FUZZY PREFERENCE STRUCTURES WITHOUT INCOMPARABILITY

In this paper, are establish important relationships between the basic properties of the components of a fuzzy preference structure without incomparability. This study is carried out for the fuzzy preference st ructures introduced recently by De Baets, Van de Walle and Kerre. A se t of remarkable theorems gives detailed insight in the relationships b etween the sup-T transitivity of the fuzzy preference and indifference relations and the sup-T transitivity of the fuzzy large preference re lation. Several paths of thought, involving t-norms with or without ze ro-divisors, are explored and, where required, illustrative counterexa mples confirm the falsity of certain implications. Finally, we introdu ce the (T,N)-Ferrers property of a binary fuzzy relation and show that the fuzzy preference and fuzzy large preference relations share certa in types of this Ferrers property.