Teoria Fuzzy Para Aplicar En Sistemas Expertos

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 28, NO. 2, MARCH 1998

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A Multilevel Weighted Fuzzy Reasoning Algorithm for Expert Systems
D. S. Yeung and E. C. C. Tsang
Abstract—The applications of fuzzy production rules (FPR’s) are rather limited if the relative degree of importance of each proposition in the antecedent contributing to theconsequent (i.e., the weight) is ignored or assumed to be equal. Unfortunately, this is the case for many existing FPR’s and most existing fuzzy expert system development shells or environments offer no such functionality for users to incorporate different weights in the antecedent of FPR’s. This paper proposes to assign a weight parameter to each proposition in the antecedent of a FPR and a new fuzzyproduction rule evaluation method (FPREM) which generalizes the traditional method by taking the weight factors into consideration is devised. Furthermore, a multilevel weighted fuzzy reasoning algorithm (MLWFRA) incorporating this new FPREM, which is based on the reachability and adjacent place characteristics of a fuzzy Petri net, is developed. The MLWFRA has the advantages that i) it offersmultilevel reasoning capability; ii) it allows multiple conclusions to be drawn if they exist; iii) it offers a new fuzzy production rule evaluation method; and iv) it is capable of detecting cycle rules.

Petri nets. It is based on the backward chaining technique which offers the capabilities of handling different weights for different conclusions, fast processing time, provision of single or multiplegoals, and minimal adjacent place (AP) and reversed immediate reachable place (RIRP) tables. This algorithm can be incorporated into a fuzzy expert system as an inference engine. In Section II, the definitions of the WFPR and the fuzzy Petri net (FPN) model, and how the WFPR’s are mapped into the FPN model, are described. A detailed description of the proposed FPREM is presented in Section III.The MLWFRA together with an example to show its inference steps is discussed in Section IV. Comparisons to existing fuzzy reasoning algorithms are presented in Section V. Future research in determining certain parameters of the FPR’s is discussed in Section VI. II. MAPPING FUZZY PRODUCTION RULES INTO FUZZY PETRI NETS In this section, we shall review the definition of FPN’s and define three types ofWFPR’s. A method of mapping FPR’s into the FPN’s based on [4] is also described. A. Definition of Weighted Fuzzy Production Rules The WFPR defined here is similar to the conventional production rules with the exception that fuzzy values such as “fat” or “small” are allowed in the propositions. A weight is assigned to each proposition in the antecedent part, and a certainty factor is also assigned toeach rule. A WFPR is defined as: R: IF THEN ), Th, , where is the antecedent portion which comprises of one or more propositions connected by either “AND” or “OR”. Each proposition can have the format “ is ”, where is an element of a set of fuzzy sets . The consequent of the rule can be expressed as “ is ”, where is also an element of . The parameter is the certainty factor of the rule R and itrepresents the strength of belief of the rule. The symbol represents a set of threshold values specified for the propositions in the antecedent . The set of weights assigned to the propositions , is given by . The weight of a proposition shows the degree of importance of contributing to the consequent when comparing to other propositions , for . It is obvious that when there is only one proposition inthe antecedent of a WFPR, the weight is meaningless. The

I. INTRODUCTION

A

N EXPERT system, as its name implies, is a computer software that has expert-like ability to solve a domain specific problem. Building an expert system involves different phases of development. The most important ones are knowledge acquisition and representation. In this paper, we propose to assign a weight to...