Relationships between T-transitivity indicators in (T,S,n)-fuzzy preference structures with rotation invariant t-norms

Abstract

In this paper, based on rotation invariant t-norms, we investigate the T-transitivity indicators of various fuzzy preference relations in the setting of $(T,S,n)$-fuzzy preference structures. The investigation is twofold: (1) equivalent expressions of the T-transitivity indicator of the large preference and the strict preference relation, and (2) the relationships between the T-transitivity indicators of the large preference and those of other preference relations. As a consequence, some results on transitivity in the crisp and fuzzy preference structures are extended to their indicator versions.