scholarly journals Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Topological Spaces ◽  
Relative Significance ◽  
Approximation Operators ◽  
Covering Rough Set

The reductions of covering information systems in terms of covering approximation operators are one of the most important applications of covering rough set theory. Based on the connections between the theory of topology and the covering rough set theory, two kinds of topological reductions of covering information systems are discussed in this paper, which are characterized by the belief and plausibility functions from the evidence theory. The topological spaces by two pairs of covering approximation operators in covering information systems are pseudo-discrete, which deduce partitions. Then, using plausibility function values of the sets in the partitions, the definitions of significance and relative significance of coverings are presented. Hence, topological reduction algorithms based on the evidence theory are proposed in covering information systems, and an example is adopted to illustrate the validity of the algorithms.

Interpretations of belief functions in approximation operators by covering

2021 ◽  
pp. 1-11
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Sufficient Conditions ◽  
Belief Functions ◽  
Belief Structure ◽  
Approximation Operators ◽  
Necessary And Sufficient ◽  
Covering Rough Set

The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented.

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.

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.

Topological structures of a type of granule based covering rough sets

Filomat ◽  
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.

On Characterization of Relation Based Rough Set Algebras

2010 ◽  
pp. 69-91
Author(s):  
Wei-Zhi Wu ◽  
Wen-Xiu Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Axiomatic Approach ◽  
Topological Spaces ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Topological Spaces

Rough set theory is one of the most advanced areas popularizing GrC. The basic notions in rough set theory are the lower and upper approximation operators. A rough set algebra is a set algebra with two additional lower and upper approximation operators. In this chapter, we analyze relation based rough set algebras in both crisp and fuzzy environments. We first review the constructive definitions of generalized crisp rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators. We then present the essential properties of the corresponding lower and upper approximation operators. We also characterize the approximation operators by using the axiomatic approach. Finally, the connection between fuzzy rough set algebras and fuzzy topological spaces is established.

scholarly journals Attribute Reduction Based on Consistent Covering Rough Set and Its Application

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jianchuan Bai ◽  
Kewen Xia ◽  
Yongliang Lin ◽  
Panpan Wu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Relevance Vector Machine ◽  
Support Vector ◽  
Processing Step ◽  
Important Processing ◽  
Continuous Attribute ◽  
Covering Rough Set

As an important processing step for rough set theory, attribute reduction aims at eliminating data redundancy and drawing useful information. Covering rough set, as a generalization of classical rough set theory, has attracted wide attention on both theory and application. By using the covering rough set, the process of continuous attribute discretization can be avoided. Firstly, this paper focuses on consistent covering rough set and reviews some basic concepts in consistent covering rough set theory. Then, we establish the model of attribute reduction and elaborate the steps of attribute reduction based on consistent covering rough set. Finally, we apply the studied method to actual lagging data. It can be proved that our method is feasible and the reduction results are recognized by Least Squares Support Vector Machine (LS-SVM) and Relevance Vector Machine (RVM). Furthermore, the recognition results are consistent with the actual test results of a gas well, which verifies the effectiveness and efficiency of the presented method.

Rough set theory for the interval-valued fuzzy information systems

2008 ◽  
Vol 178 (8) ◽  
pp. 1968-1985 ◽  
Author(s):  
Zengtai Gong ◽  
Bingzhen Sun ◽  
Degang Chen
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Information ◽  
Interval Valued
Sign in / Sign up

Export Citation Format

Share Document