (Z _{B1 =} H _I is set _{as a} sufficient condition _{for )} Or, S _B2 = L _I , Z _B2 = H _I , others are DC (Same as above, S _B2 only needs to be 0A or less, and Z _B2 needs to 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 the break point.) Or, S _B1 = H _I , Z _B2 = L _I , S _B2 =DC (Z _B1 is also the break point in this case.) Or, S _B1 = H _I , S _B2 = L _I , Z _B1 = L _I (In this case, Z _B2 is the break point.
Further, S _B2 only needs to be 0A or less. ) S function Z _B1 = L _I , Z _B2 = L _I , S _B2 = DC (In this case, S _B1 is the break point.) Or, Z _B1 = L _I , S _B2 = H _I , Z _B2 = DC (S _B1 is the break point in this case as well.) Or Z _B1 = L _I , S _B1 = H _I , Z _B2 = H _I (S _B2 is the break point in this case.
S _B2 only needs to have a value larger than the maximum input current value. ) π function Z _B1 = L _I , S _B1 = H _I , S _B2 ≦Z _B2 (Break points are S _B2 and Z _B2 . _{S B2}
= Z _B2 , the shape is triangular as shown by the chain line in FIG. ) U function S _B2 = H _I , Z _B2 = DC, Z _B1 +I0≦S _B1 −I0 (Break points are Z _B1 and S _B1 . _{Z B1}
In the case of +I0=S _B1 -I0, the shape is shown by the chain line in FIG. ) Or, Z _B2 = L _I , S _B2 = DC, Z _B1 +I0≦S _B1 −
I0 N function Z _B1 = L _I , S _B2 ≦Z _B2 ≦ S _B1 −2I0 (Break points are S _B2 , Z _B2 , S _B1 .) И function S _B1 = H _I , Z _B1 +2I0≦S _B2 ≦Z _B2 (Break points are Z _B1 , S _B2 , Z _B2 .) W function Z _B1 +2I0≦S _B2 ≦Z _B2 ≦S _B1 −2I0 (As described above.) In Fig. 19, the sign The circuit shown in 55
It is easy to understand that by replacing the MAX circuit and 56 with the MIN circuit, 9 of the 10 functions shown in FIG. 4, excluding the W function, can be realized.

(3.7) MIN circuit and MAX circuit (Fig. 22, 2
Figure 3, Figure 24, Figure 25, Figure 26, Figure 27
28) The details of the MIN (fuzzy AND) circuit and MAX (fuzzy OR) circuit used in the programmable multi-membership function circuit shown in FIG.
59-57121), but I will briefly explain it here.

The MIN operation is defined as follows _: μ _X ∩ _{Y = μ Y μ X ( μ} each represents.

The second circuit is a MIN circuit realized with MOS FETs.
This is shown in Figure 2. The input current is conveniently expressed as _μX and _μY
The output current (MIN calculation result) is given by _μZ .

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

A source input current μ _X and a sink input current μ _Y are applied to the wired OR 62 , and the wired OR 62 is connected to a current mirror 63 .
The current mirror 63 also acts as a diode, and the wired OR 62 and the current mirror 63 constitute a fuzzy limit difference circuit. Therefore, the sink output current of the current mirror 63 is given by the following equation.

_{μ Y} μ _X = μ _Y − μ _X 0 (μ _Y ≧ μ _X ) ( μ _Y < μ this
The source output current of the MIN circuit is given by the following equation.

μ _Z = μ _Y − ( μ _Y − μ _X ) = μ _X μ _Y −0 = μ _Y ( μ _Y ≧ _{μ X} ) ( μ _Y < μ 5) is the same as formula.

An example in which the MIN circuit is constructed using bipolar transistors is shown in FIG. 22nd
In comparison with the circuit in the figure, the circuit in Figure 23 is MIN
It is easy to understand how the calculations are performed.

FIG. 24 shows the measurement results of the input/output characteristics of the circuit shown in FIG. 23. One input μ _Y is used as a parameter. In the circuit of Fig. 23,
TA57 was used as the PNP transistor, and TA78 was used as the NPN transistor.

In FIG. 19, the input of the MAX circuit 56 is 3
It is one. Generally, a 2-input MAX circuit can be easily configured. To configure a three-input MAX circuit, two-input MAX circuits 56A and 56B may be connected in two stages, as shown in FIG.

