The Modified Modal Operators over the Generalized Interval Valued Intuitionistic Fuzzy Sets

Abstract

Interval valued intuitionistic fuzzy set (IVFS) as an extension of intuitionistic fuzzy sets isdescribed by two parameters, namely membership degree and non-membership degree which areexpressed in terms of intervals rather than crisp numbers. IVFS can be used to handle uncertaintyand vagueness in real world decision making problems and operators of IVFSs have a key role inthis filed. Thus, in this work we define newly defined modal operators over generalized intervalvalued intuitionistic fuzzy sets by modifying the existing operators. The new proposed operatorsare the integrity and comprehensive. Then, we describe the desirable properties of the proposedoperators and discuss the special cases of them in details. Furthermore, the relationship betweenoperators is examined. Finally, an illustrative example is provided for comparison.