Constructing overlap and grouping functions on complete lattices by means of complete homomorphisms

In this paper, construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete 0L,1L-endomorphisms are investigated. At first, we propose the notion of O-generator triple of overlap functions. Then, properties such as (α,B,C)-migrativity, (B,C)-hom...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 427; pp. 71 - 95
Main Authors Wang, Yuntian, Hu, Bao Qing
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.01.2022
Subjects
Complete homomorphism
Complete lattice
Grouping function
Overlap function
Complete homomorphism
Overlap function
Grouping function
Complete lattice
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Summary:In this paper, construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete 0L,1L-endomorphisms are investigated. At first, we propose the notion of O-generator triple of overlap functions. Then, properties such as (α,B,C)-migrativity, (B,C)-homogeneity, idempotency and cancellation law for the overlap functions obtained by such generator triples are discussed. Finally, we give an analogous discussion on grouping functions on complete lattices.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2021.03.015