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Characterizations Of Monoids By The Properties Of Their Intuitionistic Fuzzy Subacts

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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)

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    Abstract

    In this paper, we initiate the study of intuitionistic fuzzy subacts of an S-act, where S is a monoid with zero and S-acts are representations of S. 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 of S admits the structure of a topological space, called the pure intuitionistic fuzzy spectrum of S. We also define a pure intuitionistic fuzzy subact of an S-act and call an S-act intuitionistic fuzzy normal if each of its intuitionistic fuzzy subact is pure. Monoids, of which all S-acts are intuitionistic fuzzy normal, are characterized. It is shown among other results that such monoids are right weakly regular.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 06 (2010)
    Issue (Month): 01 ()
    Pages: 31-48

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    Handle: RePEc:wsi:nmncxx:v:06:y:2010:i:01:p:31-48

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    Related research

    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 normal S-acts; regular and weakly regular semigroups;

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