Kybernetika 57 no. 4, 647-670, 2021

Distributivity of ordinal sum implications over overlap and grouping functions

Deng Pan and Hongjun ZhouDOI: 10.14736/kyb-2021-4-0647

Abstract:

In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.

Keywords:

ordinal sum, distributivity, fuzzy implication functions, overlap functions, grouping functions

Classification:

03B52, 03E72

paper.pdf

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