JPH04143835A - Arithmetic unit - Google Patents

Abstract

PURPOSE:To detect the inconsistency of a rule with high accuracy in a simple hardware constitution by obtaining the centroid of a function and the variance around the centroid based on the contents of the 1st - 3rd storage means when the count value of a counter means reaches the number of pieces of discrete value. CONSTITUTION:The value of a function corresponding to the input discrete value is outputted from a function value storage means, and the function value corresponding to each input discrete value of a membership function is added to a 1st addition result obtained by the addition means 1 and 4 respectively. This added value is added to the 2nd addition result obtained by the addition means 2 and 5. Furthermore this addition result is added to the 3rd addition result by the addition means 3 and 6. Then these addition results are repetitively stored in three storage means against all input discrete values. Based on each final addition result, an arithmetic means 11 obtains the centroid of the membership function and the variance around the centroid. Thus a hardware constitution is simplified and at the same time the inconsistency of a rule can be detected. Then the calculating accuracy is improved for an arithmetic unit.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to an arithmetic device for fuzzy arithmetic, and more specifically, to an arithmetic device for fuzzy inference. The present invention relates to an arithmetic device for finding a variance centered on .

[Conventional technology]

First, the conventional technology will be explained.

Fuzzy inference performs fuzzy operations based on predetermined fuzzy rules (inference rules, hereinafter referred to as rules) for one or more inputs, and outputs the results as inference results.

By the way, the above rule is that the input is XO,
XI, X2..., when the outputs are yi, y2..., IF xo-A and xl=B and
x2=A-THEN yl=P, y2=Q・
It is expressed in the form of... Among these, “IF xo=A and xi =B and x
The part 2=A- is called the antecedent part, and the part ``THEN yl= P, y2= Q... is called the consequent part.And this rule is: If XO is the value A and xl is B If the value is , and x2 is the value A, and..., output the value P as yl, and the value Q as y2.
It means that.

Here, the values of A, B, P, Q, etc. are called fuzzy variables, but in fuzzy theory, these are not single values, but triangular or fishing mirror-shaped variables that represent the degree of fitness, as shown in the graph of Figure 5. Defined by a function.

In FIG. 5, the horizontal axis represents input values or output values, and the vertical axis represents fitness.

FIG. 5 shows two fuzzy variables A and B for variable x1. For example, if the value of ×1 is Xll, the goodness of fit for fuzzy variables A and B is sal
, sbl. Furthermore, when the value of xl is xl2, they similarly become O and sb2, respectively. In other words, in fuzzy theory, the description xi-A is not evaluated as a binary value of true or false, but as a continuous value using goodness of fit.

A function representing such a degree of fitness is called a membership function.

In addition, in the above rule, the descriptions "xl=A", "X2=B', "x3=A" in the antecedent part and the description "yl=P"%yl=Q" in the consequent part are all 1. As long as it's more than that, any number is fine. Hereinafter, in order to simplify the explanation, the present invention will be described using an example in which the description of the antecedent part is 2 and the description of the consequent part is 1.

Now, regarding fuzzy inference, several methods are known. Among them, here is 5in-II
The lax-center of gravity method will be explained, but +gin-wax
Not only the centroid method but also fuzzy inference calculates the above rules with their meanings intact.

For example, as shown in FIG. 6, IF xi =A and X2=B T)IEN
3' =P (Rule 1) IF xi =Cand
Inference based on the two rules X2=B THEN )'=Q (Rule 2) is performed as follows.

First, regarding the description "xl=A" which is the antecedent part of Rule 1, the degree of suitability sll indicating how well the input x1 matches A is determined based on the membership function that defines A. Similarly, for the description "X2=B", the goodness of fit s12 for the input x20B is determined. Then, as an operation called "and", the smaller one of the two is selected and set as Sl (this is called an -inimum operation). The sl obtained in this way is the degree of conformity for Rule 1.

Similarly for Rule 2, find the fitness degree s21 of xl for the description "xl=C" and the fitness degree s22 of x2 for the description "X2=B", and use the inisum operation to find the smaller of both. Select one and set it as s2. The above is the processing related to the antecedent part.

Next, processing regarding the consequent part will be explained.

