A new insight of the distributivity for S-uninorms

Document Type : Research Paper

Authors

1 School of Mathematical Sciences, Shandong Normal University, Jinan, PR China

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

3 Foundational Courses Department, Wuhan Donghu College, Wuhan, PR China

Abstract

Although the scholars studied the distributivity for S-uninorms, at least, the underlying
uninorm of one S-uninorm in the distributivity equations was assumed to be in Umin except
the distributivity for S-uninorms over t-(co)norms. In this paper, we further characterize the
distributivity for S-uninorms, where the conjunctive underlying uninorms of the S-uninorms
in the distributivity equations are not fixed in Umin but arbitrary. Firstly, we discuss the
distributivity between S-uninorms. Secondly, we analyze the distributivity for S-uninorms
over T-uninorms. Moreover, we obtain the distributivity for T-uninorms over S-uninorms by
duality. Thirdly, we investigate the distributivity for S-uninorms over disjunctive uninorms.
Because S-uninorms in those distributivity equations are arbitrary, our results are extensions
of the previous results on the distributivity for S-uninorms.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 22, Issue 4
July and August 2025
Pages 17-35

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