A study on soft rough semigroups and corresponding decision making applications

Abstract

Abstract:In this paper, we study a kind of soft rough semigroups according to Shabir's idea. We define the upper and lower approximations of a subset of a semigroup. According to Zhan's idea over hemirings, we also define a kind of new C -soft sets and C C -soft sets over semigroups. In view of this theory, we investigate the soft rough ideals (prime ideals, bi-ideals, interior ideals, quasi-ideals, regular semigroups). Finally, we give two decision making methods: one is for looking a best a parameter which is to the nearest semigroup, the other is to choose a parameter which keeps the maximum regularity of regular semigroups.

A Study on Soft Multi-Granulation Rough Sets and Their Applications

“…But the situation is not straightforward in the case of SRSs proposed by Feng et al [8] and MSRSs of Shabir et al [56]. However, there are certain techniques proposed by Ma et al [45], Pan and Zan [46], [47], Wang et al [48], and Zan et al [49]. These techniques are independent of each other.…”

“…The concept of SRSs have studied by many authors, such as [11], [19], [29], [30], [38], [39], [42]- [45], [48]- [50], [57]. Since BRs play a fundamental role in both pure and applied sciences.…”

“…In almost all kinds of data analysis, DM plays an imperative role in collecting an appropriate substitute among various choices. In order to find a wise decision, several commodious techniques have constructed by innumerable experts and researchers (see [5], [19], [39], [41], [45], [46], [48]- [50]). This section presents an algorithm for DM by using our proposed concept of SMGRSs over groups defined in the previous section.…”

Soft ideals of soft ternary semigroups

“…As we have developed various area of soft ideals of soft ternary semigroup this is a motivational work for future. We may generalize soft rough semigroups of [23] and soft filters of ordered semigroup of [24] in soft ternary semigroup and soft ordered ternary semigroup also.…”