The novel approach for ranking generalized interval type-2 trapezoidal fuzzy numbers based on integral value

Interval type 2 fuzzy sets (IT2FS) give us with additional value of membership function to represent the uncertainty and the fuzziness of the real word than type 1 fuzzy sets (T1FS). In real problem, the ranking of interval type 2 fuzzy numbers is an important component in the fuzzy decision making system. The existing ranking approaches i.e. centroid is cited by many researchers and has wide application, and then integral value also often developed by researchers both in the form of T1FS and newly in the form IT2FS. However, the existing ranking approaches still have shortcomings of the ranking function. In this paper, the concepts of left and right of interval type-2 trapezoidal fuzzy numbers (IT2TrFN) i.e the novel total integral value with index of optimistic is proposed to overcome the shortcomings of the existing ranking approaches. By using several examples, the new total integral value is capable to cover the shortcomings of the existing approaches and has well-consistency in ranking IT2TrFN with equal and different bight value.