FIG. 26 shows an example in which a two-input MAX circuit (56A or 56B) is configured using MOS FETs. The fuzzy MAX operation is defined by the following formula.

_{μ X ∪ Y = μ X} μ _Y ( _μ
This causes two currents μ _Y with opposite directions to the input current
is generated, one is input to wired OR 72, and the other is reversed in direction by current mirror 75 and given to wired OR 74.

An input current _μX is also input to the wired OR72. The wired OR72 and the diode 73 constitute a limit difference circuit, and the diode 73 outputs a current given by the following formula, and the wired
It flows into OR74.

μ _X μ _{Y =} μ _X − μ _Y 0 (μ _{X >} μ _{Y )} ( _μ
Since the current μ _Y is added to the current μ Y, the output current μ _Z is as follows.

μ _{Z =} μ _X − μ _{Y +} μ _Y = μ _X 0 + _{μ Y} = μ _{Y (} μ It represents the content.

FIG. 27 shows an example in which the MAX circuit is composed of bipolar transistors. In FIG. 27, parts corresponding to those shown in FIG. 26 are indicated by the same reference numerals with the letter A added thereto. The circuit of FIG. 27 does not completely correspond to the circuit of FIG. 26.
The two current mirrors 71 and 75 in FIG.
In the figure it has been replaced by three current mirrors 76, 77, 78.

When a multi-output current mirror is constructed using bipolar transistors with multiple collectors,
When at least one output collector is opened, saturation occurs in that collector, causing an error in the output current of the other output collectors. In order to avoid saturation of the collector of the multi-output current mirror in any case, it is necessary to ensure a certain amount of collector-emitter voltage.
The circuit of FIG. 27 prevents collector saturation by connecting a circuit with low input resistance, such as current mirror 78, to the collector of multi-output current mirror 77. Measures to avoid collector saturation in multi-output current mirrors are detailed in the applicant's patent application, Japanese Patent Application No. 59-263386.

FIG. 28 shows an example of the measurement results of the input/output characteristics of the MAX circuit shown in FIG. 27 using μ _Y as a parameter.

(3.8) Simplified programmable multi-
Membership function circuit (Figures 29 and 30)
Figure 29 shows a simplified programmable multi-membership function circuit based on the S function circuit. Here, P-MOS
FET is used. Therefore, the direction of the current is opposite to that of the S-function circuit shown in FIG. 9. Further, the input current is indicated by x _i and the output current is indicated by Z.

The multi-output current mirror 81 generates three currents x _i having the same value and opposite directions from one input current x _i . These currents x _i serve as input currents for the three circuits described below.

The first S-function circuit is composed of a wired OR 84, a current mirror 85, a wired OR 87, and a diode-connected MOS FET 88.
In contrast to Figure 9, these elements are wired.
OR34, current mirror 35, wired OR37
and diode-connected MOS FET38, respectively. The wired OR84 has a break.
A source input current with a value of x ₁ +1 is given as a point. The operation of the first S-function circuit can be easily understood from the comparison with FIG. 9 and from the graph shown corresponding to the arrows indicating the direction of the current in FIG.

The second S function circuit includes a wired OR 94, a current mirror 95, a wired OR 97, and a current mirror 98. The current mirror 98 has the function of reversing the direction of current as well as the function of a diode. The break point is _x2 , and for convenience of explanation, it is assumed that the condition _x2-1 ≧ _x1 +1 is satisfied.

Furthermore, a circuit is provided that generates a function (hereinafter referred to as an upslope function) having an upslope value (slope is 1) from the break point x ₃ (x ₃ ≧x ₂ ), and this circuit can be used as a wired It consists of an OR92 and a diode-connected MOS FET93.
A source input current with a value of x ₃ is given to the wired OR 92.

The output current of this upward slope function circuit is input to the second S function circuit at the wired OR 96. In this wired OR96, the output current of the up slope function circuit is subtracted, and the current mirror 9
Since reverse current is blocked by 8, the output current of current mirror 98 represents a π function (break points x ₂ , x ₃ ).

The current representing this π function is wired OR8
6 into the first S-function circuit and is subtracted from the current flowing therethrough. Therefore, the output current Z is as if the π function was subtracted from the S function, and this represents an N function.

