Compatibility in Fuzzy Inference

Abstract

Processing information in fuzzy rule-based systems generally employs one of three patterns of inference: composition, compatibility modification, or interpolative reasoning. Compositional inference originated as a generalization of binary logical deduction to fuzzy logic. Compatibility modification was developed to facilitate the evaluation of rules by separating the evaluation of the input from the generation of the output. The first step in compatibility modification inference is to assess the degree to which the input matches the antecedent of a rule. The result of this assessment is then combined with the consequent of the rule to produce the output. Interpolative and analogical reasoning consider rules to define paradigmatic examples and inference is based on proximity to these examples. Interpolative techniques have been developed to compensate for sparse data and to produce small rule bases. The premises underlying these approaches and their dependence on compatibility assessment are presented in the following sections. Various aspects of the role of compatibility measurement in fuzzy inference have been examined in [53, 70, 247, 26] and their use in fuzzy rule base simplification in [191].