Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

2021 ◽  
pp. 1-13
Author(s):  
Jing Pang ◽  
Bingxue Yao ◽  
Lingqiang Li
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Decision Model ◽  
Incomplete Information System ◽  
Basic Properties ◽  
Model Based ◽  
Incomplete Information Systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.

scholarly journals Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Do Van Nguyen ◽  
Koichi Yamada ◽  
Muneyuki Unehara
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Incomplete Information System ◽  
Tolerance Relation ◽  
The Core ◽  
Mathematical Properties ◽  
Incomplete Information Systems

This paper discusses and proposes a rough set model for an incomplete information system, which defines an extended tolerance relation using frequency of attribute values in such a system. It first discusses some rough set extensions in incomplete information systems. Next, “probability of matching” is defined from data in information systems and then measures the degree of tolerance. Consequently, a rough set model is developed using a tolerance relation defined with a threshold. The paper discusses the mathematical properties of the newly developed rough set model and also introduces a method to derive reducts and the core.

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 Fuzzy Set-Valued Information Systems and the Algorithm of Filling Missing Values for Incomplete Information Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Zhaohao Wang ◽  
Xiaoping Zhang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Fuzzy Set ◽  
Missing Values ◽  
Rough Set Theory ◽  
Similarity Measures ◽  
New Information ◽  
Incomplete Information Systems

How to effectively deal with missing values in incomplete information systems (IISs) according to the research target is still a key issue for investigating IISs. If the missing values in IISs are not handled properly, they will destroy the internal connection of data and reduce the efficiency of data usage. In this paper, in order to establish effective methods for filling missing values, we propose a new information system, namely, a fuzzy set-valued information system (FSvIS). By means of the similarity measures of fuzzy sets, we obtain several binary relations in FSvISs, and we investigate the relationship among them. This is a foundation for the researches on FSvISs in terms of rough set approach. Then, we provide an algorithm to fill the missing values in IISs with fuzzy set values. In fact, this algorithm can transform an IIS into an FSvIS. Furthermore, we also construct an algorithm to fill the missing values in IISs with set values (or real values). The effectiveness of these algorithms is analyzed. The results showed that the proposed algorithms achieve higher correct rate than traditional algorithms, and they have good stability. Finally, we discuss the importance of these algorithms for investigating IISs from the viewpoint of rough set theory.

UNCERTAINTY MEASURE OF ROUGH SETS BASED ON A KNOWLEDGE GRANULATION FOR INCOMPLETE INFORMATION SYSTEMS

2008 ◽  
Vol 16 (02) ◽  
pp. 233-244 ◽  
Author(s):  
JUNHONG WANG ◽  
JIYE LIANG ◽  
YUHUA QIAN ◽  
CHUANGYIN DANG
Keyword(s):  
Information Systems ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Computer Applications ◽  
Mathematical Tool ◽  
Uncertainty Measure ◽  
Definition Of ◽  
Incomplete Information Systems

Rough set theory is a relatively new mathematical tool for computer applications in circumstances characterized by vagueness and uncertainty. In this paper, we address uncertainty of rough sets for incomplete information systems. An axiom definition of knowledge granulation for incomplete information systems is obtained, under which a measure of uncertainty of a rough set is proposed. This measure has some nice properties such as equivalence, maximum and minimum. Furthermore, we prove that the uncertainty measure is effective and suitable for measuring roughness and accuracy of rough sets for incomplete information systems.

NEIGHBORHOOD SYSTEM BASED ROUGH SET: MODELS AND ATTRIBUTE REDUCTIONS

2012 ◽  
Vol 20 (03) ◽  
pp. 399-419 ◽  
Author(s):  
XIBEI YANG ◽  
ZEHUA CHEN ◽  
HUILI DOU ◽  
MING ZHANG ◽  
JINGYU YANG
Keyword(s):  
Information System ◽  
Incomplete Information ◽  
Rough Set ◽  
Rough Sets ◽  
Attribute Reduction ◽  
Incomplete Information System ◽  
Numerical Examples ◽  
Neighborhood System ◽  
Support Sets

The neighborhood system based rough set is a generalization of Pawlak's rough set model since the former uses the neighborhood system instead of the partition for constructing target approximation. In this paper, the neighborhood system based rough set approach is employed to deal with the incomplete information system. By the coverings induced by the maximal consistent blocks and the support sets of the descriptors, respectively, two neighborhood systems based rough sets are explored. By comparing with the original maximal consistent block and descriptor based rough sets, the neighborhood system based rough sets hold the same lower approximations and the smaller upper approximations. Furthermore, the concept of attribute reduction is introduced into the neighborhood systems and the corresponding rough sets. The judgement theorems and discernibility functions to compute reducts are also presented. Some numerical examples are employed to substantiate the conceptual arguments.

scholarly journals INCREMENTALLY UPDATING APPROXIMATION IN INCOMPLETE INFORMATION SYSTEMS UNDER THE VARIATION OF OBJECTS

2020 ◽  
Vol 36 (4) ◽  
pp. 365-379
Author(s):  
Tran Thi Thanh Huyen ◽  
Le Ba Dung ◽  
Nguyen Do Van ◽  
Mai Van Dinh
Keyword(s):  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Rough Sets ◽  
Membership Functions ◽  
Approximation Space ◽  
The Third ◽  
Incomplete Information Systems ◽  
The Relationship ◽  
Over Time

Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we introduce a new method to update the approximation sets with rough membership functions in covering approximation space. Firstly, we present the third types of rough membership functions and study their properties. And then, we consider the change of them while simultaneously adding and removing objects in the information system. Based on that change, we propose a method for updating the approximation sets when the objects vary over time.

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