On Minimal Fuzzy Ideals of Semigroups | Zendy

Madad Khan | Zendy; Feng Feng | Zendy; Muhammad Nouman Aslam Khan | Zendy

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On Minimal Fuzzy Ideals of Semigroups

Author(s) -

Madad Khan,

Feng Feng,

Muhammad Nouman Aslam Khan

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/475190

Subject(s) - mathematics , semigroup , fuzzy logic , ideal (ethics) , fuzzy subalgebra , kernel (algebra) , discrete mathematics , fuzzy measure theory , fuzzy number , pure mathematics , algebra over a field , fuzzy set , artificial intelligence , computer science , philosophy , epistemology

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 insemigroup is explored. It has been shown that every fuzzy ideal of a semigroupcontains 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. Ithas been shown that the product of minimal fuzzy left ideal and minimal fuzzyright 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 idealand minimal fuzzy right ideal are shown. The fuzzy kernel of a semigroup is basicallythe class sum of all the minimal fuzzy left (right) ideals of a semigroup. Finallythe sufficient condition of fuzzy kernel to be completely simple semigroup has beenproved

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