The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

Kazancı, O.; Yamak, Sultan; Davvaz, Bijan

doi:10.1016/j.ins.2008.01.006

Cited by 48 publications

(20 citation statements)

References 55 publications

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“…Rough modules have been investigated by Davvaz and Mahdavipour [11], also see [14]. In [35], the concepts of set-valued homomorphism and strong set-valued homomorphism of a module were introduced.…”

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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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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“…As one of the three branches of granular computing, rough set theory is first proposed by Pawlak [20,21] for dealing with vagueness and granularity in information systems. In theory, rough sets have been connected with matroids [10,14,18,27,29,30,37,47], lattices [5,8,16,31], hyperstructure theory [35], topology [12,13,44], fuzzy sets [11,32], and so on. Rough set theory is built on equivalence relations or partitions.…”

Section: Introductionmentioning

confidence: 99%

Applications of repeat degree to coverings of neighborhoods

Yao

Zhu

2014

Int. J. Mach. Learn. & Cyber.

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Covering of neighborhoods is an important concept in covering-based rough sets. There are many unsolved issues related to coverings of neighborhoods. The concept of repeat degree is proposed to study under what condition a covering of neighborhoods is a partition. It enables us to deal with many issues related to coverings of neighborhoods when coverings are incomplete. This paper applies repeat degree to solve some fundamental issues in coverings of neighborhoods. First, we investigate under what condition a covering of neighborhoods is equal to the reduct of the covering which induces the covering of neighborhoods. Then we study under what condition two coverings induce the same relation and the same covering of neighborhoods. Finally, we propose an approach to calculate coverings through repeat degree.

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“…Li et al [32] introduced and investigated TL-fuzzy rough ideals in a ring. The characterization of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in a commutative ring was introduced by Kazancı and Davvaz [19], and the lower and upper approximations in a quotient hypermodule with respect to fuzzy sets were studied by Kazancı et al [21].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

Yin

Zhan

Corsini

2010

Neural Comput & Applic

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This paper considers the relationships among L-fuzzy sets, rough sets and n-ary hypergroup theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy n-ary subhypergroups of a commutative n-ary hypergroup is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy n-ary subhypergroup are introduced and studied. Then, a new algebraic structure called (invertible) L-fuzzy rough n-ary subhypergroups is defined, and the (strong) homomorphism of lower and upper L-fuzzy rough approximation operators is studied.Keywords n-ary hypergroups Á (Invertible) L-fuzzy n-ary hypergroups Á Lower (Upper) L-fuzzy rough approximations Á (Strong) homomorphism 1 Introduction

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The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

Cited by 48 publications

References 55 publications

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

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

Applications of repeat degree to coverings of neighborhoods

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

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