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Bipolar fuzzy S-acts |
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PP: 57-67 |
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Author(s) |
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Muhammad Shabir,
Zahid Iqbal,
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Abstract |
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| In this paper, we initiate the study of bipolar 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 bipolar fuzzy ideal, purely maximal bipolar fuzzy ideal and purely prime bipolar
fuzzy ideal of a monoid. It is shown that the set of purely prime bipolar fuzzy ideals of S admits the structure of a topological space.
We also define pure bipolar fuzzy subact of an S-act and call an S-act bipolar fuzzy normal if each of its bipolar fuzzy subact is pure.
Monoids, all of which S-acts are bipolar fuzzy normal are characterized. It is shown among other results that such monoids are right
weakly regular. |
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