An overview on interval-valued intuitionistic fuzzy sets

Intuitionistic fuzzy sets on a universe was introduced as a generalization of fuzzy sets. The concept of intuitionistic fuzzy sets can be viewed as an appropriate approach in case where available information is not sufficient to define the impreciseness by the conventional approach. In the fuzzy sets theory, only the degree of acceptance is considered but in case of intuitionistic fuzzy sets both membership function and non-membership function is considered so that the sum of these two values add up to one. However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic fuzzy sets as well as algebraic operations. In this study, we first focus on the representation theorem of interval-valued intuitionistic fuzzy sets by use of the concept of level sets. Then, we study the extension principles of these sets to develop the common operators such as addition, subtraction, multiplication and division operations.

کلیدواژه ها:

Fuzzy set theory ، Intuitionistic fuzzy sets ، interval-valued intuitionistic fuzzy sets