The modularity equation for Mayor's aggregation operators and uninorms

Document Type : Research Paper

Authors

School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Abstract

The focus of this paper is to investigate the modularity equation involving uninorms and Mayor's aggregation operators.  Necessary and sufficient conditions are established for this equation. And, it finds that the
modularity equation of a Mayor's aggregation operator over a uninorm is reduced to the modularity
of a commutative semi-t-norm over a uninorm and the modularity equation of a uninorm over a Mayor's aggregation operator is reduced to the modularity equation of a uninorm over a commutative semi-t-conorm. Among them, the cases of a uninorm which is locally internal on the boundary are studied in \cite{Su_Riera_Aguilera_Torrens_2019}. In this paper, we consider whether the neutral element $e$ of the uninorm is idempotent element of the Mayor's aggregation operator in modularity equation to get solutions in the corresponding cases.

Keywords


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