Complementation Of Fuzzy Sets Research Articles

Modifications of Bellman-Giertz's theorem

Bellman and Giertz have proposed the conditions that the operations of union, intersection and complementation of fuzzy sets satisfy Zadeh's definitions. We have proved that some of the conditions in Bellman-Giertz's theorem are not necessary. The Bellman-Giertz's theorem is modified and the independence of some conditions is discussed.

A New Family of Fuzzy Set Algebras Derived from Information Theory

One of main problems which arise in implementing intelligent systems via approximate reasoning based on fuzzy sets is the suitable selection of the corresponding fuzzy set algebra, which depends upon the kind of problems under consideration. In this way, it may be of interest to have several algebras at hand, and the purpose of the present paper is to provide such other alternatives. This new approach works via information theory, and proposes new definitions for the union, the intersection and the complement of fuzzy sets. The relation with the min-max modelling is exhibited.

Complement of fuzzy k-partitions

We define the unary operation of complementation on the set of all fuzzy k-partitions of a finite set of objects. We show that for k = 2 the complement of fuzzy k-partition results in Zadeh's complementation of fuzzy sets. Some further properties of the complement of fuzzy k-partitions are investigated.