Abstract
AbstractIn this paper, we introduce the notion of hesitant fuzzy (implicative) filters and get some results on BE- algebras and show that every hesitant fuzzy implicative filter is a hesitant fuzzy filter but not the converse. Finally, we state and prove the relationship between hesitant fuzzy (implicative) filters and γ-inclusive sets.
Highlights
IntroductionH. Kim introduced the notion of a BE-algebra as a generalization of a dual BCKalgebra [3]
Walendziak introduced the notion of a normal filter in BE-algebras and showed that there is a bijection between congruence relations and filters in commutative BEalgebras [13]
The notion of γ-inclusive set which denoted by iA(hA; γ) is defined
Summary
H. Kim introduced the notion of a BE-algebra as a generalization of a dual BCKalgebra [3]. A. Borumand Saeid et al defined some types of filters in BE-algebras and showed the relationship between them [2]. Walendziak introduced the notion of a normal filter in BE-algebras and showed that there is a bijection between congruence relations and filters in commutative BEalgebras [13]. Fuzzy sets were introduced in 1965 by Zadeh [15] and fuzzification ideas have been applied to other algebraic structures such as groups and BL-algebras. We introduce the notion of hesitant fuzzy (implicative) filters and get some useful properties. We show that in self distributive BE-algebras two concepts of hesitant fuzzy implicative filter and hesitant fuzzy filter are equivalent. The notion of γ-inclusive set which denoted by iA(hA; γ) is defined
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