JPH04335433A - Device and method for calculating adaptation of antecedent part and device and method for compressing membership function - Google Patents

Abstract

PURPOSE:To reduce the capacity of a memory for storing membership function data by storing data for showing one new membership function in a memory instead of two membership functions. CONSTITUTION:A fuzzy inference arithmetic unit 10 can be constituted of a programmed computer, this unit 10 is constituted of an arithmetic control part 11 containing a CPU, a memory 12, an input interface 13 and an output interface 14. In such a state, by the arithmetic control part 11, a fuzzy inference operation containing a compression processing of membership function data and an adaptation arithmetic processing is executed. In the memory 2, data for showing a membership function is stored. In this constitution, two are extracted from plural membership functions which are set, and whether they are the same or similar is decided. When it is decided that they are the same or similar, a new membership function is generated, and its data is stored in the memory 12 instead of the data of these two membership functions.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an antecedent fitness calculation device and method and a membership function compression device and method in fuzzy inference calculations.

0002

[Prior Art] Fuzzy inference operations are generally performed using If,
It is executed according to a fuzzy rule called the then rule. This rule has an antecedent part starting with If,
It consists of the consequent part after then. In both the antecedent part and the consequent part, one or more propositions each consisting of a pair of input variables and membership functions are an
Connected with d or or.

[0003] Therefore, in addition to data representing these rules, data representing membership functions is stored in advance in the memory of the fuzzy inference calculation device.

0004

[Problem to be solved by the invention] Membership functions are often defined for each rule or for each input variable. Therefore, as the number of rules or the number of types of input variables increases, the number of types of membership functions also increases. do. In some cases, identical or very similar membership functions may be set and you may not be aware of it. In such a case, similar calculations are performed redundantly in the fitness calculation for the antecedent part. Also,
Memory usage efficiency decreases because the same or similar membership functions are stored redundantly in memory.

[0005] An object of the present invention is to improve memory usage efficiency.

[0006]

[Means for Solving the Problems] An antecedent fitness calculation device according to the present invention has areas for storing data representing membership functions specified in set rules, and areas for storing these membership functions. A memory comprising a first address storage area for storing a first address in correspondence with a membership function, a memory that retrieves two membership function data from said memory, determines whether they are the same or similar, and if they are the same or similar, Create a new membership function to represent them, store the data representing this new membership function in the storage area of one of the two membership function data, and write the new membership function as described above. Membership function compression means that stores the start address of the area where the data represented is stored in the above two membership functions in correspondence with the above start address storage area, and corresponds to the membership functions specified in the above rules. Read the first address to be read from the first address storage area, use this first address to read membership function data from the membership function data storage area, use the read membership function data and the input data corresponding to it, It includes means for calculating the degree of compatibility of input data with respect to the membership function.

[0007] The antecedent fitness calculation method according to the present invention is as follows:
The data representing the membership functions specified in the set rules are stored in the membership function data storage areas of the memory, and the start addresses of these membership function storage areas are stored in correspondence with the membership functions at the start addresses of the memory. area, retrieve the two membership function data from the above memory, determine whether they are the same or similar, and if they are the same or similar, create a new membership function to represent them, and use this The data representing the new membership function is stored in one of the storage areas of the above two membership function data, and the start address of the area where the data representing the new membership function is stored is stored in the above two storage areas. The first address corresponding to the membership function specified in the above rules is read from the first address storage area, and the first address is used to store the first address in the first address storage area in correspondence with one of the membership functions. The membership function data is read from the membership function data storage area, and the degree of suitability of the input data to the membership function is calculated using the read membership function data and the corresponding input data.

In the above process, the determination of whether two pieces of membership function data are the same or similar and the creation of new membership function data are repeated for all membership functions.

[0009] Furthermore, when one rule has multiple propositions consisting of membership functions and input variables, a predetermined calculation is performed between the fitness degrees calculated for each proposition, and the results of this calculation are applied to the above rule. Let the fitness of

The membership function compression device according to the present invention has an area for storing data representing a plurality of membership functions, and a start address for storing the start addresses of these membership function storage areas in correspondence with the membership functions. a memory having a storage area;
and extracts two membership function data from the above memory, determines whether they are the same or similar, and if they are the same or similar, creates a new membership function to represent them, and represents this new membership function. The data is stored in one of the storage areas for the above two membership function data, and the start address of the area where the data representing the above new membership function is stored is made to correspond to the above two membership functions. Membership function compression means is provided for storing membership functions in the first address storage area.