In the consequent part, first, the membership function 6 that defines the fuzzy variable P based on the description °y1=p'' of Rule 1
Let us consider a function H1 that cants a portion larger than the fitness S1 with respect to 1. Similarly, regarding the membership function 62 that defines the fuzzy variable Q, consider the interval number H2 obtained by canting a portion larger than s2.

Then, for both functions [1 and 82, the function F that selects the larger one of the two for each value of y is set as the output membership function (such processing is called maximum value calculation: ma
(referred to as ximtv+ operation).

The number F is the function shown in the lower right of Figure 6,
This is nothing but an expression of what Rule 1 and Rule 2 mean, weighted by the suitability of each rule.In other words, Rule 1 instructs the central value p of function 61 to be output as y. However, rule 1
Since the fitness S1 of is quite large as shown in the figure, the function H1 is not cut off much at the top. On the other hand, Rule 2 instructs to output the center value q of the function 62 as y, but the fitness degree s of Rule 2
2 is quite small as shown in the figure, so the function H2 has a large cut off at the top.

Therefore, it is easy to understand that the final output value of y should be the average value of the function unit and F2. However, in this case, in the main-wax-centroid method, the function H1
, F2 is not taken, but the function vector and F2 are subjected to the maximum-operation to obtain the function F, and the center of gravity of this function F is set to the semantic average of the double open numbers H1, 82. do. In other words, the center of gravity r of the function F shown in FIG. 6 is the inference result and becomes the output value of y.

The above is the fuzzy inference method using the -in-wax-centroid method.

By the way, in fuzzy inference, it is also necessary to evaluate the validity of the inference result, that is, the inconsistency of the defined rules. For example, the function Fl shown in FIG.
Various combinations of functions having the same centroid value r, such as F2, can be considered, but in fuzzy inference, it is necessary to evaluate this shape.

Now, consider the two functions Fl and F2 shown in FIG.

First, in the function F1, the 2
Function unit 1. )1) The distance between the two is large, and both have large values. This is the function unit 1. )1
)2 respectively.Rule 1). This indicates that Rule 12 has mutually contradictory meanings. That is, when the input is in the state shown in FIG. 7, rule 1) strongly instructs to output pl as output y, and rule 12 strongly instructs to output ql. Even in such a case, the inference result is the function F1
Of course, it is possible to find the center of gravity r of , but in this case, only the intermediate value between the requirements of two contradictory rules is found, and it must be said that the reliability of that value is extremely low.

On the other hand, in the function F2, although the two functions H21 and 822 that are the targets of the maxisu+l operation are slightly apart, the interval number 1 (21 has a much smaller value than the interval number 1 (22). (In such cases, double arithmetic)
121. ) 122 respectively. Rule 21. Rule 22 is p2. It instructs to output Q2.

However, since the input conditions that match them are different, this does not mean that they are contradictory.

This is because the input state shown in Figure 7 is Rule 2.
Although it satisfies the antecedent part of Rule 2, it hardly matches the antecedent part of Rule 21, so the instructions of Rule 22 will be largely reflected in the output, and the instructions of Rule 21 will hardly fit the antecedent part of Rule 21. This is because it is not reflected. In other words, there is no problem even if two rules instruct to output different values.

In this way, in fuzzy inference, there are cases where the rules are semantically inconsistent, so it is necessary not only to simply perform inference, but also to detect inconsistencies in the rules that define the inference.

An example of a fuzzy inference device for detecting such rule contradictions is disclosed in Japanese Patent Laid-Open No. 61-26441. (hereinafter referred to as JP-A No. 61-26441)
The method for detecting inconsistency in fuzzy rules disclosed in the publication will be briefly explained with reference to FIG. 8, which is a schematic explanatory diagram thereof.

In the method disclosed in Japanese Patent Application Laid-open No. 61-26441, it is determined that the rules are inconsistent if the finally obtained membership function has two or more large peaks. As shown in FIG. 8, the above-mentioned large peak is detected at the maximum peak value g of the membership function.

The first and second largest peak values g. and the minimum value of the membership function between those peaks! , and find gA+=gsz Or, if gM□≠gHz, set rg as a constant (usually rg-1) (gsz Il+ ) / (gxt gllg)
If ≧rg, this is performed by assuming that there are two or more large peaks.

