Uninorms introduced by Yager in 1996 are a new class of aggregation operators, which are also an important generalization of t-norms and t-conorms. At present, uninorms have been widely used in lots of fields such as expert system, decision making, fuzzy reasoning, image processing and so on. In the theoretical study about this class of operators, several subclasses emerged, and some extensions...

In this paper we introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are no t-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative t-norm, as already shown by other authors) and that the only migrative ...

There has been a growing interest in the study of the notion of $alpha$-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms.This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results tha...

In this work we extend to the interval-valued setting the notion of an overlap functions and we discuss a method which makes use of interval-valued overlap functions for constructing OWA operators with interval-valued weights. . Some properties of intervalvalued overlap functions and the derived interval-valued OWA operators are analysed. We specially focus on the homogeneity and migrativity pr...

In this paper we summarize our results obtained recently on continuous triangular norms that are migrative with respect to an arbitrary continuous triangular norm. We start with the original notion of migrativity and completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent t-norm classes, the characterization and construc...

In this paper we address the problem of a-migrativity (for a fixed a) for semicopulas, copulas and quasi-copulas. We introduce the concept of an a-sum of semicopulas. This new concept allows us to completely characterize a-migrative semicopulas and copulas. Moreover, a-sums also provide a means to obtain a partial characterization of a-migrative quasicopulas. 2010 Elsevier Inc. All rights reser...

In this work we study overlap degrees expressed in terms of overlap functions. We present the basic properties that from our point of view must satisfy these overlap functions. We study a construction method, we analyze which t-norms are also overlap functions and we prove that if we apply particular aggregations to such functions we recover the overlap index between fuzzy sets as defined by Du...