The membership function compression method according to the present invention stores data representing a plurality of membership functions in respective membership function data storage areas of a memory.
The start addresses of these membership function storage areas are stored in the start address storage areas of the above memory in correspondence with the membership functions, and two pieces of membership function data are retrieved from the above memory to determine whether they are the same or similar. If they are the same or similar, a new membership function is created to represent them, and data representing this new membership function is stored in the storage area of one of the two membership function data mentioned above. At the same time, the start addresses of the areas in which data representing the new membership functions are stored are stored in the start address storage areas in correspondence with the two membership functions.

0012

[Operation] Compression processing of membership functions is performed as follows.

Two membership function data are retrieved from the memory. It is determined whether these are the same or similar. If they are the same or similar, a new membership function is created to represent them. The data representing this new membership function is stored in the storage area of one of the above two membership function data, and the start address of the area where the data representing the new membership function is stored is are respectively stored in the start address storage area in correspondence with the two membership functions.

[0014] The determination of whether two pieces of membership function data are the same or similar and the creation of new membership function data are repeated for all membership functions.

The antecedent suitability is calculated as follows.

[0016] A start address corresponding to the membership function specified in the rule is read from the above-mentioned start address storage area, and membership function data is read from the above-mentioned membership function data storage area using this start address. Using the obtained membership function data and the corresponding input data, the goodness of fit of the input data to the membership function is calculated.

[0017] When one rule has multiple propositions consisting of membership functions and input variables, a predetermined operation (for example, M
IN calculation) is performed, and the result of this calculation becomes the degree of conformity of the above rule.

[0018]

[Effects of the Invention] According to the present invention, one new membership function is created from two identical or similar membership functions, and data representing one new membership function is substituted for the above two membership functions. is stored in the memory, so the memory capacity can be reduced.

[0019] Furthermore, since the start address of the storage area storing new membership function data is stored corresponding to each of the above two membership functions, in the fitness calculation, the above start address is used for these two membership functions. New membership function data can be read by referring to . That is, in the rule, the above two membership functions are written as they are, rather than a new membership function. Therefore, even if two membership functions are compressed into one new membership function, there is no need to change the rule description, and the set rule can be used as is.

[0020]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows the configuration of a fuzzy inference calculation device.

[0021] The fuzzy inference arithmetic device 10 can be constituted by a programmed computer (eg, a microcomputer). This device 10 has a CPU
It is composed of an arithmetic control section 11 including a memory 12, an input interface 13, and an output interface 14.

The calculation control unit 11 performs fuzzy inference calculations including membership function data compression processing and fitness degree calculation processing, which will be described later.

The memory 12 includes an area for storing set rules, an area for storing data representing membership functions (MF), and data input from the input interface 13, as will be described in detail later. An area for storing input data, an area for storing output data obtained as a result of fuzzy inference calculations, etc. are provided.

The rules for fuzzy inference are If, t
This is called a hen rule, and an example is as follows.

Rule 1: If x1=MF1, x2=MF3,
x3=MF4, then
y1=MF8 Rule 2: If x1=MF5,x
4=MF2, x5=MF6,
then y1=MF3 ...... Rule j: If x1=MF2, x4=MF1,
x6=MF7, then
y2=MF9

[0026] Here, x1, x2, x3,
x4, x5, x6, etc. are input variables, MF1, MF2, MF
3, MF4, MF5, MF6, MF7, MF8, MF9
etc. are membership functions, and y1, y2, etc. are output variables.

The part starting from "If" is the antecedent part, and the part after "then" is the consequent part.

As shown in the above rule, the antecedent part generally includes a plurality of propositions each consisting of a pair of input variables and membership functions, and these propositions are
are tied together.

FIG. 2 shows an example of a membership function. Here, for simplicity, it is assumed that the membership function is represented by a triangle.

FIG. 3 shows an example of storage areas set in the memory 12. The memory 12 is provided with a membership function (MF) data storage area and a start address storage area to store data related to membership functions.

The membership function data storage area stores data representing each membership function. If the membership function is triangular as shown in Figure 2, the data representing the membership function are the coordinates of the vertices of the triangle (if the grade is always 1, only the coordinates of the variables are required) and It is composed of data representing the slope or the coordinates of both ends of the base. The data representing the membership function may be a mathematical formula representing a triangle, or all coordinate data on a line representing a triangle. If the membership function is a Gaussian distribution function, the average value and standard deviation will be employed as the membership function data. In this way, the membership function data may be determined as appropriate depending on the form of the membership function, etc. Each membership function MF1, MF2, MF3, MF4, M
The starting addresses of the areas that store data representing F5 are shown as ad1, ad2, ad3, ad4, and ad5.

