“…Kuroki and Mordeson [28] discussed the structure of rough sets and rough groups. At that point in [29], Kuroki presented the thought of rough ideals in semigroup. Rough prime ideals and rough fuzzy prime ideals in semigroups were proposed by Xiao and Zhang [17].…”
The paper examines the generalized rough fuzzy ideals of quantales. There are some intrinsic relations between fuzzy prime (primary) ideals of quantales and generalized rough fuzzy prime (primary) ideals of quantales. Homomorphic images of "generalized rough ideals, generalized rough prime (primary) ideals, and generalized rough fuzzy prime (primary) ideals" which are incited by quantale homomorphism are examined.
“…Kuroki and Mordeson [28] discussed the structure of rough sets and rough groups. At that point in [29], Kuroki presented the thought of rough ideals in semigroup. Rough prime ideals and rough fuzzy prime ideals in semigroups were proposed by Xiao and Zhang [17].…”
The paper examines the generalized rough fuzzy ideals of quantales. There are some intrinsic relations between fuzzy prime (primary) ideals of quantales and generalized rough fuzzy prime (primary) ideals of quantales. Homomorphic images of "generalized rough ideals, generalized rough prime (primary) ideals, and generalized rough fuzzy prime (primary) ideals" which are incited by quantale homomorphism are examined.
“…In addition, some properties of the lower and the upper approximations with respect to the normal subgroups were studied in [5,13,[26][27][28]. Also, Kuroki [12], introduced the notion of a rough ideal in a semigroup. Davvaz [6], introduced the notion of rough subring with respect to an ideal of a ring.…”
Abstract. In this paper, we introduced the notion of near subsemigroups, near ideals, near biideals and homomorphisms of near semigroups on near approximation spaces. Then we give some properties of these near structures.
“…With the development of rough sets, some models of generalized rough sets were investigated, just as in [5,6]. Later, rough sets were also established over algebraic structures, such as in [7][8][9][10].…”
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.
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