Rough set theory for the incomplete interval valued fuzzy information systems

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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Rough Sets for Discovering Concurrent System Models from Data Tables

Rough Computing ◽

10.4018/978-1-59904-552-8.ch012 ◽

2011 ◽

pp. 239-268 ◽

Cited By ~ 7

Author(s):

Krzysztof Pancerz ◽

Zbigniew Suraj

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Petri Net ◽

Rough Set Theory ◽

Research Trend ◽

Concurrent System ◽

System Models ◽

Data Tables ◽

New Research

This chapter constitutes the continuation of a new research trend binding rough set theory with concurrency theory. In general, this trend concerns the following problems: discovering concurrent system models from experimental data represented by information systems, dynamic information systems or specialized matrices, a use of rough set methods for extracting knowledge from data, a use of rules for describing system behaviors, and modeling and analyzing of concurrent systems by means of Petri nets on the basis of extracted rules. Some automatized methods of discovering concurrent system models from data tables are presented. Data tables are created on the basis of observations or specifications of process behaviors in the modeled systems. Proposed methods are based on rough set theory and colored Petri net theory.

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Reduction of Neighborhood-Based Generalized Rough Sets

Journal of Applied Mathematics ◽

10.1155/2011/409181 ◽

2011 ◽

Vol 2011 ◽

pp. 1-22 ◽

Cited By ~ 3

Author(s):

Zhaohao Wang ◽

Lan Shu ◽

Xiuyong Ding

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Open Problems ◽

The Third ◽

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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THE ALGORITHM ON KNOWLEDGE REDUCTION IN INCOMPLETE INFORMATION SYSTEMS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s021848850200134x ◽

2002 ◽

Vol 10 (01) ◽

pp. 95-103 ◽

Cited By ~ 119

Author(s):

JIYE LIANG ◽

ZONGBEN XU

Keyword(s):

Information System ◽

Information Systems ◽

Incomplete Information ◽

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Np Hard ◽

Knowledge Reduction ◽

Np Hard Problem ◽

Incomplete Information Systems

Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|2|U|). An illustrative example is provided that shows the application potential of the algorithm.

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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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