The start address storage area stores start addresses ad1, ad2 of areas in which data representing these membership functions are stored, corresponding to each membership function MF1, MF2, MF3, MF4, MF5.
, ad3, ad4, and ad5 are stored. In this embodiment, addresses ad1 to ad5 are stored in the order of membership functions MF1 to MF5. The rules described above are expressed by appropriate codes assigned to input variables, membership functions, and output variables, respectively. The corresponding area of the start address storage area is accessed using the membership function code used in the rule. The code of the membership function represents, for example, the address of the start address storage area.

[0033] Therefore, the rule is decoded, the start address storage area is accessed from the membership function code included in the rule, the start address stored in the corresponding area is read, and the membership function is executed using this start address. The membership function data stored therein can be read by accessing the corresponding area within the data storage area.

FIG. 5 shows the procedure of membership function data compression processing performed prior to antecedent fitness calculation processing.

First, two pieces of membership function data are read from the membership function data storage area (step 21). As shown in Figure 2, the membership function M
Assume that F1 and MF3 are read.

It is determined whether the distance a between the vertices of these two membership functions is less than or equal to 1/10 of the overall resolution (step 22).

In this embodiment, it is assumed that the membership function variable is represented by 12 bits. The resolution is 12 bits = 4096 gradations, and 1/10 of that is 409.6
It is a gradation.

The coordinates of the vertex of membership function MF1 are 1300, and the coordinates of the vertex of membership function MF3 are 1.
000, the interval is a=300. Therefore, a is 1/10 or less of the resolution.

In such a case, it is determined that the two membership functions MF1 and MF3 are the same or similar.

[0040] In addition to the above, various methods of determining the identity (or similarity) of two membership functions can be considered. For example, the determination can be made based on the magnitude of the cross-correlation value between two membership functions.

In any case, if it is determined that the two membership functions are the same or similar, by taking the average of these two membership functions MF1 and MF3, a new A membership function MF1A is created (step 23). There are various other ways to create new membership functions. For example, one of the two membership functions may be used as the new membership function.

The data representing the new membership function MF1A created in this way is stored in the membership function storage area as shown in FIG.
The data of one of the two membership functions MF1 or MF3 is stored in the area where it was stored (in this example, the area with the start address ad1), and the data of the other is stored in the area where the data of the other one (in this example, with the start address ad3) was stored.
The data in the area) is erased, and the data in the areas with lower addresses are sequentially shifted and stored (step 24). The data of the membership functions MF4 and MF5 are shifted and stored in the areas of the start addresses ad3 and ad4, respectively.

Next, in order to match the membership function data in the membership function data storage area with the start address, in the start address storage area,
As shown in Figure 4, the above two membership functions M
The start address (ad1
, ad3) are updated with the start address (ad1) of the area of the new membership function MF1A, and the shifted membership functions MF4 and MF5 are updated.
Corresponding to each new area address (ad3,
ad4) is stored (step 25).

In this way, the membership function MF
1 and MF3, it becomes possible to access the data of the new membership function MF1A using address ad1, and the shifted membership function M
Regarding F4 and MF5, it becomes possible to access the data of the corresponding MF4 and MF5 using addresses ad3 and ad4.

The above process is repeated for all combinations of two membership functions selected from all membership functions (step 26).
.

FIG. 6 shows the antecedent suitability calculation processing procedure.

[0047] First, rules are extracted (step 31).
. As an example, assume that the above-mentioned rule 1 is extracted.

Rule 1 includes three propositions. The first proposition x1=MF1 is first calculated. For the membership function MF1, the corresponding start address ad1 is read from the start address storage area, and using this start address ad1, the data of the membership function MF1A from the membership function data storage area is read (step 32).

Next, the corresponding input data x1 (this input data is also represented by x1) is taken in (step 33),
The goodness of fit of this input data x1 to the membership function MF1A (the function value of the membership function MF1A when the input data x1 is given) (this is set as a1;
(see FIG. 2) is calculated (step 34).

Since this is the first proposition, the degree of conformity a1 is obtained by performing a MIN operation between grade 1 and the degree of conformity a1 (a1<1) obtained (step 35).

Similarly for the second proposition of rule 1, the membership function MF3 of input data x2 is
The goodness of fit a2 for (MF1A) is calculated, and the goodness of fit a
A MIN calculation of 1 and a2 is performed.

Furthermore, in the same way, for the third proposition, the goodness of fit a3 of the input data x3 with respect to the membership function MF4 is determined, and the goodness of fit (MIN of a1 and a2) is calculated.
A MIN calculation is performed between and a3. This final MI
The N calculation result becomes the degree of conformity of rule 1 (step 36)
.

The above processing is performed for all rules (step 37).

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the configuration of a fuzzy inference calculation device.

FIG. 2 is a graph showing an example of a membership function.

FIG. 3 shows the contents of the memory.

FIG. 4 shows updated memory contents.

FIG. 5 is a flow chart showing membership function compression processing.

