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On Minimal Fuzzy Ideals of Semigroups

Author

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  • Madad Khan
  • Feng Feng
  • M. Nouman Aslam Khan

Abstract

The present paper contains the sufficient condition of a fuzzy semigroup to be a fuzzy group using fuzzy points. The existence of a fuzzy kernel in semigroup is explored. It has been shown that every fuzzy ideal of a semigroup contains every minimal fuzzy left and every minimal fuzzy right ideal of semigroup. The fuzzy kernel is the class sum of minimal fuzzy left (right) ideals of a semigroup. Every fuzzy left ideal of a fuzzy kernel is also a fuzzy left ideal of a semigroup. It has been shown that the product of minimal fuzzy left ideal and minimal fuzzy right ideal of a semigroup forms a group. The representation of minimal fuzzy left (right) ideals and also the representation of intersection of minimal fuzzy left ideal and minimal fuzzy right ideal are shown. The fuzzy kernel of a semigroup is basically the class sum of all the minimal fuzzy left (right) ideals of a semigroup. Finally the sufficient condition of fuzzy kernel to be completely simple semigroup has been proved.

Suggested Citation

  • Madad Khan & Feng Feng & M. Nouman Aslam Khan, 2013. "On Minimal Fuzzy Ideals of Semigroups," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, January.
    • Handle: RePEc:hin:jjmath:475190
    DOI: 10.1155/2013/475190
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