In other words, the above two formulas are indicators of how much larger the second peak is compared to the ]th peak, so by evaluating these formulas you can determine whether there are two or more peaks. A determination is made whether or not.

[Problem to be solved by the invention]

However, the method of detecting inconsistency in rules as disclosed in the above-mentioned Japanese Patent Laid-Open No. 61-26441 evaluates only the magnitude relationship of the peaks of membership functions. In other words, only the vertical axis of the membership function is evaluated, and the horizontal axis is not considered at all. When there are two membership functions that have peaks of , but have different distances between them, it is impossible to distinguish between the case of ta+ and the case of Okayama) in FIG. That is, the numbers shown in Fig. 9 fa+, (bl) are goI+ gxz+
'I has the same value, and (gWt /+) / (gPI+ gnz) ≦
It is I.

Therefore, it is determined that there is no contradiction in the rules using the method disclosed in the above-mentioned Japanese Patent Laid-Open Publication No. 61-26441.

However, although the example shown in Figure 9 (al) is correct, the example shown in Figure 9 (bl) clearly instructs the two rules to output greatly different values, creating a contradiction. should be judged as such.

In this way, the method for detecting inconsistency in rules as disclosed in Japanese Patent Laid-Open No. 61-26441) is unable to detect inconsistency even when it would be appropriate to determine that there is inconsistency. The problem is that it is possible. In other words, the accuracy of detecting inconsistency in rules is low.

In view of these circumstances, the inventor of the present application first filed a patent application
No. 64853, he proposed the invention of a "fuzzy inference method" aimed at solving the above-mentioned problems. However, in the invention of Japanese Patent Application No. 2-64853, the invention of the fuzzy inference method is implemented using an arithmetic circuit with a conventional configuration, so its arithmetic efficiency is low, and it cannot be realized as an actual device. However, the problem remains that the amount of hardware increases when
The object of the present invention is to provide an arithmetic device for fuzzy arithmetic that can detect inconsistency in rules with high precision with a simple hardware configuration.

[Means to solve the problem]

When executing fuzzy operations, the arithmetic device according to the present invention performs statistical analysis that takes into account not only the value of the function (value on the vertical axis) but also the position of the function (value on the horizontal axis) for the membership function after the maximum- operation. It is used to calculate the variance, which is a scientific value, and to judge the inconsistency of the rule according to this result, and is configured to perform the sum-of-products calculation necessary for calculating the variance by three-stage addition. . That is, the arithmetic device of the present invention includes a function value storage means that stores each function value corresponding to a plurality of input discrete values; three storage means each storing the second and third addition results;
an addition means for performing addition of the addition result and the second addition result, and addition of the addition result and the third addition result, respectively;
a counting means for counting the number of input discrete values; a control means for causing the addition means to perform addition processing for each discrete value; It is provided with calculation means for determining the center of gravity of the function and the variance around the center of gravity based on the contents of the three storage means.

[Operation] In the arithmetic device of the present invention, in order to obtain the center of gravity of a function (membership function) for fuzzy operation and the variance around the center, the value of the function corresponding to the input discrete value is stored from the function value storage means. The function values that are output and correspond to each input discrete value of the membership function are added to the first addition result, this value is added to the second addition result, and this addition result and the third addition result are added. The process of adding and storing the respective addition results in three storage means is repeatedly executed for all input discrete values, and the calculation means uses the final addition results to calculate the centroid of the membership function and its value. By determining the variance centered on , the sum-of-products calculation required for calculating the variance is performed only by an adder using three-stage addition.

[Embodiments of the invention]

Hereinafter, the present invention will be explained in detail with reference to the drawings showing embodiments thereof.

First, prior to a detailed explanation of the present invention, a method for determining the center of gravity and variance in fuzzy calculations using digital enka will be explained.

In digital enka, the function F, a, is a discrete integer value F fO in (y=o, 1.2-n) + F (1), F C + + F as shown in Figure 2.
+x,”・F +, +−1)+F (1) Defined in 1.

