Reduction of Neighborhood-Based Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

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Model of Covering Rough Sets in the Machine Intelligence

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.548.735 ◽

2012 ◽

Vol 548 ◽

pp. 735-739

Author(s):

Hong Mei Nie ◽

Jia Qing Zhou

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Equivalence Relation ◽

Rough Sets ◽

Rough Set Theory ◽

Machine Intelligence ◽

Upper Approximation ◽

Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

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Uncertainty Measurement for Covering Rough Sets

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s021848851450010x ◽

2014 ◽

Vol 22 (02) ◽

pp. 217-233 ◽

Cited By ~ 9

Author(s):

Jianhua Dai ◽

Debiao Huang ◽

Huashi Su ◽

Haowei Tian ◽

Tian Yang

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Accuracy Measure ◽

Uncertainty Measurement ◽

Covering Rough Set ◽

Measure Entropy ◽

Theoretical Results ◽

Generalized Rough Sets

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

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Stone Algebras: 3-valued Logic and Rough Sets

10.21203/rs.3.rs-576563/v1 ◽

2021 ◽

Author(s):

Arun Kumar ◽

Shilpi Kumari

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

The Third ◽

Soundness And Completeness

Abstract In this article, we propose 3-valued semantics of the logics compatible with Stone and dual Stone algebras. We show that these logics can be considered as 3-valued by establishing soundness and completeness results. We also show that rough set theory can be modelled by these logics where the third value can be interpreted as not certain but possible.

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Some Topological Approaches for Generalized Rough Sets via Ideals

Mathematical Problems in Engineering ◽

10.1155/2021/5642982 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Tareq M. Al-shami ◽

Hüseyin Işık ◽

Ashraf S. Nawar ◽

Rodyna A. Hosny

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Binary Relations ◽

Topological Structures ◽

Geometric Idea ◽

Generalized Rough Sets ◽

Better Than

The idea of neighborhood systems is induced from the geometric idea of “near,” and it is primitive in the topological structures. Now, the idea of neighborhood systems has been extensively applied in rough set theory. The master contribution of this manuscript is to generate various topologies by means of the concepts of j -adhesion neighborhoods and ideals. Then, we define a new rough set model derived from these topologies and discussed main features. We show that these topologies are finer than those given in the previous ones under arbitrary binary relations. In addition, we elucidate that these topologies are finer than those topologies initiated based on different neighborhoods and ideals under reflexive relations. Several examples are provided to validate that our model is better than the previous ones.

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Foundations of Rough Sets from Vagueness Perspective

Rough Computing ◽

10.4018/978-1-59904-552-8.ch001 ◽

2011 ◽

pp. 1-37 ◽

Cited By ~ 9

Author(s):

Piotr Wasilewski ◽

Dominik Slezak

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Algebraic Structures ◽

Approximation Spaces ◽

Types Of Knowledge

We present three types of knowledge, which can be specified according to the Rough Set theory. Then, we present three corresponding types of algebraic structures appearing in the Rough Set theory. This leads to three following types of vagueness: crispness, classical vagueness, and a new concept of “intermediate” vagueness. We also propose two classifications of information systems and approximation spaces. Based on them, we differentiate between information and knowledge.

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KNOWLEDGE REPRESENTING FEATURES IN ROUGH SETS THEORY

Environment Technology Resources Proceedings of the International Scientific and Practical Conference ◽

10.17770/etr2009vol2.1045 ◽

2015 ◽

Vol 2 ◽

pp. 169

Author(s):

Oļegs Užga-Rebrovs

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Mathematical Formalism ◽

Rough Sets Theory ◽

Sets Theory

Knowledge discovering and representing in information systems has evolved into an important area of research because of theoretical challenges and practical representing unknown knowledge in data. Rough set theory is a mathematical formalism for representing uncertainty that can be considered a special extension of the set theory. In this paper is analyzed knowledge representing problem and attribute signification’s problem, based on rough sets approach.

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Interval Granules in Incomplete Information Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.418-420.1915 ◽

2011 ◽

Vol 418-420 ◽

pp. 1915-1918

Author(s):

Xiao Hui Chen ◽

Ren Pu Li ◽

Zhi Wang Zhang

Keyword(s):

Information Systems ◽

Incomplete Information ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Mathematical Theory ◽

Rough Set Theory ◽

Incomplete Information Systems ◽

Structure Of Knowledge ◽

Knowledge Granularity

Rough set theory is an efficient mathematical theory for data reduction and knowledge discovery of various fields. However, classical rough set theory is not applicable for knowledge induction of incomplete information systems. In this paper, a concept of interval granule is presented. Based on this concept, the hierachical structure of knowledge granularity and approximation of rough sets in incomplete information systems are studied, and related properties are given. An example show that the interval granule have better results than existing models for knowledge induction and approximation.

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Analysing diabetes using rough sets

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.2.1 ◽

2020 ◽

pp. 533-538

Author(s):

S. Arjun Raj ◽

M. Vigneshwaran

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

International Diabetes Federation ◽

Published Data ◽

Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

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