A NEW METHOD FOR MEASURING THE UNCERTAINTY IN INCOMPLETE INFORMATION SYSTEMS

2009 ◽  
Vol 17 (06) ◽  
pp. 855-880 ◽  
Author(s):  
YUHUA QIAN ◽  
JIYE LIANG ◽  
FENG WANG
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Information Gain ◽  
Incomplete Information System ◽  
Uncertainty Measurement ◽  
Nature Of Information ◽  
Knowledge Content ◽  
Incomplete Information Systems ◽  
The Relationship

Based on an intuitionistic knowledge content nature of information gain, the concept of combination entropy CE(A) in incomplete information systems is first introduced, and some of its important properties are given. Then, the conditional combination entropy CE(Q | P) and the mutual information CE(P;Q) are defined. Unlike all existing measures for the uncertainty in incomplete information systems, the relationships among these three concepts can be established, which are formally expressed as CE(Q | P) = CE(P ⋃ Q)-CE(P) and CE(P;Q) = CE(P)-CE(P | Q). Furthermore, a variant CE(CA) of the combination entropy with maximal consistent block nature is introduced to measure the uncertainty of an incomplete information system in the view of maximal consistent block technique. Its monotonicity is the same as that of the combination entropy. Finally, the combination granulation CG(A) and its variant CG(CA) with maximal consistent block nature are defined to measure discernibility ability of an incomplete information system, and the relationship between the combination entropy and the combination granulation is established as well. These results will be very helpful for understanding the essence of knowledge content and uncertainty measurement in incomplete information systems. Note that the combination entropy also can be further extended to measure the uncertainty in non-equivalence-based information systems.

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.

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.

COMBINATION ENTROPY AND COMBINATION GRANULATION IN ROUGH SET THEORY

2008 ◽  
Vol 16 (02) ◽  
pp. 179-193 ◽  
Author(s):  
YUHUA QIAN ◽  
JIYE LIANG
Keyword(s):  
Mutual Information ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Information Gain ◽  
Heuristic Function ◽  
Nature Of Information ◽  
Knowledge Content ◽  
Incomplete Information Systems ◽  
The Relationship

Based on the intuitionistic knowledge content nature of information gain, the concepts of combination entropy and combination granulation are introduced in rough set theory. The conditional combination entropy and the mutual information are defined and their several useful properties are derived. Furthermore, the relationship between the combination entropy and the combination granulation is established, which can be expressed as CE(R) + CG(R) = 1. All properties of the above concepts are all special instances of those of the concepts in incomplete information systems. These results have a wide variety of applications, such as measuring knowledge content, measuring the significance of an attribute, constructing decision trees and building a heuristic function in a heuristic reduct algorithm in rough set theory.

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.

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

2021 ◽  
pp. 1-17
Author(s):  
Zhanhong Shi ◽  
Dinghai Zhang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Dominance Relation ◽  
General Description ◽  
Fuzzy Information ◽  
Inclusion Degree ◽  
Attribute Weights ◽  
Incomplete Information Systems ◽  
Interval Valued

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

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.

scholarly journals Approximate Accuracy Approaches to Attribute Reduction for Information Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Deshan Liu ◽  
Dapeng Wang ◽  
Deqin Yan ◽  
Yu Sang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Rough Sets ◽  
Attribute Reduction ◽  
New Approach ◽  
Rough Sets Theory ◽  
Incomplete Information Systems ◽  
Sets Theory ◽  
Novel Algorithm

The key problem for attribute reduction to information systems is how to evaluate the importance of an attribute. The algorithms are challenged by the variety of data forms in information system. Based on rough sets theory we present a new approach to attribute reduction for incomplete information systems and fuzzy valued information systems. In order to evaluate the importance of an attribute effectively, a novel algorithm with rigorous theorem is proposed. Experiments show the effect of proposed algorithm.

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