MODEL OF FUZZY REASONING THROUGH MULTI-VALUED LOGIC AND SET-THEORY

Various interpretations of conditional propositions are considered, which include relational definitions using Łukasiewicz logical implication rule and Zadeh's Maximin rule. Theorems are presented which describe the relationship between the interpretations. An example of reasoning in ordinary set theory is presented as a special case of the method used for approximate reasoning with fuzzy propositions. Models of reasoning from multiple conditional propositions of high dimensional state are constructed and theorems for reducing dimensionality are presented. Problems of dimensionality using the Łukasiewicz implication rule are discussed and an alternative method based on fuzzy logic is indicated briefly. © 1979, Academic Press Inc. (London) Limited. All rights reserved.