Subtraction and division operations on intuitionistic fuzzy sets derived from the Hamming distance.

Intuitionistic fuzzy values, each characterized by a membership degree and a nonmembership degree, are the basic components of intuitionistic fuzzy sets. Arithmetic operations on intuitionistic fuzzy values/sets are of importance in practical problem solving. In this paper, the subtraction and division operations over intuitionistic fuzzy values/sets are derived from the Hamming distance between them by the optimization method. Compared with the existing operations, the developed operations are complete, that is, any two intuitionistic fuzzy values/sets can be performed by these two operations. Then, fundamental properties of the modified arithmetic operations are extensively investigated for intuitionistic fuzzy values/sets. Finally, the continuity and the derivative operation of intuitionistic fuzzy functions are introduced based on the proposed operations, which provides a novel basis for the intuitionistic fuzzy differential calculus. [ABSTRACT FROM AUTHOR]