CHARACTERIZATIONS OF MONOIDS BY THE PROPERTIES OF THEIR INTUITIONISTIC FUZZY SUBACTS

Muhammad Shabir () and Muhammad Shoaib Arif ()
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Muhammad Shabir: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Muhammad Shoaib Arif: Department of Mathematics, Air University, Islamabad, Pakistan

New Mathematics and Natural Computation (NMNC), 2010, vol. 06, issue 01, 31-48

Abstract: In this paper, we initiate the study of intuitionistic fuzzy subacts of anS-act, whereSis a monoid with zero andS-acts are representations ofS. We introduce the notions of pure intuitionistic fuzzy, purely intuitionistic maximal and purely intuitionistic fuzzy prime ideals of a monoid. It is shown that the set of purely intuitionistic fuzzy prime ideals ofSadmits the structure of a topological space, called the pure intuitionistic fuzzy spectrum ofS. We also define a pure intuitionistic fuzzy subact of anS-act and call anS-act intuitionistic fuzzy normal if each of its intuitionistic fuzzy subact is pure. Monoids, of which allS-acts are intuitionistic fuzzy normal, are characterized. It is shown among other results that such monoids are right weakly regular.

Keywords: S-acts; Intuitionistic fuzzy subacts; pure intuitionistic fuzzy ideals; purely intuitionistic fuzzy maximal and purely intuitionistic fuzzy prime ideals; pure intuitionistic fuzzy spectrum; intuitionistic fuzzy normalS-acts; regular and weakly regular semigroups (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S179300571000158X

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