A Study On T-S-Semitransitivity Based On The Rotation Invariant T-Norms

In this paper, we study the properties of T-S-semitransitivity if the involved t-norms are rotation invariant. The main results are summarized as follows:Firstly, we review the concept and properties of fuzzy logic connectives, and some results on the semitransitivity of a crisp relation and equivalent versions of the semitransitivity of weak and strict preferences in crisp preference structures.Secondly, we conduct research on the T-S-Semitransitivity of fuzzy relations. We systematically summarize the conclusions of T-S-Semitransitivity in the literature. Then we give some equivalent versions of the T-S-Semitransitivity of a fuzzy relation and investigate the relationship between T-S-Semitransitivity and Strong Wφ’-completeness.Thirdly, we deal with the T-S-Semitransitivity of the weak preference and strict preference relation in additive φ-fuzzy preference structures. we first give some equivalent versions of the T-S-Semitransitivity of the weak preference and the strict preference. Next, we study the relationships between the T-S-Semitransitivity of strict preference relation, P(?)T P(?)T I(?)P(or I(?)T P(?)T P(?)p), (p(?)T P)∩(I(?)T I)=(?) and Condition S2. With preference structures without incomparability, we prove their equivalence under the the condition that the inclusion P(?)T1 I(?)T2 P(?)P is valid, where T1 is a t-norm without zero divisor.Through our study, we have a further understanding of the T-S-Semitransitivity. As a result, some equivalencies of semitransitivity in the crisp case is generalized to those in the fuzzy case.