Fuzzy ordered sets and aggregations

Abstract

After an extended introduction, we take care to the so-called cutworthy property. "A special property (P) will be called cutworthy when it is true that a fuzzy relation possesses (P) (in the fuzzy sense) if and only if every α-cut of the relation possesses (P) (in the crisp sense)", where many results concerning the L-fuzzy ⊗-equivalence relations L-fuzzy ⊗-E-partial orderings are established. In addition, we have investigated the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are explored