In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semant...In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.展开更多
It is well known that Zadeh's fuzzy logic is not a Boolean algebra because it does not satisfy the Law of Excluded Middle or the Law of Contradiction, but the two-valued propositional logic does. On the other hand...It is well known that Zadeh's fuzzy logic is not a Boolean algebra because it does not satisfy the Law of Excluded Middle or the Law of Contradiction, but the two-valued propositional logic does. On the other hand, a recently proposed measure-based fuzzy logic(MBFL) satisfies all the axioms of Boolean algebra. In this paper, a complete and thorough proof is given for this.展开更多
文摘In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.
文摘It is well known that Zadeh's fuzzy logic is not a Boolean algebra because it does not satisfy the Law of Excluded Middle or the Law of Contradiction, but the two-valued propositional logic does. On the other hand, a recently proposed measure-based fuzzy logic(MBFL) satisfies all the axioms of Boolean algebra. In this paper, a complete and thorough proof is given for this.