In the circuit of Figure 29, diode connection
MOS FET99 and 89 have been added.
These FETs work as follows. In other words, the current mirror 81 and the diode-connected MOS FET 93
A threshold voltage between the source and gate of the current mirror 98 and the diode-connected MOS FET 99 is applied between the source and drain of the transistor to enable their normal operation. Also, diode connected MOS
A voltage between the sources and drains of the two diode-connected MOS FETs 88 and 89 (that is, the sum of these threshold values) is applied between the sources and drains of the FET 99 and the current mirror 98 to enable normal operation. .

The circuit shown in FIG. 29 can realize seven of the ten functions described above, excluding the И function, W function, and M function, as follows.

φ function x ₁ = H _I , x ₂ , x ₃ = DC ( _HI means set to [maximum input current] + I _{0. I 0} is the current value corresponding to grade 1. φ function In this case, x ₁ ≥ [maximum input current] is sufficient.) Or, x ₂ = L _I , x ₃ = H _I , x ₁ = DC (L ₁ means set to -I ₀ In the case of the φ function, it is sufficient that x ₂ ≦0. Also, it is sufficient that x ₃ ≧ [maximum 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] is sufficient. _{x 2} −1
becomes the break point. ) S function x ₂ = H _I , x ₃ = DC (x ₁ + 1 is the break point.) Or x ₁ = L _I , x ₂ = L _I (x ₂ ≦ 0 is fine. _{x 3} +1 is the break point.) π function x ₃ = H _I (x ₃ ≧ [maximum input current] is sufficient. _{x 1} + 1,
x ₂ -1 is the break point. ) U function x ₁ = L _I (x ₂ and x ₃ are break points.) N function The above conditions, that is, x ₁ + 2 ≦ x ₂ ≦ x ₃ + 2 The circuit in Figure 29 is based on the S function circuit. . A simplified programmable multi-membership function circuit can also be realized by using a Z function circuit as the basis. In other words, a Z function circuit having values as shown in FIG. 30A and with x ₁ as a break point is
Provided in place of the S function circuit. Then, by subtracting a π function as shown in FIG. 30B from this Z function, a И function output as shown in FIG. 30C is obtained. However, the condition is that x ₂ ≦x ₃ ≦x ₁ −1.

In such a circuit, by changing the conditions of x ₁ , x ₂ , x ₃ , N functions among the above 10 functions,
It is easy to understand that seven types of functions except the W function and the M function can be realized.

(3.9) Extended programmable multi-membership function circuit (Figs. 31, 32,
(FIG. 33) FIG. 31 is an expanded version of the membership function circuit of FIG. 29. Expansion has two meanings. One of them is that two types of grades α and β are provided. In all the circuits mentioned above,
The maximum grade was always fixed at 1, but from 1 to
Variable values α and β between 0 are prepared as new grade parameters. The other is the third
As can be seen from the graph of output current Z in Figure 1, with the introduction of new grade parameters, M
The point lies in the creation of a new membership function form, which can be called a type transformation.

In FIG. 31, elements that are the same as those shown in FIG. 29 are indicated by the same reference numerals with the letter A added thereto. Hereinafter, only the points different from those shown in FIG. 29 will be explained.

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

In the first S-function circuit, wired OR8
A source input current of value x ₁ is given to 4A. The wired OR87A is given a source input current having a value of α.

Two wired OR87s in the first S-function circuit
Newly wired OR89 between A and 86A
is provided, into which the output current of the newly provided up-slope function circuit (first up-slope function circuit) flows. This first upward slope function circuit is
Wired OR82 and diode connected MOS FET
83, and its break point is x ₄ .

Therefore, the first π function (break points x ₁ , x ₄ , grade is α) is generated by the first S function circuit and the first upward slope function circuit.

In the second S-function circuit, the wired
The OR94A is given a source input current of x ₂ +β, and the wired OR97A is given a source input current of β.

Wired OR9 of the up slope function circuit (second up slope function circuit) attached to this S function circuit
A source and source input current of x ₃ -β is given to 2A. The current mirror 99 is for inverting the source input of β to the sink input.

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

A second S-function circuit and a second upslope circuit generate a second π-function of grade β with break points at x ₂ +β and x ₃ −β.

As a result of subtracting the second π function from the first π function number described above using the wired OR 86A, an M function having a maximum grade of α and a depression of β in the center is obtained. However, α≧β, x ₁ ≦x ₂ , x ₂ +2β≦x ₃ ≦
x ₄ conditions are required.

The circuit shown in Fig. 31 can be controlled to generate 9 of the 10 functions mentioned above, excluding the W function, and can also create variations of them by setting α and β. You can also do it.

