Fuzzy stabilizers in BL-algebras

Xiao-yun Cheng, Xiao Long Xin, Jun Tao Wang, Peng Fei He


The primary goal of this paper is to develop fuzzy stabilizer theory in BL-
algebras. Two types of fuzzy stabilizers are introduced and their related properties
are given. Also, the relationships between fuzzy stabilizers and several fuzzy filters
are discussed. Finally, by means of fuzzy stabilizers, it is proven that the collection
of all fuzzy filters in BL-algebras forms a residuated lattice. These results will
provide a solid algebraic foundation for the consequence connectives in fuzzy logic.

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