Here, Qe −F (force) Q(−+ = Qe ” F +, +−+, +1
(1≦1nn) Pa”O P +, + = P + ” Qe (1≦i
<n) Q, -〇Qi-+ ” Qi +P i-+ (1≦1n
n) That is, Ql=F fn) + Fl, 1-1) + F
(1)-21”...10F +++-1oll
"F fm-i) P H= q, ++ Q, l-+
+ Qll-! +...+Q ll-i * 1 vi = P m" P a-1" P , -, + "
...If 10P, l-4+I''P, l-1, then QeQ.

P=P.

V=V.

is expressed as below.

Qe F (Ill + F +, + 10F ur +
-...10F (s-1)10F In.

P = I X F (1+ + 2 X F, t)
+...-+(n-1)XF+n-n+nxF++uV
”1/2X (IX(1+1)xF (1)+2X(2
41) XF la) +...-+ (n-1)
n-1+1) F 1n-1) +nX (n+1)
F l1l) )=1/2X (1”X F (1)+
2"X F,z,""...-+(n-1)'xF
+, +-1) fn”X F fn)+IXF+++”2
XF+n"°... -+ (n-1) X F fn-1)+ nX F
(al l=1/2X (1”X F (++ +
2”X F, z, + −−−−+ (n−1)”x
F'(@-1)fn"X F tel + P) By the way, the center of gravity r of the function F(a) as described above is r =
The dispersion S defined by P/Q and centered at the center of gravity r is U=
(0-r)”XFn++(1-r)”XF+u+ (2
-r)"x F tzr + ・= + (n-1-r
)"X F (a-1++(n-r)" )+2”X
F (g) + =-・= + (n-1)"X F
(++-1)”nzxF fm)2XrX (OXF
+o++IXFu++2XF+z+""-...+(n-
1) X F (1)-1)+ n X F (al)+
r” Q-2xrxP/Q+r”=2XV
/Q-r-2xr” +r”-2XV/Q r”
Therefore, if Q, P, and V are obtained, the center of gravity r
and variance S can be easily calculated by several times of division, multiplication, and subtraction. In addition, Q, P, and V are each n as described above.
It can be obtained by repeating the addition times, and no multiplication is required.

Examples of the present invention based on the above method will be described below.

FIG. 1 is a block diagram showing an example of the configuration of an arithmetic device of the present invention for fuzzy arithmetic operations.

In FIG. 1, reference numbers 1.2 and 3 are both adders;
4, 5 and 6 are all accumulators, 7 is a memory, 8 is a detector,
9 is an address selector, 10 is a counter, 1) is a general purpose arithmetic unit, 12 is a control circuit, and 13 is a bus.

The control circuit 12 controls the entire summer recovery device shown in FIG. 1, but its control signals are omitted for the sake of brevity.

The general-purpose arithmetic unit 1) is specifically composed of an arithmetic unit and registers, and mainly performs processing related to the antecedent part and
- Perform operations. The input/output of general-purpose arithmetic unit 1) is bus 13.
The final calculation result is stored in the memory 7 as a membership function F in the state shown in FIG. That is, the function F is stored at address O in the memory 7. 〉
However, at address 1 there is a function F, 1. But..., address n
is the function F. , is stored.

Note that, in the present invention, known techniques may be used for the antecedent part processing and maximum calculation procedure, so the description thereof will be omitted here.

adders 1, 2 and 3, accumulators 4, 5 and 6, detector 8,
An address selector 9 and a counter 10 are provided for center of gravity calculation and distributed calculation. Note that, as shown in FIG. 1, the adder 1 and the accumulator 4 are the
and accumulator 5 form the second stage, and adder 3 and accumulator 6 form the third stage.
Each of the stages constitutes an adder circuit.

The counter 10 counts the value manually input from the bus 13 and outputs the counted value to the address selector 9 and the detector 8.

The address selector 9 selects either the value input from the bus 13 or the value given from the counter 10 and outputs it to the memory 7 as the address.

The detector 9 detects when the count value of the counter 10 becomes "0" and outputs a detection signal to the control circuit 12.

As described above, the memory 7 has each address associated with the data stored therein, takes in data from the bus 13 under the control of the control circuit 12, and also transfers the value stored in itself to the adder 1. Output to the first input. Note that the address at that time is given from the address selector 9.

As mentioned above, the adder l inputs the output of the memory 7 to the first input, and also supplies the output to the accumulator 4, and the output of the accumulator 4 is input to the second input of the adder 1. It is an input. Then, the adder 1 adds the forces of both people and outputs the result to the accumulator 4.

