Neighborhood operator systems and approximations

Wu, Wei-Zhi; Zhang, Wenxiu

doi:10.1016/s0020-0255(02)00180-9

Cited by 211 publications

(60 citation statements)

References 13 publications

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“…denote the successor and the predecessor neighborhoods of x induced by the binary relation R. Additional neighborhoods defined by a binary relation have also been studied [12,17]. Different classes of binary relations can be obtained by considering the following properties:…”

Section: Binary Relationsmentioning

confidence: 99%

Semantics of Fuzzy Sets in Rough Set Theory

Yao

2004

Transactions on Rough Sets II

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Abstract. The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper approximation of rough set theory, are investigated. It is demonstrated that both theories share the same qualitative properties. Interpretations of fuzzy sets in rough set theory lead to constraints on membership values. Two types of constraints on membership values are studies, namely, constraints on membership values of related elements and constraints on membership values of related sets. The classical rough set model and generalized rough set models are discussed.

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Section: Binary Relationsmentioning

confidence: 99%

Semantics of Fuzzy Sets in Rough Set Theory

Yao

2004

Transactions on Rough Sets II

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“…Pawlak's rough approximations may be generalized to nonequivalence relations [10,16,37,38,41,43,47,49]. The extensions of Pawlak's rough set model may be used in reasoning and knowledge acquisition in incomplete decision tables [5,8,11,[18][19][20][21][22].…”

Section: Classical Definitions Of Lower and Upper Approximations Sommentioning

confidence: 99%

A Rough Set Approach for the Discovery of Classification Rules in Interval-Valued Information Systems

Leung

Fischer

et al. 2008

SSRN Journal

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A novel rough set approach is proposed in this paper to discover classification rules through a process of knowledge induction which selects optimal decision rules with a minimal set of features necessary and sufficient for classification of real-valued data. A rough set knowledge discovery framework is formulated for the analysis of interval-valued information systems converted from real-valued raw decision tables.The optimal feature selection method for information systems with interval-valued features obtains all classification rules hidden in a system through a knowledge induction process. Numerical examples are employed to substantiate the conceptual arguments.

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“…This technique has led to many practical applications in various areas such as, but not limited to, medicine learning, knowledge discovery, economics, finance, engineering and even arts and culture [18,22,23,27,30,31,32,33,40,41,44]. Combined with other complementary concepts such as fuzzy sets, statistics, and logical data analysis, rough sets have been exploited in hybrid approaches to improve the performance of data analysis tools.…”

Section: Introductionmentioning

confidence: 99%

“…This family is called a neighborhood system of the element, and each member in the family is called a neighborhood of the element. Any subset of the universe can be approximated based on neighborhood systems of all elements in the universe, also see [9,10,33,34]. In [4,24,45] the concept of a cover of a universe was presented to construct the upper and lower approximations of an arbitrary set.…”

Section: Introductionmentioning

confidence: 99%

“…To address this issue, several known generalizations of the rough model have been reported in the literature. For instance, the notions of approximations are extended to general binary relations, covering, neighborhood systems, completely distributive lattices, fuzzy lattices, set-valued functions and Boolean algebra [4,33,32]. Davvaz introduced the concept of a set-valued homomorphism for groups, which is a generalization of ordinary homomorphism.…”

Section: Introductionmentioning

confidence: 99%

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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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Neighborhood operator systems and approximations

Cited by 211 publications

References 13 publications

Semantics of Fuzzy Sets in Rough Set Theory

Semantics of Fuzzy Sets in Rough Set Theory

A Rough Set Approach for the Discovery of Classification Rules in Interval-Valued Information Systems

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

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