Session Program

Abstract - Copulas are a special kind of aggregation functions that have been deeply investigated because of their applications in many fields, specially in Statistics and Economy. An important research topic from the theoretical point of view is the study of new construction methods of copulas. In this line, this paper presents two construction methods based on probabilistic implications and survival implications. From these construction methods, the axiomatic characterization of these families of fuzzy implication functions, which are in fact the same, is presented.

Abstract - A relationship between real-valued and lattice-valued F-transforms and aggregation functions is analyzed. For each direct F-transform, we find an axiomatic characterization of the corresponding mapping. We show that the real-valued F-transform is a set of images of linear aggregation functions and that the lattice-valued F-transforms are images of linear-like maps. In all cases, the involved maps respect certain partitions of the universe.

Abstract - Measures of k-specificity are generalizations of Yager's measures of specificity of fuzzy sets or possibility distribution to measure the tranquility when choosing one element, extended to choose k elements from the universe of discourse. In this paper a new measure of k-specificity is defined, a definition of measures of crispness is provided, and an example of measure of crispness is given.

Abstract - The aim of this work is to study a fuzzy implication called (T,N)-implication, obtained by the composition of a fuzzy negation and a t-norm. It discusses under which conditions such functions preserve the main properties of fuzzy implications, in which some are related to the laws of contraposition. Finally, we prove a result that ensure the necessary and sufficient conditions for a function I : [0; 1]\^{}2 -$>$ [0; 1] to be a (T,N)-implication.

Abstract - In this paper we apply an extension method via e-operator to extend lattice-valued uninorms and nullnorms from a sublattice to a greater one, in order to verify which algebraic properties of them are preserved by the extension method.

Abstract - Hesitant Fuzzy Sets are useful to represent the information given by several experts. However, this possibility usually require to deal with sets of values with different cardinality and the necessity to compare them, it is, not all experts evaluate all the elements in the universe. In this paper it is proposed a new nomenclature for Hesitant Fuzzy Sets called Hesitant Fuzzy Sets using Lists. It is proposed a new partial order relation between lists of membership degrees. This partial order relation allows to handle lists with different lengths. In addition, Hesitant Fuzzy Relations on Lists operations are defined and the T-transitive closure of a Hesitant Fuzzy Relation is given. It is proved this T-transitive closure always exists and it is unique. Finally, an algorithm to compute the T-transitive closure of a Hesitant Fuzzy Relation is proposed and several examples are given.

Abstract - In this contribution new ways of constructing of ordinal sum of fuzzy implications are proposed. These methods are based on a construction of ordinal sums of overlap functions. Moreover, preservation of some properties of these ordinal sums of fuzzy implications are examined. Among others neutrality property, identity property, and ordering property are considered.