Accumulator 4 accumulates the output of adder 1. Further, the accumulator 4 outputs its accumulated value to the bus 13 and the second input of the adder 1, and also provides it to the first input of the adder 2.

The adder 2 provides its output to a first input of an accumulator 5 and an adder 3, and the output of the accumulator 5 serves as a second input of the adder 2. Then, the adder 2 adds up the forces of both people and outputs the result to the accumulator 5.

The accumulator 5 accumulates the output of the adder 2 and outputs the output to the bus 13 and the second input of the adder 2.

Further, the adder 3 provides its output to an accumulator 6, and the output of the accumulator 6 serves as the second input of the adder 2. Then, the adder 2 adds the forces of both people and outputs the result to the accumulator 6.

The accumulator 6 accumulates the output of the adder 3 and outputs the output to the bus 13 and the second input of the adder 3.

The calculation procedure for determining the center of gravity and variance of a function executed by the arithmetic device of the present invention for fuzzy calculations configured as described above will be explained with reference to the flowchart of FIG. 4.

In this calculation procedure, the counter 10 receives the value of n-1, the accumulator 4 receives the value of Q, the accumulator 5 receives the value of P3, and the accumulator 6 receives the value of
, respectively.

Therefore, the control circuit 12 controls the address selector 9 so that the contents of the counter 10 are given as the address input to the memory 7 (step S1).

Next, control circuit 12 controls adders 1, 2 and 3 so that they all output O. The control circuit 12 also initializes the accumulators 4.5 and 6 to "O", and the outputs of the adders L2 and 3 (both "0#") are stored in the accumulators 4.5 and 6, respectively. Furthermore, the control circuit 12 presets the contents of the counter 10 to n via the bus 13 (step S2).

Due to the above, j=n Q, =P, =V, = 0 becomes.

After this, the control circuit 12 controls the adders 1.2 and 3 so that the adder 1 inputs the contents of the accumulator 4 and the output of the memory 7, and the adder 2 inputs the contents of the accumulator 5 and the output of the memory 7. 4 and adder 3
adds the contents of accumulator 6 and the output of adder 2, respectively.

As a result, adder 1 outputs a value of Ql+F(1)-1°, and adder 2 outputs a value of Pi+Qi, that is, Qt++-P i41, respectively.

Further, the adder 3 has v, +p, that is, ■. , will be output.

At this time, as mentioned above, the contents of the accumulators 4.5 and 6 are both 0 in the initial state, that is, Qi=Pi=Vi=0, and the contents of the counter 10 is n, so the adder 1 The outputs of .2 and 3 are respectively Fr, 0. O
.

That is, they become Q o, P o, and V a, respectively.

The control circuit 12 controls the outputs of these adders 1, 2 and 3 to be taken into the accumulators 4, 5 and 6, respectively (
Step 33). As a result, the contents of each accumulator 4.5 and 6 become Q o, P o, and V o, respectively.

Next, the control circuit 12 subtracts 1 from the contents of the counter 10 (step S4). As a result, the outputs of each adder 182 and 3 become Q+, Pz, and V+, respectively.

Hereinafter, each adder 1 by each of the above-mentioned accumulators 4, 5 and 6,
The acquisition of the outputs of 2 and 3 and the subtraction of the counter 10 are repeated until the count value of the counter 10 becomes "0" (step 33. S4. S5). As a result, each accumulator 4, Q, P, and V are obtained as the contents of 5 and 6 (
Step 36). Note that the detector 8 detects that the count value of the counter 10 has reached 0'' in step S5 described above.

Finally, the control circuit 10 transfers Q, P, and V obtained as the contents of each accumulator 4, 5, and 6 to the general-purpose arithmetic unit 1), and transfers the above-mentioned r=P/Q s=2XV/Q- By performing the calculation r2-r, the center of gravity r and the variance S are determined (step 37).

In the above embodiment, the three stages of addition are sequentially performed by independent adders, but by adopting the configuration shown in Part 10, for example, one adder can be It is also possible to adopt a configuration in which it is divided and used.

