Fuzzy filters in pseudo hoops

The aim of this paper is to introduce the notions of fuzzy filters, fuzzy (positive) implicative filters and fuzzy fantastic filters in pseudo hoops and investigate some of their properties. Some characterizations of fuzzy filters and fuzzy implicative filters are derived. The relation among these f...

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Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 32; no. 3; pp. 1997 - 2007
Main Authors Alavi, S.Z., Borzooei, R.A., Aaly Kologani, M.
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2017
Subjects
Boolean algebra
Hoops
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Summary:The aim of this paper is to introduce the notions of fuzzy filters, fuzzy (positive) implicative filters and fuzzy fantastic filters in pseudo hoops and investigate some of their properties. Some characterizations of fuzzy filters and fuzzy implicative filters are derived. The relation among these fuzzy filters are investigated and it is proved that any fuzzy fantastic and fuzzy positive implicative filter is a fuzzy implicative filter. Finally, we define a congruence relation by fuzzy filters on pseudo hoops and prove that if μ is a fuzzy normal implicative filter or fuzzy positive implicative filter, then A/μ is a Boolean algebra.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-161586