Distributivity of ordinal sum implications over overlap and grouping functions. (English) Zbl 07478633

Pan, Deng; Zhou, Hongjun

Kybernetika 57, No. 4, 647-670 (2021).

Summary: In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Y. Su et al. [Inf. Sci. 293, 251–262 (2015; Zbl 1355.03018)]. 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.

MSC:

03B52	Fuzzy logic; logic of vagueness
03E72	Theory of fuzzy sets, etc.

Keywords:

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

Citations:

Zbl 1355.03018