scholarly journals Lower Approximation Reduction Based on Discernibility Information Tree in Inconsistent Ordered Decision Information Systems

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 696 ◽  
Author(s):  
Jia Zhang ◽  
Xiaoyan Zhang ◽  
Weihua Xu
Keyword(s):  
Information System ◽  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Common Method ◽  
New Method ◽  
Lower Approximation ◽  
Dominance Relations

Attribute reduction is an important topic in the research of rough set theory, and it has been widely used in many aspects. Reduction based on an identifiable matrix is a common method, but a lot of space is occupied by repetitive and redundant identifiable attribute sets. Therefore, a new method for attribute reduction is proposed, which compresses and stores the identifiable attribute set by a discernibility information tree. In this paper, the discernibility information tree based on a lower approximation identifiable matrix is constructed in an inconsistent decision information system under dominance relations. Then, combining the lower approximation function with the discernibility information tree, a complete algorithm of lower approximation reduction based on the discernibility information tree is established. Finally, the rationality and correctness of this method are verified by an example.

On Quasi Discrete Topological Spaces in Information Systems

2012 ◽  
Vol 3 (2) ◽  
pp. 38-52 ◽  
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.

THE ALGORITHM ON KNOWLEDGE REDUCTION IN INCOMPLETE INFORMATION SYSTEMS

2002 ◽  
Vol 10 (01) ◽  
pp. 95-103 ◽  
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.

scholarly journals Multigranulations Rough Set Method of Attribute Reduction in Information Systems Based on Evidence Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Minlun Yan
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Decision Rules ◽  
Evidence Theory ◽  
Point Of View ◽  
Upper Approximation

Attribute reduction is one of the most important problems in rough set theory. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. It is necessary to study the issue of attribute reduction based on multigranulations rough set. To acquire brief decision rules from information systems, this paper firstly investigates attribute reductions by combining the multigranulations rough set together with evidence theory. Concepts of belief and plausibility consistent set are proposed, and some important properties are addressed by the view of the optimistic and pessimistic multigranulations rough set. What is more, the multigranulations method of the belief and plausibility reductions is constructed in the paper. It is proved that a set is an optimistic (pessimistic) belief reduction if and only if it is an optimistic (pessimistic) lower approximation reduction, and a set is an optimistic (pessimistic) plausibility reduction if and only if it is an optimistic (pessimistic) upper approximation reduction.

On Correctness of Decision Algorithms in Information Systems

1988 ◽  
Vol 11 (3) ◽  
pp. 219-239
Author(s):  
Anita Wasilewska
Keyword(s):  
Information System ◽  
Information Systems ◽  
Decision Rule ◽  
Direct Product ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Decision Algorithm ◽  
Decision Algorithms

The concept of an information system, with manipulation based on the rough set theory, was introduced by Pawlak in 1982. The information system is defined by its set of objects, set of attributes, set of values of attributes, and a function, which maps the direct product of the first two sets onto the set of values of attributes. We introduce here, after [Pawlak 1985(1)], concepts of the decision rule, decision algorithm, static learning and describe the automatic procedures of deciding whether a given decision rule or decision algorithm is correct.

scholarly journals Parametric Matroid of Rough Set

2015 ◽  
Vol 23 (06) ◽  
pp. 893-908 ◽  
Author(s):  
Yanfang Liu ◽  
Hong Zhao ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Independent Set ◽  
Approximation Operator ◽  
Approximation Number ◽  
Lower Approximation ◽  
The One

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

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