Positive fuzzy quasi-orders on semigroups-Reference-Cited by-同舟云学术

Positive fuzzy quasi-orders on semigroups

Published:2023 Issue:5 Volume:37 Page:1341-1365
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Ciric Miroslav¹^ORCID,Ignjatovic Jelena¹,Popovic Zarko²^ORCID,Stamenkovic Aleksandar¹^ORCID

Affiliation:

1. University of Niš, Faculty of Sciences and Mathematics, Department of Computer Science, Niš, Serbia

2. University of Niš, Faculty of Economics, Niš, Serbia

Abstract

In this paper we study certain types of positive fuzzy quasi-orders on semigroups and their links with completely semiprime fuzzy ideals, completely prime fuzzy ideals, and fuzzy filters. We characterize various properties of a positive fuzzy quasi-order Q in terms of the properties of its left and right eigen spaces IQ and CQ, the solution sets of eigen fuzzy set equations corresponding to Q. We also demonstrate certain applications of the obtained results to semilattice decompositions of semigroups. The results of this paper shed new light on the known links between positive (crisp) quasi-orders, completely semiprime ideals, completely prime ideals, and filters of semigroups, and make these links much clearer.

Funder

Ministry of Education, Science and Technological Development of the Republic of Serbia

Publisher

National Library of Serbia

Subject

General Mathematics

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