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Generalized(\((\xi,\zeta)\)-) soft interior \(\Gamma\)-hyperideals of \(\Gamma\)-semihypergroups. (English) Zbl 1392.20055

Summary: In this paper, we introduce the notion of (\(\xi,\zeta\))-soft \(\Gamma\)-hyperideals and (\(\xi,\zeta\))-soft interior \(\Gamma\)-hyperideals of \(\Gamma\)-semihypergroups by a new approach called soft intersection (briefly, S. I.). It is proved that in regular \(\Gamma\)-semihypergroups the (\(\xi,\zeta\))-soft \(\Gamma\)-hyperideals and the (\(\xi,\zeta\))-soft interior \(\Gamma\)-hyperideals coincide. Further, we introduce the concept of (\(\xi,\zeta\))-soft simple \(\Gamma\)-semihypergroup and characterize the simple \(\Gamma\)-semihypergroups in terms of (\(\xi,\zeta\))-soft \(\Gamma\)-hyperideals and (\(\xi,\zeta\))-soft interior \(\Gamma\)-hyperideals.

MSC:

20N25 Fuzzy groups
20M99 Semigroups
20N20 Hypergroups
20M12 Ideal theory for semigroups
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