Uninorms on bounded lattices with the underlying t-norms and t-conorms

Uninorms are a generalization of the concepts of triangular norms (t-norms) and triangular conorms (t-conorms) that admit a neutral element as any element in a bounded lattice. In this study, we discuss the characterization of uninorms on bounded lattices. We introduce some new constructions for uni...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 395; pp. 107 - 129
Main Author Çaylı, Gül Deniz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.09.2020
Subjects
Bounded lattice
Idempotent uninorm
Neutral element
t-conorm
t-norm
Uninorm
Bounded lattice
t-conorm
t-norm
Idempotent uninorm
Neutral element
Uninorm
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Summary:Uninorms are a generalization of the concepts of triangular norms (t-norms) and triangular conorms (t-conorms) that admit a neutral element as any element in a bounded lattice. In this study, we discuss the characterization of uninorms on bounded lattices. We introduce some new constructions for uninorms on bounded lattices, which are derived from both t-norms and t-conorms. In particular, two idempotent uninorms on bounded lattices are obtained. We also provide some corresponding examples to help understand the structure of these new classes of uninorms. In addition, we provide an answer to the open problem proposed by Çaylı (2019) [14].
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2019.06.005