General Interval-valued Grouping Functions

Grouping functions are aggregation functions used in decision making based on fuzzy preference relations in order to express the measure of the amount of evidence in favor of either of the two alternatives when performing pairwise comparisons. They have been also used as a disjunction operator in some important problems, such as image thresholding and the construction of a class of implication functions for the generation of fuzzy subsethood and entropy measures. Some generalizations of this concept were recently proposed, such as n-dimensional and general grouping functions, which allowed their application in ndimensional problems, such as fuzzy community detection. Also the concept of interval-valued overlap functions was presented, in order to deal with the uncertainty when defining membership functions. The aim of this paper is to introduce the concepts of n-dimensional interval-valued grouping functions and general interval-valued grouping functions, studying representability, characterization and construction methods.