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 Topologies on Z n that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1072 ◽  
Author(s):  
Sang-Eon Han ◽  
Saeid Jafari ◽  
Jeong Kang
Keyword(s):  
Applied Sciences ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Discrete Topology ◽  
Separation Axiom ◽  
Different Types

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

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.

The Position of Rough Set in Soft Set

2012 ◽  
Vol 3 (3) ◽  
pp. 33-48
Author(s):  
Tutut Herawan
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Set Theory ◽  
Soft Set ◽  
General Topology ◽  
Discrete Topology ◽  
Special Case

In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper describes that a “general” topology is a special case of soft set. Hence, it is concluded that every rough set can be considered as a soft set.

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.

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 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.

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
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