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On \(k\)-regularities in fuzzy semihyperrings. (English) Zbl 1397.16045

Summary: We introduce the notion of interval-valued (\(i\).\(v\).) fuzzy \(k\)-quasi ideals and \(i\).\(v\). fuzzy \(k\)-bi-ideals of a semihyperring and deduce certain characterizations for \(k\)-regularities in semihyperring by using these \(i\).\(v\). fuzzy \(k\)-hyperideals. Finally, our goal is to establish a relation between different types of \(k\)-hyperideals of a semihyperring and \(i\).\(v\). fuzzy \(k\)-hyperideals of the associated \(i\).\(v\). fuzzy semihyperring and also to find out the relation between \(k\)-regularity, \(k\)-intra-regularity of semihyperring and the associated \(i\).\(v\). fuzzy semihyperring.

MSC:

16Y99 Generalizations
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