Characterizing idempotent nullnorms on a special class of bounded lattices

Nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms. This paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 427; pp. 161 - 173
Main Authors Wu, Xinxing, Liang, Shudi, Çaylı, Gül Deniz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.01.2022
Subjects
Idempotent nullnorm
Lattice
Nullnorm
Zero element
Zero element
Nullnorm
Lattice
Idempotent nullnorm
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Summary:Nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms. This paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only two distinct elements incomparable with a. Furthermore, some basic properties for the bounded lattice containing only two distinct elements incomparable with a are presented.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2020.11.016