Some Remarks on the Concept of Approximations from the View of Knowledge Engineering

The concepts of approximations in granular computing (GrC) vs. rough set theory (RS) are examined. Examples are constructed to contrast their differences in the Global GrC Model (2nd GrC Model), which, in pre-GrC term, is called partial coverings. Mathematically speaking, RS-approximations are “sub-base” based, while GrC-approximations are “base” based, where “sub-base” and “base” are two concepts in topological spaces. From the view of knowledge engineering, its meaning in RS-approximations is rather obscure, while in GrC, it is the concept of knowledge approximations.

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Topological structures of a type of granule based covering rough sets

Filomat ◽

10.2298/fil1809129z ◽

2018 ◽

Vol 32 (9) ◽

pp. 3129-3141

Author(s):

Yan-Lan Zhang ◽

Chang-Qing Li

Keyword(s):

Set Theory ◽

Rough Set ◽

Granular Computing ◽

Rough Set Theory ◽

Equivalence Relations ◽

Topological Spaces ◽

Topological Properties ◽

Binary Relations ◽

Upper Approximation ◽

Approximation Operators

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

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THE INFORMATION ENTROPY, ROUGH ENTROPY AND KNOWLEDGE GRANULATION IN ROUGH SET THEORY

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488504002631 ◽

2004 ◽

Vol 12 (01) ◽

pp. 37-46 ◽

Cited By ~ 220

Author(s):

JIYE LIANG ◽

ZHONGZHI SHI

Keyword(s):

Set Theory ◽

Rough Set ◽

Information Entropy ◽

Granular Computing ◽

Rough Set Theory ◽

Computer Applications ◽

Mathematical Tool

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.

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Rough Set Theory, Granular Computing on Partition

Encyclopedia of Database Systems ◽

10.1007/978-0-387-39940-9_3495 ◽

2009 ◽

pp. 2453-2453

Keyword(s):

Set Theory ◽

Rough Set ◽

Granular Computing ◽

Rough Set Theory

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Multi-Granular Computing through Rough Sets

Advances in Secure Computing, Internet Services, and Applications - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-4666-4940-8.ch001 ◽

2014 ◽

pp. 1-34 ◽

Cited By ~ 1

Author(s):

B. K. Tripathy

Keyword(s):

Set Theory ◽

Rough Set ◽

Equivalence Relation ◽

Rough Sets ◽

Intelligent Systems ◽

Granular Computing ◽

Rough Set Theory ◽

Point Of View ◽

Information Granules ◽

Computing Platform

Granular Computing has emerged as a framework in which information granules are represented and manipulated by intelligent systems. Granular Computing forms a unified conceptual and computing platform. Rough set theory put forth by Pawlak is based upon single equivalence relation taken at a time. Therefore, from a granular computing point of view, it is single granular computing. In 2006, Qiang et al. introduced a multi-granular computing using rough set, which was called optimistic multigranular rough sets after the introduction of another type of multigranular computing using rough sets called pessimistic multigranular rough sets being introduced by them in 2010. Since then, several properties of multigranulations have been studied. In addition, these basic notions on multigranular rough sets have been introduced. Some of these, called the Neighborhood-Based Multigranular Rough Sets (NMGRS) and the Covering-Based Multigranular Rough Sets (CBMGRS), have been added recently. In this chapter, the authors discuss all these topics on multigranular computing and suggest some problems for further study.

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On Quasi Discrete Topological Spaces in Information Systems

International Journal of Artificial Life Research ◽

10.4018/jalr.2012040104 ◽

2012 ◽

Vol 3 (2) ◽

pp. 38-52 ◽

Cited By ~ 1

Author(s):

Tutut Herawan

Keyword(s):

Information System ◽

Information Systems ◽

Topological Space ◽

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Topological Spaces ◽

Discrete Topology

This paper presents an alternative way for constructing a topological space in an information system. Rough set theory for reasoning about data in information systems is used to construct the topology. Using the concept of an indiscernibility relation in rough set theory, it is shown that the topology constructed is a quasi-discrete topology. Furthermore, the dependency of attributes is applied for defining finer topology and further characterizing the roughness property of a set. Meanwhile, the notions of base and sub-base of the topology are applied to find attributes reduction and degree of rough membership, respectively.

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The Incremental Knowledge Acquisition Based on Hash Algorithm

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488516500173 ◽

2016 ◽

Vol 24 (03) ◽

pp. 347-366 ◽

Cited By ~ 3

Author(s):

Qing-Hua Zhang ◽

Long-Yang Yao ◽

Guan-Sheng Zhang ◽

Yu-Ke Xin

Keyword(s):

Knowledge Acquisition ◽

Set Theory ◽

Rough Set ◽

Granular Computing ◽

Rough Set Theory ◽

Attribute Reduction ◽

Algorithm Analysis ◽

Data Sets ◽

Hash Algorithm ◽

Acquisition Method

In this paper, a new incremental knowledge acquisition method is proposed based on rough set theory, decision tree and granular computing. In order to effectively process dynamic data, describing the data by rough set theory, computing equivalence classes and calculating positive region with hash algorithm are analyzed respectively at first. Then, attribute reduction, value reduction and the extraction of rule set by hash algorithm are completed efficiently. Finally, for each new additional data, the incremental knowledge acquisition method is proposed and used to update the original rules. Both algorithm analysis and experiments show that for processing the dynamic information systems, compared with the traditional algorithms and the incremental knowledge acquisition algorithms based on granular computing, the time complexity of the proposed algorithm is lower due to the efficiency of hash algorithm and also this algorithm is more effective when it is used to deal with the huge data sets.

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