Conditional distributivity of continuous triangular norms over 2-uninorms

Document Type : Research Paper

Authors

School of Mathematics and Statistics, Jiangxi Normal University, 330022 Nanchang, PR China

Abstract

Conditional distributivity of aggregation functions, which has received wide attention from the researchers, is vital for many different fields, for example, integration theory, utility theory and so on. This article is mainly devoted to dealing with the conditional distributivity of continuous t-norms over 2-uninorms. As the first step for investigating the conditional distributivity of 2-uninorms, we give the complete characterization of all pairs $(T,\mathcal{H})$ {fulfilling} this property. Compared to the case of distributivity of continuous t-norms over 2-uniorms, which leads to the 2-uninorm must be idempotent, the results obtained in this paper demonstrate that conditional distributivity and  distributivity on this topic, are not equivalent.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 20, Issue 2
March and April 2023
Pages 69-82

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