Just to be sure, we will show the sufficient conditions for generating 6 functions excluding the φ function and 1 function from the 9 functions.

Z function x ₁ = x ₂ = x ₃ = L _I , α = 1, β = DC (x ₄ is the break point) or x ₁ = L _I , α = 1, β = 1, x ₃ = x ₄ =
H _I (x ₂ is the break point) S function x ₂ = x ₃ = x ₄ = H _I , α = 1, β = DC (x ₁ is the break point) or x ₁ = x ₂ = L _I , α = β = 1, x ₄ = H _I (x ₃ is the break point) π function α = 1, β = 0, x ₂ , x ₃ = DC (x ₁ , x ₄ is the break point.) Or x ₃ = x ₄ = H _I , α = β = 1 (x ₁ , x ₂ are the break points.) Or x ₁ = x ₂ = L _I , α = β = 1 (x ₃ and x ₄ are break points.) U function x ₁ = L _I , x ₄ = H _I , α = β = 1 (x ₂ and x ₃ are break points. ) N function x ₄ = H _I , α = β = 1 (x ₁ , x ₂ , x ₃ are break points.) И function x ₁ = L _I , α = β = 1 (x ₂ , x ₃ , x ₄ is the break point.) M function α≦x ₁ ≦x ₂ , x ₂ +2β≦x ₃ ≦x ₄ , α=β=1 (x ₁ , x ₂ , x ₃ , x ₄ are break points) (This is a key point.) The circuit in Figure 31 is also based on the S function, but it goes without saying that an expanded programmable multi-membership function circuit can also be realized by using the Z function as the basis. Nor.

FIG. 32 shows a modification of the circuit of FIG. 31 so that the slope can be switched between 1 and 2. Current mirrors 85A, 95 in FIG.
A is replaced by slope-switchable current mirrors 85B and 95B, respectively. These current mirrors 8
5B and 95B are the same as the current mirror 25A in FIG. 15 and the current mirror 35A in FIG. 17.

The diode-connected FETs 83, 93A are also replaced by slope-switchable current mirrors 83B, 93B and are preceded by current mirrors 83C, 93C, respectively, to correct the current direction.

For simplicity, wired ORs 94A and 92A are given currents x ₂ and x ₃ , respectively.

Since the current mirrors 85B, 83B, 95B, and 93B are composed of P-MOS FETs, when their control voltage signals V _C1 to V _C4 go to L level, the switching FETs are turned on and the slope becomes 2 or -2. , the output current Z takes the form shown by the broken line in FIG. Of course, it goes without saying that the control voltages V _C1 to V _C4 can be adjusted independently of each other.

(3.10) S-function circuit applicable to crisp sets (Figures 34 and 35) The circuit in Figure 34 is an S-function circuit (Figure 9 or Figure 32) that has been improved so that it can also be applied to crisp sets. be. A gradient switching circuit is also provided here. Figure 9 (or Figure 32)
In comparison, the wired OR104 is 3
4 (or 84A), switchable current mirror 1
05 to the current mirror 35 (or 85B), wired OR107 to the same 37 (or 87A),
Diode 108 is diode-connected FET38
(or 88) respectively. Slope switching is performed by control signal V _C1 .

Therefore, the P-MOS FET 106 as a switching element is connected between the wired OR 104 and the current mirror 105, and the switching element is connected in parallel between the wired OR 107 and a current source (not shown) having a value of α. N- as
A MOS FET 101 and a P-MOS FET 102 are newly provided. The FETs 102 and 106 are controlled on and off by a control signal V _C2 . FET
101 is controlled by the potential at node 109. This node 109 is provided between the wired OR 104 and a current source (not shown) having a value of _x1 , and its level changes to H or L level depending on the magnitude of the current flowing into or out of this node.

In a fuzzy set, whether something belongs to the fuzzy set is expressed by the degree of belonging, that is, by a continuous value from 1 to 0. Therefore, the membership function expressing this degree is
As mentioned above, it has sloped parts. On the other hand, in the crisp set, whether something belongs to the crisp set is clearly expressed as 1 or 0. The membership function of the crisp set has a part that changes discontinuously from 1 to 0 or from 0 to 1 (a part with an infinite gradient).

Now, in FIG. 34, 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. 34 works as a fuzzy set membership S function circuit. When the control voltage V _C1 is H, the slope is 1, and when it is L, the slope is 2. The input/output characteristics at this time are shown in FIG. 35 by solid lines and broken lines, respectively.