In the configuration shown in FIG. 1O, the adder is referenced 1
Only one adder is provided, and data selectors 14 and 15 for switching the input to this adder 1 are provided. The data selector 14 selects whether to input the output of the memory 7 or the contents of the accumulator 5 to the first input of the adder 1, and the data selector 15 selects whether to input the output of the memory 7 or the contents of the accumulator 5 to the second input of the adder 1. 4 or the contents of the accumulator 6 to be input. Other configurations are similar to those of the embodiment shown in FIG.

The three-stage addition by the adder 1 and each accumulator 4, 5, and 6 in the configuration shown in FIG.
The subtraction of is controlled by the control circuit 12 as follows.

First, by switching the data selector 14 to the accumulator 5 side and the data selector 15 to the accumulator 4 side, the contents of accumulators 5 and 4 are added by the adder 1, and the result is added to the accumulator 5. is stored in Next, by switching the data selector 14 to the memory 7 side and the data selector 15 to the accumulator 4 side, the contents of the memory 7 and the accumulator 4 are added by the adder 1, and the result is transferred to the accumulator 4. is stored in Then, by switching the data selector 14 to the accumulator 5 side and the data selector 15 to the accumulator 6 side, the contents of accumulators 5 and 6 are added by the adder 1, and the result is accumulated. It is stored in the calculator 6. Finally, the contents of the counter 10 are decremented by "1".

The above processing is performed as in the case of the first embodiment, and the counter 1
By repeating until the content of 0 becomes “0”, the first
Results similar to those in Example 1 are obtained.

〔Effect of the invention〕

As described in detail above, the arithmetic device of the present invention calculates the variance of the membership function finally obtained in the fuzzy operation, evaluates the inconsistency of the rule based on that value, and evaluates the reliability of the inference. The circuit is configured in such a way that the product-sum calculation when determining variance and center of gravity for use as an index can be performed using only three stages of addition circuits consisting of an adder and an accumulator, and a control circuit for them. Since no multiplier is used, the hardware configuration is simplified and calculation accuracy is improved.

Furthermore, in the second embodiment, one adder is used in a time-division manner so that it has substantially the same configuration as a three-stage addition circuit, making it possible to further reduce the amount of hardware. .

[Brief explanation of the drawing]

Fig. 1 is a schematic diagram showing an example of the configuration of an arithmetic device for fuzzy calculations according to the present invention, Fig. 2 is a schematic diagram showing a method of defining functions in digital calculations, and Fig. 3 is the same as Fig. 1. A schematic diagram showing the storage state of the membership function obtained by the -aximum operation in the fuzzy inference device shown in FIG. Figure 5 is an explanatory diagram of the membership function, Figure 6 is a flowchart showing the membership function.
The figure is a schematic diagram showing a general method of fuzzy inference, Figure 7 is a schematic diagram showing contradictions that occur in fuzzy rules, and Figure 8 is an explanatory diagram of a conventional method for detecting contradictions in fuzzy rules. FIG. 9 is a schematic diagram showing the problem, and FIG. 10 is a block diagram showing another embodiment of the present invention. 1, 2. 3... Adder 4.5. 6...Accumulator 7...Memory 8...Detector 9...
Address selector 10... Counter 1)... General purpose arithmetic unit 12... Control circuit Note that in the drawings, the same reference numerals indicate the same or equivalent parts. Agent Masu Oiwa Address data (b)

Claims (1)

[Claims] (1) An arithmetic device for determining a center of gravity and a variance around the center of gravity for a given function, comprising a function value storage means that stores values of the function corresponding to a plurality of discrete values that are input. , first, second, and third storage means; a first addition of the stored content of the function value storage means and the stored value of the first storage means; a first addition of the stored value of the first storage means and the stored value of the first storage means; an addition means for performing a second addition with a value stored in a second storage means and a third addition between the second addition result and a value stored in the third storage means; and the first addition result. is stored in the first storage means,
storing the second addition result in the second storage means;
a control means for sequentially executing a process for storing the third addition result in the third storage means for each of the discrete values; a counting means for counting the number of times the processing is performed by the control means; and a count value of the counting means. calculation means for calculating the center of gravity of the function and the variance around the center of gravity, based on the contents of the first, second and third storage means, when the number of discrete values is reached. A computing device characterized by: