Narrow Results

This paper presents a characterization of a new family of operators. Namely, all non-decreasing, associative binary operators U: [0, 1]² → [0, 1] with a left (or right) neutral element e ∈ [0, 1], and such that they satisfy an additional hypothesis on continuity which is called here left (or right) pseudocontinuity.

We study some properties of De Morgan triplets. Firstly, we introduce submodular De Morgan triplets and we study its relationships with subdistributive ones. Moreover, we characterize them both in the strict and non strict archimedean cases. Secondly, we introduce the concepts of modularity, distributivity and (S, T)-distributivity degrees and we give some general results. Afterwards we apply these concepts to two particular cases, Lukasiewicz triplets and a kind of strict De Morgan triplets (Product triplets). For the Lukasiewicz ones we prove that all three degrees range over (0, 1/2]. For Product triplets, a recipe to calculate these degrees is given. In particular we present examples with distributivity degree r for all r ∈ (0, 1) and examples with (S, T)-distributivity and modularity degrees taking all values in (0, 3/4].

This paper looks over a class of operators introduced in ([2]), called t–operators. Introduced in order to be applied to fuzzy preorders, their properties lead them to be also appropriate in some fields like aggregation problems and expert systems. We characterize these operators as a special combination of a t-norm and a t-conorm on [0, 1] in a similar way of uninorms in ([5]). We study duality and self duality on t–operators with respect to a strong negation N. We also give a classification of continuous t–operators through ordinal sums. Finally, we obtain from some t–operators (those idempotent) a special kind of E.A.F. by extending them to E=∪_n≥1[0,1]ⁿ.