JPH04340627A - Membership function register - Google Patents

Abstract

PURPOSE:To quickly calculate a membership value Y by calculating it without division only be comparison, subtraction, and bit shift. CONSTITUTION:With respect to a trapezoidal membership function 1, lengths L1 and L2 of inclined side parts 2 of the trapezoid projected to a base set 3 are set to 2<n> (n is an integer). A part corresponding to the denominator side of the membership function is set to 2<n> in this manner. Thus, the membership value Y is calculated only by comparison, subtraction, and bit shift.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for registering membership functions in fuzzy sets, and in particular, to an apparatus that can calculate membership values at high speed.

0002

[Prior Art] Conventionally, when dealing with fuzzy sets,
In order to reduce memory capacity or speed up calculation time, trapezoidal, triangular, or one-sided membership functions as shown in FIG. 2 are used.

By the way, in the membership function set by linear approximation as shown in FIG. 3, the membership value Y is calculated from equation (1). Y=(X-X1)/(X2-X1)*(Y2-
Y1)+Y1...(1) On the other hand, in a trapezoidal, triangular, or one-sided membership function as described above, the membership value Y is calculated from a series of equations (2). Y=0 {X≦X1, X≧X4} =
1 {X2≦X≦X3}

=(X-X1)/(X2-X1)
{X1<X<X2}
= (X4-X)/(X4-X3) {X
3 < X < Ru. Y=0 {X≦X1, X≧X4} =
Y0 {X2≦X≦X3}

=(X-X1)*Y0/(X2-X
1) {X1<X<X2}
=(X4-X)*Y0/(X4-X3){X3
<X<X4}…(3)

0004

[Problem to be Solved by the Invention] However, when calculating the membership value Y using the above equations (1) to (3), these equations include division that takes a considerable amount of time. Therefore, especially when the membership value Y corresponding to the input variable X corresponds to the hypotenuse part of the membership function, that is, when the input variable
3 < X < There is a problem with this.

[0005] The present invention has been made in view of these conventional problems, and it is an object of the present invention to solve the above problems by calculating the membership value Y without performing division.

[0006]

[Means for Solving the Problems] In order to achieve the above object, the present invention is drawn in a broken line shape, and the length of the hypotenuse portion of the broken line shape projected onto a set of platforms is 2 n. It is characterized by having a membership function that is a power.

[0007]

[Operation] According to this invention, since the portion corresponding to the denominator side of division in the membership function is 2 to the nth power, when calculating the membership value, instead of performing division, the numerator side is n bits. Since it is only necessary to shift, membership values can be calculated quickly.

[0008]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the membership function device according to the present invention will be described below with reference to FIG.

This membership function registration device has the following functions:
As shown in (a), the membership function drawn in a trapezoidal shape among the polygonal lines, the so-called trapezoidal membership function 1
is registered, and in this trapezoidal membership function 1, the lengths L1 and L of the hypotenuse 2 of the trapezoid projected onto the platform set 3 are
2 is set to the nth power of 2 (n: integer) as shown in equation (4). L1=(X2-X1)=2n(=a1)
L2=(X4-X3)=2n(=a2)
...(4) Here, by substituting equation (4) into equation (3) above, if the denominator side of equation (3) is set to the nth power of 2, such division will be performed on the numerator side in binary system. Since it is only necessary to shift n bits, "n bit shift" is indicated by the symbol ">>n", and a series of equations (5) are obtained. Note that if n is positive, the bits are shifted to the right, and if n is negative, the bits are shifted to the left. Y=0 {X≦X1, X≧X4} =
Y0 {X2≦X≦X3}

={(X-X1)*Y0)} >>a
1 {X1<X<X2}
={(X4-X)*Y0)} >>a
2{X3<X<X4}...(5) On the other hand, the formula (
In 5), the normalization constant Y0 is set as “Y0=2n(=b)
”, equation (5) can be expressed as equation (6). Y=0 {X≦X1, X≧X4} =
Y0 {X2≦X≦X3}

=(X-X1) >>(a1-b)
{X1<X<X2}
=(X4-X) >>(a2-
b) {X3<X<X4}...(6
) That is, in such a membership function registration device, the membership value Y is determined from the above equation (5) or equation (6).
is calculated. At this time, the membership value Y is calculated only by comparison, subtraction, and bit shifting.

[0010] Furthermore, in equation (6), the exponent part n (=a1
-b, a2-b) is fixed, when the input variable -X1,X
4-X) by simply bit-shifting the membership value Y
is calculated. If such a calculation is implemented in hardware, the amount of bit shift is determined to be n, so it may be configured to directly pick up designated bits from the subtraction results (X-X1, X4-X).

[0011] Therefore, according to the embodiment described above, membership values are calculated only by comparison, subtraction, and bit shift without performing division, so membership values can be calculated at high speed, and such calculations can be performed easily. If this is done using software or hardware, the program capacity or circuit scale can be reduced.

In the above embodiment, a trapezoidal membership function was explained as an example of a membership function drawn in the form of a polygonal line, but another example is shown in FIG.
As shown in (b) and (c), even if the membership functions 4 and 5 are triangular or one-sided, the length of the shaded part 2 projected onto the platform set 3 is 2 to the nth power. If set to , the same effect as above can be obtained.

[0013]

Effects of the Invention The membership function registration device according to the present invention draws a broken line shape as described above, and the length of the hypotenuse portion of the broken line shape projected onto a set of platforms is 2.
Since we have a membership function that is the nth power of 2, the part corresponding to the denominator of division in the membership function is 2 n
Since it is a multiplication, when calculating the membership value, it is only necessary to shift the numerator by n bits instead of performing division. This allows for fast calculation of membership values and
In addition, when such calculations are performed using software or hardware, the program capacity or circuit scale can be reduced.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram of membership functions registered in a device according to the present invention.

FIG. 2 is an explanatory diagram of membership functions registered in a conventional device.

FIG. 3 is an explanatory diagram of membership functions registered in a conventional device.

[Explanation of symbols] 1 Membership function 2 Hypotenuse part 3 cars set

Claims (1)

[Claims] [Claim 1] While drawing a broken line shape, the length of the hypotenuse portion of the broken line shape projected onto a set of platforms is 2.
A membership function registration device characterized by having a membership function that is the nth power of .