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It has been established that the fuzzy sets do not hold the Complement laws of Boolean algebra. The aim of this article is to introduce and study a kind of family of fuzzy subsets of a finite set which holds the Complement laws. The complement operation has redefined for this purpose. Further, it has been established that the introduced fuzzy subsets can form Boolean lattice and also Boolean algebra. General Terms Fuzzy Sets, Boolean algebra, the laws of Boolean algebra.

An Introduction to a Family of Fuzzy Subsets forming Boolean algebra