Similarity and (α, β)-equalities of intuitionistic fuzzy choice functions based on triangular norms

In this paper, we define (α, β)-equalities of intuitionistic fuzzy sets and (θα, ϕβ)-equalities of T, S-residual implications and their algebraic operations. Meanwhile (α, β)-equalities with respect to intuitionistic fuzzy relations, extension principle and dual triangular norms are studied. In addition, we discuss the intuitionistic fuzzy choice functions and their properties. Finally, a ordered method of intuitionistic fuzzy choice functions is proposed by using some examples.