Geodesic
Positive fuzzy quasi-orders on semigroups
Filomat, Tome 37 (2023) no. 5, p. 1341

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DOI

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 I Q and C Q , 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.
DOI : 10.2298/FIL2305341C
Classification : 20M10, 20M12, 03F72, 06F05, 06F07, 06A15
Keywords: Positive fuzzy quasi-order, cm-property, cp-property, lower-potency, completely semiprime fuzzy ideal, completely prime fuzzy ideal, fuzzy filter, semilattice decomposition 
Miroslav Ćirić; Jelena Ignjatović; Zarko Popović; Aleksandar Stamenković. Positive fuzzy quasi-orders on semigroups. Filomat, Tome 37 (2023) no. 5, p. 1341 . doi: 10.2298/FIL2305341C
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     title = {Positive fuzzy quasi-orders on semigroups},
     journal = {Filomat},
     pages = {1341 },
     year = {2023},
     volume = {37},
     number = {5},
     doi = {10.2298/FIL2305341C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305341C/}
}
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