On the distributivity property of uninorms locally internal on the boundary over noncontinuous t-(co)norms

Document Type : Research Paper

Authors

1 Foundational Courses Department, Wuhan Donghu University

2 School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, PR China

3 School of Mathematics and Statistics, Shandong Normal University, Jinan, PR China

Abstract

This paper characterizes a uninorm distributive over a noncontinuous t-(co)norm, where the uninorm is locally internal on the boundary. Firstly, when the uninorm is disjunctive, the necessary conditions (resp. the sufficient conditions) for a uninorm distributive over a noncontinuous t-norm are analyzed under the certain condition. Secondly, the distributivity of a conjunctive uninorm over a noncontinuous t-conorm is characterized by duality. In particular, this paper is related to the open question recalled by Klement in the Linz2000 closing session, which provides the noncontinuous solutions of that question.

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References

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Iranian Journal of Fuzzy Systems
Volume 20, Issue 4
July and August 2023
Pages 137-152

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