In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to h...In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.展开更多
Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate rea...Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure is used in fuzzy inference mechanism. This research proposes that similarity based approximate reasoning-modelling generalised modus ponens/generalised modus tollens—can be used to derive a resolution—like inference pattern in fuzzy logic. The proposal is well-illustrated with artificial examples.展开更多
文摘In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.
文摘Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-similarity relation is used in fuzzification while, similarity measure is used in fuzzy inference mechanism. This research proposes that similarity based approximate reasoning-modelling generalised modus ponens/generalised modus tollens—can be used to derive a resolution—like inference pattern in fuzzy logic. The proposal is well-illustrated with artificial examples.
