Objectives: This study deals with the algebraic structure intuitionistic fuzzy soft (IFS) Г-semi group is defined that is a natural extension of IFS semi group and fuzzy soft Г-semi groups. The notion of IFS Г-ideals over Г-semi groups are introduced. Also, the basic concepts of the ideals are studied. Methods: Using approaches given in IFS semi groups to enlarge fuzzy soft Г-semi groups offer the required algebraic structure. Findings: The ideaI F Ssoft Г-semi group is the natural consequence of viewing collectively the IFSsemigroup and fuzzy soft Г-semi groups. Applications: Fuzzy soft set theory, IF set theory, etcetera are well celebrated mathematical concepts handling the uncertainties in the fields of engineering, economy, social science.
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