Comparison between interval type-2 fuzzy sets based on a fuzzy preference relation with probability degree

Interval Type-2 Fuzzy Set (IT2 FS), with membership grades which are intervals of a subset of [0, 1], is useful in circumstances where it is difficult to determine the exact membership function. IT2 FS has been widely used in many applications, where the comparison between IT2 FSs plays a significant role. A new comparison method based on a fuzzy preference relation with the probability degrees between two IT2 FSs is proposed in this paper. Comparing with the current two methods, the proposed method overcomes the conflicts between comparison results and human intuitive, preserves the consistency of ranking, and it makes the comparison results more precisely by attaching the probability degrees with the comparison results. The numerical example showed its validity.