A new approach to inference in approximate reasoning

Abstract We introduce a new approach to inference in approximate reasoning based on truth value restriction. The degree to which the actual given value A of a variable X agrees with the antecedent value B in a production “If X is B then Y is C ” is represented as a fuzzy subset of a truth space. We introduce a new form of implication based on the exponential operation. A new compatibility relation based on the input value A and the antecedent value B is defined. A fuzzy truth value true derived from the antecedent value B is also defined. It is shown that by mapping this compatibility relation into the truth space, a fuzzy truth value is generated which produces an exponential family of the fuzzy truth value true . We show that the inferred consequent can be generated from this truth value. Theoretical results showing the validity of this method to (1) chain rules consisting of several single fuzzy conditional propositions, and (2) conjunctive fuzzy conditional propositions, are also presented. Theoretical and simulation results demonstrate that our method is superior to the existing methods when intuitively correct responses are required.

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