When the control voltage V _C2 becomes H level, FET10
6 and 102 are both turned off. Therefore,
When FET 106 is off, input current x _i does not flow into current mirror 105 and wired OR 104
will flow toward the node 109.
When FET102 is off, wired OR10
Whether the source input current α is given to 7 is
It depends on the state of FET101.

When x _i <x ₁ , the potential at node 109 is at L level and 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 10
1 is turned on. Current α is wired OR107
The current flows from FET 101 through FET 101. current mirror 1
Since the output current of 05 is 0, the output current Z becomes equal to α after all. In this way, an output Z is obtained which inverts from 0 to 1 at x _i =x ₁ , as shown by the chain line in FIG. When the control voltage V _C2 is at H level, the level of the control voltage V _C1 may be either H or L.

The only difference between the S-function circuit and the Z-function circuit is the direction of the current that determines the break point, as described above. Therefore, by applying the concept of the circuit in Figure 34 as is,
By appropriately selecting the MOS FET as P type or N type, Z
Functional circuits can also be constructed in the same way.

Circuit 100 shown in dashed lines excluding diode 108
will be used later in FIG. 40, so for the sake of convenience it will be referred to as the main part of the S-sensor selection circuit.

(3.11) Upgradient function circuit applicable to crisp sets (Figures 36 and 37) The circuit in Figure 36 is an upgradient function circuit (wired) with slope switching function shown in Figure 32.
OR82, a circuit consisting of a current mirror 83C, and a current mirror 83B whose slope can be switched, or a circuit consisting of a wired OR92A, a current mirror 93C, and a current mirror whose slope can be switched 93B) has been improved so that it can be applied to crisp sets. .

In comparison with Figure 32, wired OR1
02 is same as 82 (or 92A), current mirror 1
03C to 83C (or 93C), and slope-switchable current mirror 103B to 83B (or 93C).
3B) respectively. However, the current mirror 103C and the slope switchable current mirror 103B
The connection order is current mirror 83C (or 93C)
and slope switchable current mirror 83B (or 93
The connection order in B) is reversed. Furthermore, the P type and N type FETs constituting these current mirrors are switched. Thus, the slope-switchable current mirror 103B has a current mirror 108 having two output drains and a FET 1 that switches one of the output drains.
It consists of 09. The FET 109 is controlled on and off by the control signal V _C3 . Also,
An N-MOS FET 107 is newly added to open the gate-connected drain of the current mirror 108. This FET 107 is controlled by a control signal V _C4 .

The configuration of the circuit shown in FIG. 36 can be clearly seen when compared with FIG. 15. In the circuit shown in FIG.
Only FET 107 and current mirror 103C are added.

When the control signal V _C4 is at H level, this circuit functions in the same way as the up-slope circuit for fuzzy set shown in FIG. 32. That is, if V _C4 is H, FET 107 is turned on. At this time,
The function of the output current Z is determined by the control signal V _C3 , and the output current Z exhibits input/output characteristics shown by solid lines and broken lines in FIG. 37.

When the control voltage V _C4 becomes L level, the FET 107 is turned off. With FET 107 turned off, FET 108 no longer acts as a current mirror, but simply an amplifier.

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

If x _i ≧ x ₁ and there is a current that tries to flow into FET 108 even if it is a small value, this will cause the current to flow into FET 108.
8, and a rapidly increasing current flows through its output side. Therefore, as shown by the chain line in FIG. 37, an input/output characteristic of the output current Z that rises almost vertically when x _i =x ₁ is obtained.

The circuit of FIG. 36 is specifically labeled 110 because it is used in FIG.

(3.12) Programmable multi-membership function circuit applicable to crisp sets (38th
38 shows the main part of the S function circuit 100 applicable to the crisp set shown in FIG. 34 and the up slope function circuit 110 applicable to the crisp set shown in FIG. A programmable multi-membership function circuit applicable to crisp sets obtained by applying and improving the extended programmable multi-membership function circuit shown in the figure is shown.

In FIG. 38, the same components as those shown in FIG. 32 are given the same reference numerals. Also, the 34th
Since two circuits 100 in the figure are used, they are indicated by 100A and 100B. Similarly, two circuits 110 in FIG. 36 are also used, and these are indicated by 110A and 110B.

