On cuts of Atanassov’s intuitionistic fuzzy sets with respect to fuzzy connectives

A new approach to t-norm and t-conorm based α-cuts of intuitionistic fuzzy sets is studied. Strong and weak cuts for intuitionistic fuzzy sets are defined, and their various properties are investigated. We show that strong cuts contained in the average cuts and average cuts contained in the weak cuts and it is also observed that for some special cases, average cuts are same. We investigate the strong, weak, and average cut sets of intuitionistic fuzzy sets under the fuzzy sets operations: finite (infinite) intersection and union with respect to fuzzy connectives. Some relevant counter examples are indicated.