TRANSLATION AND DENSITY OF A BIPOLAR-VALUED FUZZY SET IN UP-ALGEBRAS

Abstract

We apply the notion of bipolar fuzzy translations of a bipolar-valued fuzzy set to UP-algebras.  For any bipolar-valued fuzzy set φ = (A; φ^-, φ⁺) in a UP-algebra A, the notions of bipolar fuzzy (α,β)-translations of φ = (A; φ^-, φ⁺) of type I and of type II are introduced, their basic properties are investigated and some useful examples are discussed.  The notions of extensions and of intensions of a bipolar-valued fuzzy set are also studied.  Moreover, we discuss the relation between the complement of a bipolar fuzzy UP-subalgebra (resp., bipolar fuzzy UP-filter, bipolar fuzzy UP-ideal and bipolar fuzzy strongly UP-ideal) and its level cuts.