SU1317454A1 - Adjunct function generator - Google Patents

Abstract

The invention makes it possible to determine the membership function of a fuzzy variable, which is a function of other fuzzy variables with a known functional relationship and membership functions of the original 7 fuzzy variables. "By means of a generator of 3 clock pulses, 4-number sensors with uniform distributions produce signals. the amplitudes that are multiplied in multipliers 7 and adders 8 into random values of the source variables. Functional converters 9 determine the values of the membership functions of the source variables, among which the minimum signal allocations in block 10 are determined, then in block 12 the random values of the desired variable are determined, for which the values of the desired membership function are determined in block 11. 4 or . i (L ffl

Description

The invention relates to a computational technique and can be used to determine the membership function of a fuzzy variable Y. which is a function of several fuzzy variables, i-1,., .. jUjj if the functional transformation connecting the desired and initial fuzzy sets is known (X | , ..., x) and the membership functions of the original fuzzy variables | fU. (x;)

The purpose of the invention is to expand the functionality of the device by generating the membership functions of the functional transformation of several variables.

FIG. 1 shows a structural diagram of the generator of membership functions; in fig. 2 block diagram of the functional converter of fuzzy variables; Fig. 3 is a block diagram of a block for allocating values of the membership function; FIG. 4 is a block diagram of a functional group converter.

The membership function generator (Fig. 1) contains the start input i ;, delay element 2, the 3 clock pulse generator S group of 4 sensors with uniform distribution, the inputs 5 specify the scatter coefficients i-ie clear variables, the inputs, 6 the offset factors fuzzy variables , group of 7 multipliers, group of 8 adders, group of 9 function converters; minimum signal extraction unit 0, function value selection unit 11: membership, functional converter 2 fuzzy variables, counter 13, delay element 14, outputs 15 of the corresponding membership function values,

The functional converter of fuzzy variables (fig 2) contains the proportional coefficients 16, the multiplier group 17 and the adder 18 "

The allocation unit of the membership function (Fig. 3) contains the input 19 of setting the value of the interval of the desired variable, divider 20, expurator 2, first group of elements 22, group of elements of comparison 23, group of memory blocks 24, group of delay elements 25, second group elements And 26,

42

The functional converter of the group (Fig. 4) contains the input 27 specifying the expected value of the desired variable, the input 28 specifying the scatter factor of the variable to be varied, the input 29 units, the first subtraction unit 30, the module 31 determining the module divider 32, the second subtracting unit 33.

The generator of membership functions works as follows.

The membership functions of the source variables are defined as linear membership functions of an exemplary

of equality

, 1x; -a; |

. (X;) - 1- (O

where are the parameters characterizing the center of grouping and the variation around this center of a fuzzy variable.

Accordingly, each of the variables x; may take values from a; - (Y :, to. The functional transformation (x ,,, x) is given in linear form,.

.

the start pulse from input 1 sets the generator to the initial state, switches on the generator of 3 clock pulses (GTI). According to the signal from the GTI 3 sensors, n generate random numbers uniformly distributed in the interval. The number of sensors corresponds to the number of source variables. The numbers produced are multiplied in multipliers x 7.1-7, n by

2 (resulting in the formation of the value 2d; G: s which is added to the left boundary of the corresponding interval in adders 8.1-8. N. As a result, n signals are formed with random amplitudes + + 2d; B-, which correspond to return values uniformly distributed values of the source variables. In the functional transform “above 12, the value of the desired variable y is formed for the corresponding values of the initial variables that are formed at the outputs of the adders 8. To do this, each value of the desired variable is multiplied in the corresponding multiplier 17 by the coefficient k; and after summation in the adder 18, the current value of the desired variable y is formed, Cro313

Moreover, in functional converters 9.1-9. The values of the membership functions for the generated values of the initial transients are formed. The formation of the values of the functional accessories is carried out by direct calculations using the formula (1). Among the generated values of the membership functions, a miniature is distinguished, which is determined by successive pairwise comparison of the values of the functions. The value of the isome variable y and the minimum value of the membership function goes to block 11 in the division of the values of the membership function, which works as follows.

