An order induced by extended t-norms on convex normal functions

In this paper, we present an order ⪯⊙T induced by extended t-norms ⊙T on normal and convex functions. First, we investigate the relationship between the meet order (resp. join order) and ⪯⊙T. And then we define the set of incomparable convex normal functions with respect to ⪯⊙T and deeply study its...

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Bibliographic Details
Published in:Fuzzy sets and systems 2023-08, Vol.465, p.108530, Article 108530
Main Author: Liu, Zhi-qiang
Format: Article
Language:English
Subjects:
Bounded lattice
Extended t-norm
Normal and convex function
Partial order
Type-2 fuzzy set
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Summary:In this paper, we present an order ⪯⊙T induced by extended t-norms ⊙T on normal and convex functions. First, we investigate the relationship between the meet order (resp. join order) and ⪯⊙T. And then we define the set of incomparable convex normal functions with respect to ⪯⊙T and deeply study its properties. •An order induced by extended t-norms on convex normal functions of type-2 fuzzy set is studied.•The relationship between the meet order (resp. join order) and the order induced by extended t-norms is obtained.•The set of incomparable convex normal functions with respect to the order induced by extended t-norms is defined.•The set of convex normal functions may form a lattice under the order induced by extended t-norms.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108530