Representability of Fuzzy Biorders and Fuzzy Weak Orders

Abstract

In this paper, we have studied representability of both fuzzy biorders and fuzzy weak orders. It has also been shown that union of a finite family of fuzzy weak orders with respect to a t-norm T is a fuzzy quasi-transitive relation with respect to T. In the last theorem, we have obtained a characterization for a TL-representable fuzzy weak order. © 2016 World Scientific Publishing Company.