Data processing: artificial intelligence – Fuzzy logic hardware – Analog fuzzy computer
Reexamination Certificate
1998-10-19
2001-03-06
Hafiz, Tariq R. (Department: 2762)
Data processing: artificial intelligence
Fuzzy logic hardware
Analog fuzzy computer
C706S001000, C706S004000, C706S005000
Reexamination Certificate
active
06199056
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for storing membership functions and to a related circuit for calculating a grade of membership of antecedents of fuzzy rules.
2. Discussion of the Related Art
A fuzzy rule is constituted by an antecedent part and by a consequent part or conclusion. The antecedent part has a grade of membership of its own, determined on the basis of a value assumed by inputs and follows semantics of the rule itself.
The antecedent part can be composed of a plurality of terms. In order to determine a weight of an individual term, according to a meaning assumed in fuzzy logic, it is necessary to determine the highest value of an intersection between a membership function and a generic input.
In general, the grade of membership &agr; is defined as follows:
&agr;=max
x
{min[
A,A′]}
where A and A′ respectively designate the input sets and the corresponding membership function, as shown in FIG.
1
.
In the case of crisp inputs, with reference to
FIG. 2
, the value &agr; is determined by a segment produced by an intersection between the straight line A defined by the equation UdD=I (where I is the input of the system and UdD is the universe of discourse) and the membership function A′.
Performing this calculation entails using a method for storing the membership function, which has a triangular shape in the example of
FIG. 1
, so that it is possible to circuitally perform the intersection with the input in the simplest and most economical manner in terms of hardware.
There are various methods for storing membership functions and for their fuzzification. One of these methods consists in storing all the points of the membership function by means of a look-up table.
Another method is the storing of triangular membership functions by means of the gradients and the central vertex of the triangle.
Another method is the storing of trapezoidal membership functions by means of the two vertices and of the distance, relative to the nearest vertex, of the points of intersection between the two sides of the triangle and the axis representing the universe of discourse (UdD), as described in the article “A Parameterized Fuzzy Processor and Its Applications”, by B. T. Chen et al., published in the journal “Fuzzy Sets and Systems”, Elsevier Science Publishers B. V., no. 59, 1993, pages 149-172.
SUMMARY OF THE INVENTION
An aim of the present invention is to provide a method for storing membership functions and the related circuit for calculating the grade of membership of the antecedent part of the fuzzy rules that determines the intersection between the membership function and the input in a simple and economical manner.
An object of the present invention is to provide a method of storing information which describes a membership function where a number of bits used is not excessive.
Another object of the present invention is to provide a method that is advantageous, in terms of time and computing simplicity, for calculating the grade of membership &agr; of the antecedent part of a fuzzy rule.
A further object of the present invention is to provide a circuit for calculating the grade of membership &agr; that is simpler than known circuits and which can, therefore, be implemented with a smaller silicon area.
Another object of the present invention is to provide a method and a circuit that are each highly reliable, relatively easy to manufacture, and competitive in costs.
This aim, these objects, and others which will become apparent hereinafter are achieved by a method for storing membership functions, characterized in that it comprises the following steps: storing a position of a vertex of a triangle that defines the membership function in the universe of discourse; storing a first distance between said position of the vertex in the universe of discourse and the point of intersection between a left side of the triangle that defines the membership function and an of the universe of discourse; storing a second distance between said position of the vertex in the universe of discourse and a point of intersection between a right side of the triangle that defines the membership function and the axis of the universe of discourse.
Further, an apparatus for calculating a grade of membership of an antecedent part of a fuzzy rule comprises a means for receiving an input value and a means for fuzzifying the input value by adopting geometric proportions that occur between homologous sides of similar triangles which define a membership function defined by position of the input value in a universe of discourse.
This aim, these objects, and others which will become apparent hereinafter are furthermore achieved with a circuit for calculating the grade of membership of the antecedent of a fuzzy rule, characterized in that it comprises means adapted to fuzzify an input variable by adopting the geometric proportions that occur between homologous sides of similar triangles defined by the position of the input value in the universe of discourse.
REFERENCES:
patent: 5150320 (1992-09-01), Nakayama
patent: 5179629 (1993-01-01), Nakamura
patent: 5258943 (1993-11-01), Gamez et al.
patent: 5305251 (1994-04-01), Shigeoka et al.
patent: 5343553 (1994-08-01), Miyazawa et al.
patent: 5598512 (1997-01-01), Niwa
patent: 5600584 (1997-02-01), Schafly
patent: 5615303 (1997-03-01), Abruzzese
Partial European Search Report from European Patent Application 95830113.7, filed Mar. 28, 1995.
Proceedings of the 2nd International Conference on Fuzzy Systems, Mar. 28-Apr. 1, 1993, San Francisco, CA, USA, vol. 1, 1993 IEEE, New York, USA, pp. 612-617, M. Lee, et al., “Integrating Design Stages of Fuzzy Systems Using Genetic Algorithms”.
IEICE Transactions on Electronics, vol. E76-c, No. 7, Jul. 1993, Tokyo, JP, pp. 1102-1111, K. Nakamura “A 12-Bit Resolution 200 kFLIPS Fuzzy Inference Processor”.
ANSI/IEEE Std 754-1985: IEEE Standard for Binary Floating-Point Arithmetic, IEEE, New York, NY, pp. 9-10, Aug. 12, 1985.
Bella Dario Di
Matranga Vincenzo
Pappalardo Francesco
Tesi Davide
Consorzio per la Ricerca sulla Microelettronica nel Mezzogiorno
Galanthay Theodore E.
Hafiz Tariq R.
Morris James H.
Starks Wilbert L.
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