The value of the desired variable is dets in divider 20 by the length of the discrete interval of its values. The resulting quotient in the binary-deciphering decoder 2-1, by taking into account only the whole part of the quotient, is converted into the number of the interval in which the value of the desired variable falls. At the corresponding output, the decoder 21 appears a signal that opens the corresponding group of elements AND 22, with the result that the minimum value of the membership function is fed to the input of the corresponding comparison element 23. In the initial state of each of these blocks, zero signals are supplied in the initial state, which are stored in memory blocks 24. In the comparison elements 23, the input signals are compared with the signals stored in the memory blocks 24. If the input signal exceeds the signal stored in the memory block 24, this input signal is recorded in the memory block 24 by the enable signal from the output of the reference element 23.

Thus, in the memory blocks 24, the values of the membership functions of the desired variable y are formed for all allocated intervals of its values. The operation of the generator ends with a signal from the overflow output of the counter 13, calculated for a given number of tests.

Claims (1)

Invention Formula The generator of membership functions, which contains a clock pulse generator, a counter, two delay elements, with the generator output being 545 These pulses are connected to the counting input of the counter, the overflow output of which through the first delay element is connected to the clock pulse stop input, which is because, in order to extend the functionality by ensuring the generation of function varieties of the functional transformation of several variables, it is entered blob of the minimum signal, a group of n (n is the number of variables, an integer number) of sensors with a uniform one. distribution, a group of n multipliers, a group of n adders, a block for assigning membership function values, a group of n functional converters for the membership function of fuzzy variables, and a functional converter for He4etKHx variables containing the multiplier group and adder, the output groups of the multipliers connected to the groups of inputs of the adder, the block of selection of values of the membership function contains a divider, a decoder, two groups of elements AND, a group of elements of comparison, a group of memory blocks, a group of delay elements, each of the n functional converters of the membership function of fuzzy variables of the group contains two subtractors, a module for determining a module and the divider, the output of the first subtraction unit through the module definition unit is connected to the first input of the divider, the output of which is connected to the first input of the second subtraction unit, the outputs of the second subtraction blocks of all functional transducers of the group are connected to the corresponding inputs of a minimum-signal block, the output of which is connected to the first inputs of elements AND of the first group of the allocation function of the membership function, the outputs of which are connected through the corresponding delay elements of the group to the information inputs of the memory blocks of the group, and the first inputs of the corresponding elements of the group comparison, the second inputs of which are connected to the first inputs of the corresponding elements AND of the second group and connected to the outputs of the corresponding memory blocks of the group, the outputs of the comparison blocks of the group are connected to the write-read enable inputs of the corresponding 51 the group’s storage units, the decoder outputs are connected to the second inputs of the AND elements of the first group, respectively, the second inputs of the AND elements of the second group are connected via a second delay element to the output of the counter, the decoder input is connected to the output of the divider function calculator, the first input of which connected to the output of the adder of the functional converter of fuzzy variables, the inputs of the multipliers of which are connected respectively to the first input of the first block of the subtraction of each functional about the converter of the group and connected to the output of the corresponding group adder, the output of the clock pulse generator is connected to the sensor polling inputs with a uniform Hbw distribution, the outputs of which are connected to the first inputs of the corresponding group multiplication blocks, the outputs of which are connected to the information inputs of the corresponding group adders, trigger input ge46 the clock pulse clock is the input to start the membership function generator, the second inputs of the group multiplication units, the group adders, multiplication units of the functional group of fuzzy variables, the divider of the block of the allocation of the values of membership functions, the divider and the first and second blocks the subtractions of each functional converter of the group are respectively the inputs for setting the spread coefficients of fuzzy variables, the offset of fuzzy variables, the proportionality coefficients of fuzzy variables, the magnitude of the interval of values of the desired variable of the spread coefficient and the expected value of the desired variable and the units, the outputs of the elements AND of the second group of the allocation function of the membership function are the outputs of the corresponding values of the membership function of the generator of membership functions. FIG. 2 -JSi Editor N.Gorvat Compiled by, Orlov Tehred c. Kadar 2426/45 Circulation 672 Subscription VNIIPI USSR State Committee for inventions and discoveries 113035., Moscow, Zh-35., 4/5 Raushsk nab. Production and printing company, Uzhgorod, st. Project, 4 M Jj N FIG. four Proofreader M. Demchik