The lower and upper approximations in a fuzzy group

Kuroki, Nobutaka; Wang, Paul P.

doi:10.1016/0020-0255(95)00282-0

Cited by 112 publications

(86 citation statements)

References 2 publications

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“…Miao et al [14] improve definitions of rough group and rough subgroup, and prove their new properties. On the other hand, Kuroki and Wang [11] presented some properties of the lower and upper approximations with respect to the normal subgroups in 1996. 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].…”

Section: Introductionmentioning

confidence: 99%

Near Ideals in Near Semigroups

Bağırmaz

2018

Eur. J. Pure Appl. Math.

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Section: Introductionmentioning

confidence: 99%

Near Ideals in Near Semigroups

Bağırmaz

2018

Eur. J. Pure Appl. Math.

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“…Yaqoob et al [1,2,17] presented some results on roughness in LA-semigroups, roughness in semigroups and roughness in Γ-AG-groupoids. Kuroki and Wang [8] gave some properties of the lower and upper approximations with respect to the normal subgroups. Also, Kuroki and Mordeson in [9] studied the structure of rough sets and rough groups.…”

Section: Introductionmentioning

confidence: 99%

Rough Approximations in Left Almost Groups

Yaqoob

2012

Int. J. of Algeb. and Stat.

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“…Kuroki [16] introduced the notion of a rough ideal in a semigroup. Kuroki and Wang [17] gave some properties of the lower and upper approximations with respect to normal subgroups. Mordeson [24] used covers of the universal set to define approximations operators on the power set of given set.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

Mirvakili

Anvariyeh

Davvaz

2017

Foundations of Computing and Decision Sciences

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Abstract. The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.

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The lower and upper approximations in a fuzzy group

Cited by 112 publications

References 2 publications

Near Ideals in Near Semigroups

Near Ideals in Near Semigroups

Rough Approximations in Left Almost Groups

Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

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