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Characterizations Of Monoids By The Properties Of Their Intuitionistic Fuzzy Subacts

Author

Listed:
  • MUHAMMAD SHABIR

    (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan)

  • MUHAMMAD SHOAIB ARIF

    (Department of Mathematics, Air University, Islamabad, Pakistan)

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.

Suggested Citation

  • Muhammad Shabir & Muhammad Shoaib Arif, 2010. "Characterizations Of Monoids By The Properties Of Their Intuitionistic Fuzzy Subacts," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 31-48.
    • Handle: RePEc:wsi:nmncxx:v:06:y:2010:i:01:n:s179300571000158x
    DOI: 10.1142/S179300571000158X
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