From the graph shown corresponding to the arrow indicating the current flowing through the circuit, it can be seen that in the circuit of FIG _{. 38} , many types of fuzzy functions including the M function can be created by changing the parameters It is easy to understand that an output current Z is obtained that represents a membership function. In addition, the control voltage V _C11 ~
By switching the levels of V _C14 , V _C21 -V _C24 , the slope can be varied and many types of crisp membership functions can be generated.

[Brief explanation of the drawing]

FIG. 1A shows a general membership function, and FIG. 1B shows a practical membership function approximated by a straight line. FIG. 2 shows the concept of the fuzzy control system. Figure 3 shows
FIG. 2 is a block diagram showing the concept of a fuzzy system with a learning function. FIG. 4 is a graph showing various types of membership functions. FIG. 5 is a circuit diagram showing a Z function circuit constructed using MOS FETs, and FIG. 6 is a graph showing its input/output characteristics. FIG. 7 is a circuit diagram showing a Z function circuit configured using bipolar transistors for measuring input/output characteristics, and FIG. 8 is a graph showing the measured input/output characteristics.
FIG. 9 is a circuit diagram showing an S function circuit constructed using MOS FETs, and FIG. 10 is a graph showing its input/output characteristics. FIG. 11 shows an S-function circuit configured using bipolar transistors for measuring input/output characteristics, and FIG. 12 is a graph showing the measured input/output characteristics. FIG. 13 is a graph showing a practical example of a membership function. FIG. 14 is a graph showing how the gradient can be arbitrarily set by making the membership function and its variables correspond to the input/output current of the circuit. FIG. 15 is a circuit diagram showing a part of a Z function circuit that can switch the gradient into two, and FIG. 16 is a graph showing its input/output characteristics. FIG. 17 is a circuit diagram showing a part of an S function circuit that can switch the gradient into three types.
Figure 8 is a graph showing its input/output characteristics. 1st
FIG. 9 is a block diagram showing an example of a programmable multi-membership function circuit. Second
FIG. 0 is a circuit diagram showing an example of a multi-fanout circuit. Figure 21A shows how the W function is generated by fuzzy MIN and fuzzy MAX calculations of the Z function and S function, and Figure 21B is a graph showing the W function with the gradient switched. be. FIG. 22 is a circuit diagram showing a MIN circuit constructed using MOS FETs. Figure 23 shows
This shows a MIN circuit constructed using bipolar transistors for measuring input/output characteristics, and FIG. 24 is a graph showing the measured input/output characteristics. Figure 25 shows two 2-input MAX
3 inputs configured by combining circuits
FIG. 2 is a block diagram showing a MAX circuit. FIG. 26 is a circuit diagram showing a MAX circuit configured using MOS FETs. FIG. 27 shows a MAX circuit constructed using bipolar transistors for measuring input/output characteristics, and FIG. 28 is a graph showing the measured input/output characteristics.
FIG. 29 is a circuit diagram showing an example of a simplified programmable multi-membership function circuit based on an S function circuit. Figure 30 shows Z
It is shown graphically that a similarly simplified programmable multi-membership function circuit can be created based on functions. FIG. 31 is a circuit diagram showing an expanded programmable multi-membership function circuit. FIG. 32 is a circuit diagram showing an extended programmable multi-membership function circuit having a slope switching function, and FIG. 33 is a graph showing its input/output characteristics. FIG. 34 is a circuit diagram showing an S function circuit applicable to crisp sets,
FIG. 35 is a graph showing its input/output characteristics.
FIG. 36 is a circuit diagram showing an upward slope function circuit applicable to crisp sets, and FIG. 37 is a graph showing its input/output characteristics. Figure 38 shows the programmable multi-module that can be applied to crisp sets.
FIG. 3 is a circuit diagram showing a membership function circuit. 25A, 35A, 83B, 85B, 93B, 1
05,103B...Slope switchable current mirror,
41, 44, 108...multi-output current mirror, 4
2, 45, 46, 109...Switching element.

Claims (1)

[Claims] 1. In a membership function device that outputs a membership function value corresponding to the value of a given input variable, means for setting the position of an inflection point on the input variable axis of the shape of the membership function; gradient setting means for selectively setting the gradient of the membership function on at least one side of the set inflection point; outputting 0 or 1 as the membership function value on at least one side of the set inflection point; 1. A membership function device comprising: crisp set setting means for setting the gradient setting means to set the gradient setting means to set the gradient setting means to set the crisp set setting means; and means for activating either the gradient setting means or the crisp set setting means in response to a given command.