On algebraic structure of intuitionistic fuzzy soft sets

Maji et al. introduced the concept of intuitionistic fuzzy soft sets which is a generalization of fuzzy soft sets and standard soft sets. In this paper, we further discuss the operation properties and algebraic structure of intuitionistic fuzzy soft sets. The lattice structures of intuitionistic fuzzy soft sets are derived. The notions of (γ,δ)(γ,δ)-intuitionistic fuzzy soft equalities are introduced and their basic properties are investigated. The relationships between (γ,δ)(γ,δ)-intuitionistic fuzzy soft equalities and soft equalities introduced by Qin and Hong are developed. The notion of a mapping on intuitionistic fuzzy soft classes is introduced and several properties of the image and inverse image of intuitionistic fuzzy soft sets are presented.