Type II Addition and Scalar Multiplication Operators for Generalized Intuitionistic Fuzzy Numbers

Mondal and Samanta's generalized intuitionistic fuzzy set is an extension of Atanassov's intuitionistic fuzzy set, however, it can not be used to handle intuitionistic fuzzy multi-criteria fuzzy decision making problems, because of not only Atanassov's addition and scalar multiplication operators can no more be used for it, but also its lack of appropriate addition and scalar multiplication operators. In this paper, for overcoming the abovementioned drawback, two novel operators, called type II addition operator and type II scalar multiplication operator, are proposed, moreover, it is pointed that Liu's partial order is operation-invariant for not only Atanassov's addition and scalar multiplication operators but also these two type II operators, some theorems about these new operators are also proposed.