Complete relations on fuzzy complete lattices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2017Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 320, pages 64-80 (issn: 0165-0114,

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Authors: Jan Konecny 0001; Michal Krupka;

doi: 10.1016/j.fss.2016.08.007 , 10.48550/arxiv.1506.03930

arXiv: 1506.03930

Complete relations on fuzzy complete lattices

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Abstract

We generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in one-to-one correspondence with extensive isotone Galois connections. Finally, we prove that fuzzy complete lattice, factorized by a complete fuzzy tolerance, is again a fuzzy complete lattice.

Preprint submitted to Fuzzy Sets and Systems

Related Organizations

Palacký University, Olomouc
Czech Republic

Keywords

FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Fuzzy lattices (soft algebras) and related topics, fuzzy tolerance, fuzzy Galois connection, Theory of fuzzy sets, etc., fuzzy order, Logic in Computer Science (cs.LO)

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