The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Reasoning with propositional knowledge based on fuzzy neural logic" (1996). In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calcu...

Recently there has been significant growth in research interest in type-2 fuzzy logic. Type-2 fuzzy logic is extension of type-1 (regular) fuzzy logic where the membership grade in a fuzzy set is itself measured as a fuzzy number. Much of this growth has only been concerned with type-2 interval fuzzy systems, a subset of type-2 fuzzy systems, where the membership grade of a fuzzy set is given a...

Fuzzy logic has rapidly become one of the most successful of today's technologies for developing sophisticated control systems. The reason for which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. It fills an important gap in engineering design methods l...

2 Vagueness, Uncertainty and Fuzzy Logic 2 2.1 Vagueness and Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Vagueness and Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 What Is Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Agenda of Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . ....