In this paper, we introduce the notion of intuitionistic fuzzy soft ideal in intuitionistic fuzzy soft set theory. Also we introduce the concept of intuitionistic fuzzy soft local function. These concepts are discussed with a view to find new intuitionistic fuzzy soft topologies from the original one. The basic structure, especially a basis for such generated intuitionistic fuzzy soft topologies also studied here. The notion of compatibility of intuitionistic fuzzy soft ideals with intuitionistic fuzzy soft topologies is introduced and some equivalent conditions concerning this topic are established here. Finally we introduce intuitionistic fuzzy soft-I-open set, intuitionistic fuzzy soft pre-I-open set, intuitionistic fuzzy soft semi-I-open set, intuitionistic fuzzy soft-α-I-open set and intuitionistic fuzzy soft-β-I-open set and discuss some of their properties.
