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\((\alpha ,\beta )\)-intuitionistic fuzzy ideals of hemirings. (English) Zbl 1232.08004

Summary: We introduce the concept of \((\alpha ,\beta )\)-intuitionistic fuzzy sub-hemiring, (left, right, two sided) ideals of hemirings, where \(\alpha ,\beta \) are any two of \(\{\in ,q,\in \vee q,\in \wedge q\}\) with \(\alpha\neq\in\wedge q\), by using belongs to relation \((\in )\) and quasi-coincidence with relation \((q)\) between intuitionistic fuzzy points and intuitionistic fuzzy sets, and investigate related properties. Moreover, we define prime (semiprime) \((\alpha ,\beta )\)-intuitionistic fuzzy ideals of hemirings and investigate some different properties of these ideals.

MSC:

08A72 Fuzzy algebraic structures
16Y99 Generalizations
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