Abstract
In this paper, we introduce the concepts of additive generators and additive generator pair of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We mainly discuss the conditions under which an n-dimensional overlap function can be expressed in terms of its generator pair.
Highlights
Bustince et al introduced overlap functions and their basic properties in [1] [2]
In [8], Dimuro and Bedregal discussed some preliminary ideas on additive generator pair of overlap function
We extend the concept of additive generator pair of overlap functions to the notion of additive generator pair of overlap n-dimensional functions and discuss some basic properties in this paper
Summary
Bustince et al introduced overlap functions and their basic properties in [1] [2]. As one new case of nonassociative fuzzy logical connective, overlap functions have developed rapidly in theoretical research and practical application. In [8], Dimuro and Bedregal discussed some preliminary ideas on additive generator pair of overlap function. On the basis of [8], Dimuro et al [9] formally introduced the notion of additive generator pair of overlap functions and studied their basic properties. Qiao and Hu [10] mainly investigated the two basic distributive laws of fuzzy implication functions over additively generated overlap and grouping functions.
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