FIG. 6 is a flow chart showing fitness calculation processing.

[Explanation of symbols]

10 Fuzzy inference calculation device 11 Arithmetic control section 12 Memory

Claims (12)

[Claims] [Claim 1] Areas for storing data representing membership functions specified in set rules, and a start address storage area for storing the start addresses of these membership function storage areas in correspondence with the membership functions. A memory comprising a The data representing the membership function is stored in the storage area of one of the above two membership function data, and the start address of the area where the data representing the new membership function is stored is stored in the storage area of one of the above two members. Membership function compression means stores the membership function in the first address storage area in correspondence with the membership function, and the first address corresponding to the membership function specified in the above rules is read from the first address storage area, and the first address is stored in the first address storage area. means for reading out membership function data from said membership function data storage area using said membership function data storage area, and calculating the goodness of fit of input data to said membership function using said read membership function data and corresponding input data;
Antecedent part fitness calculation device equipped with 2. The method further comprises means for controlling the membership function compression means to repeat determination of whether two pieces of membership function data are the same or similar and creation of new membership function data for all membership functions. The antecedent part suitability calculation device according to claim 1. [Claim 3] The fitness calculation means performs a predetermined calculation between the fitness degrees calculated for each proposition when a single rule has a plurality of propositions each consisting of a membership function and an input variable. , the antecedent part suitability calculation device according to claim 1, wherein the calculation result is used as the suitability of the rule. [Claim 4] The data representing the membership functions specified in the set rules are stored in the membership function data storage areas of the memory, and the start addresses of these membership function storage areas are stored as above in correspondence with the membership functions. Each is stored in the first address storage area of the memory, the two membership function data are retrieved from the memory, it is determined whether they are the same or similar, and if they are the same or similar, a new membership function representing them is created. , and store the data representing this new membership function in one of the storage areas for the above two membership function data, and also store the data representing the new membership function at the beginning of the area where the data representing the new membership function is stored. Addresses are stored in the above-mentioned starting address storage area in correspondence with the above two membership functions, and the starting address corresponding to the membership function specified in the above rules is read from the above-mentioned starting address storage area, and the starting address is reads the membership function data from the membership function data storage area using the method, and uses the read membership function data and the corresponding input data to calculate the goodness of fit of the input data to the membership function.
Antecedent fitness calculation method. 5. The antecedent fitness calculation method according to claim 4, wherein the determination of whether two pieces of membership function data are identical or similar and the creation of new membership function data are repeated for all membership functions. [Claim 6] When a single rule has a plurality of propositions each consisting of a membership function and an input variable, a predetermined calculation is performed between the degrees of fitness calculated for each proposition,
5. The antecedent suitability calculation method according to claim 4, wherein the calculation result is used as the suitability of the rule. 7. A memory comprising an area for storing data representing a plurality of membership functions, and a start address storage area for storing the start addresses of these membership function storage areas in correspondence with the membership functions, and extracts two membership function data from the above memory, determines whether they are the same or similar, and if they are the same or similar, creates a new membership function to represent them, and represents this new membership function. While storing the data in one of the storage areas of the above two membership function data,
Membership function compression means for storing the start address of the area in which data representing the new membership function is stored in the start address storage area in correspondence with the two membership functions. Function compressor. [Claim 8] Data representing a plurality of membership functions are stored in respective membership function data storage areas of the memory, and the start addresses of these membership function storage areas are stored in the start address storage area of the memory in correspondence with the membership functions. , retrieve the two membership function data from the above memory, determine whether they are the same or similar, and if they are the same or similar, create a new membership function to represent them, and use this new The data representing the new membership function is stored in one of the storage areas of the above two membership function data, and the start address of the area where the data representing the new membership function is stored is stored in the above two storage areas. A membership function compression method in which each of the membership functions is stored in the above-mentioned start address storage area in correspondence with the membership function. [Claim 9] Means for extracting two membership functions from a plurality of preset membership functions, determining whether they are the same or similar, and if they are the same or similar, creating a new membership function representing them. A membership function compression device comprising means for creating a function, and means for controlling the above-described same or similar determination and creation of a new membership function to be repeated for all set membership functions. 10. Claim 9, further comprising a memory for storing the start address of an area for storing data representing the newly created membership function in correspondence with each of the two membership functions. Membership function compression device as described in . [Claim 11] Pick out two membership functions from a plurality of preset membership functions, determine whether they are the same or similar, and if they are the same or similar, create a new membership function that represents them. A membership function compression method in which the above-described determination of whether they are the same or similar and creation of a new membership function are repeated for all set membership functions. 12. The method according to claim 11, wherein the start address of an area of the memory for storing data representing the newly created membership function is stored in the memory in correspondence with each of the two membership functions. Membership function compression method described.