Fuzzy sub-hoops based on fuzzy points

Using the belongs to relation (e) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (e, e)-fuzzy sub-hoop, an (e, ev q)-fuzzy sub-hoop and a (q, ev q) -fuzzy sub-hoop are introduced, and several properties are investigated. Characterizations of an (e, e)-f...

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Published inMathematical notes (Miskolci Egyetem (Hungary)) Vol. 22; no. 1; pp. 91 - 106
Main Authors Borzooei, R. A., Takallo, M. Mohseni, Kologani, M. Aaly, Jun, Y. B.
Format Journal Article
LanguageEnglish
Published Miskolc University of Miskolc 2021
Subjects
Fuzzy sets
Hoops
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Summary:Using the belongs to relation (e) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (e, e)-fuzzy sub-hoop, an (e, ev q)-fuzzy sub-hoop and a (q, ev q) -fuzzy sub-hoop are introduced, and several properties are investigated. Characterizations of an (e, e)-fuzzy sub-hoop and an (e, ev q)-fuzzy sub-hoop are displayed. Relations between an (e, e)-fuzzy sub-hoop, an (e, ev q)-fuzzy sub-hoop and a (q, ev q)-fuzzy sub-hoop are discussed. Conditions for a fuzzy set to be a (q, e vq)-fuzzy sub-hoop are considered, and condition for an (e, ev q)-fuzzy sub-hoop to be a (q, ev q)-fuzzy sub-hoop are provided.
ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2021.2849