Constructions of uni-nullnorms and null-uninorms on a bounded lattice

Recently, Wang et al. proposed the notion of a uni-nullnorm on a bounded lattice and provided two construction methods. In this paper, we point out that the first construction method is invalid since it does not always lead to a uni-nullnorm. Then we present a method to construct a uni-nullnorm on a...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 403; pp. 78 - 87
Main Authors Zhang, Hua-Peng, Ouyang, Yao, De Baets, Bernard
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.01.2021
Subjects
Lattice
Null-uninorm
Triangular conorm
Triangular norm
Uni-nullnorm
Uninorm
Null-uninorm
Uni-nullnorm
Triangular conorm
Lattice
Uninorm
Triangular norm
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Summary:Recently, Wang et al. proposed the notion of a uni-nullnorm on a bounded lattice and provided two construction methods. In this paper, we point out that the first construction method is invalid since it does not always lead to a uni-nullnorm. Then we present a method to construct a uni-nullnorm on a bounded lattice via a disjunctive uninorm and a triangular norm. Making use of existing construction methods for uninorms on a bounded lattice, we derive several construction methods for uni-nullnorms, including the second construction method by Wang et al. Dually, we present a method to construct a null-uninorm on a bounded lattice via a conjunctive uninorm and a triangular conorm, as well as several derived construction methods for null-uninorms.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2019.10.010