Lukaswize Triple-Valued Intuitionistic Fuzzy BCK/BCI-Subalgebras

Abstract

The authors studied the notion of (α,β)-intuitionistic fuzzy BCK/BCI-subalgebras by applying the Lukasiewicz 3-valued implication operator, where α,β∈{∈,q,∈∧q,∈∨q} for α≠∈∧q. In this chapter, an intuitionistic fuzzy set A is an (∈,∈) (or (∈∧q,∈) or (∈,∈∨q))-intuitionistic fuzzy subalgebras if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1]), then Ap is a fuzzy subalgebras of X respectively. Next, the authors defined intuitionistic fuzzy subalgebras with thresholds (s,t) and then provided intuitionistic fuzzy subalgebras with thresholds (0,1) (or (0,0.5) or (0.5,1)) by the concept of quasi-coincidence of fuzzy point respectively. Also, A is an intuitionistic fuzzy subalgebras with thresholds (s,t) if and only if for any p∈(s,t], then cut set A_p is a fuzzy subalgebras.