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Generalized rough \(\Gamma\)-hyperideals in \(\Gamma\)-semihypergroups. (English) Zbl 1442.20042

Summary: B. Davvaz [Inf. Sci. 178, No. 16, 3247–3252 (2008; Zbl 1154.68527)] introduced the concept of set-valued homomorphism and \(T\)-rough sets in a group. In this paper, we consider the set-valued homomorphism \(T\) on \(\Gamma\)-semihypergroup \(H\) to interpret the lower and upper approximations. We study the roughness of \((m,n)\) bi-\(\Gamma\)-hyperideals and \((m,n)\) quasi-\(\Gamma\)-hyperideals in terms of set-valued homomorphisms, which are extended notions of \((m, n)\) bi-\(\Gamma\)-hyperideals and \((m,n)\) quasi-\(\Gamma\)-hyperideals of \(\Gamma\)-semihypergroups.

MSC:

20N20 Hypergroups

Citations:

Zbl 1154.68527
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