Abstract
In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.
Highlights
Overlap functions [1] [2] and grouping functions [3] are two particular cases of bivariate continuous aggregation functions
In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n
We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h . we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions
Summary
Overlap functions [1] [2] and grouping functions [3] are two particular cases of bivariate continuous aggregation functions. Those two concepts have been applied to some interesting problems, for example, image processing, classification or decision making. In [5], Dimuro et al introduced the notion of additive generator pair for overlap functions and analyzed the influence of the migrativity, homogeneity and idempotency properties in the overlap functions obtained by such distortion and their respective additive generator pairs. Qiao and Hu [6] proposed the concept of multiplicative generator pair for overlap functions and grouping functions, and investigated the migrativity, homogeneity, idempotency, Archimedean and cancellation properties
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