A new structure for fuzzy systems: Fuzzy propositional logic and multi-universe representation of fuzzy decision processes

A new structure has been developed for fuzzy logical algebra. This is called as ''Fuzzy propositional logic structure'' in which ''Proposition'' is defined as a more generalized form of fuzzy proposition defined by Zadeh. With this structure, the fuzzy reasoning mathematics becomes very simple, and very easy to understand. The fuzzy sets and fuzzy propositions are represented in the extended universe and all logical operations can be performed by the known logical formulas already developed for nonfuzzy logic. Mutual exclusive and complementary properties of propositions have been defined. Notion of a fuzzy basis for the universe is developed. The decision formula is transformed into the output universe, hence all calculations become one-universe operations. In short, this new structure brings about unification and simplification in all stages of fuzzy decision process.