Connection Among Some Characterizations of Complete Fuzzy Preorders

Abstract

The concept of (classical) complete preorder can be characterized in several ways. In previous works we have studied whether complete fuzzy preorders can be characterized by the same properties as in the crisp case. We have proven that this is not usually the case. We have studied five possible characterizations and we have proven that only one still characterizes a fuzzy preorder. In this work we study those properties for additive fuzzy preference structures without incomparability. Despite they do not characterize complete fuzzy preorders, they can be related among them. In this contribution we show their connection when the preference structure does not admit incomparable alternatives.