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.

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.

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 A COMPARISON BETWEEN MRA AND ROUGH SET THEORY FOR MASS APPRAISAL. A CASE IN BARI

2004 ◽  
Vol 8 (4) ◽  
pp. 205-217 ◽  
Author(s):  
Maurizio D'amato
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Property Market ◽  
Specific Group ◽  
Market Data ◽  
Property Valuation ◽  
A Value ◽  
Valuation Methodology ◽  
The Relationship

Rough Set Theory is a property valuation methodology recently applied to property market data (d'Amato, 2002). This methodology may be applied in property market where few market data are available or where econometric analysis may be difficult or unreliable. This methodology was introduced by a polish mathematician (Pawlak, 1982). The model permit to estimate a property without defining an econometric model, although do not give any estimation of marginal or hedonic prices. I : ,he first version of RST was necessary to organize the data in classes before the valuation .The relationship between these classes defined if‐then rules. If a property belongs to a specific group then it will belong to a class of value. The relationship between the property and the class of value is dichotomous. In this paper will be offered a second version that improve the RST with a “value tolerance relation” in order to make more flexible the rule. In this case the results will come out from an explicit and specific relationship. The methodology has been tested on 69 transactions in the zone of Carrassi-Poggiofranco in the residential property market of Bari.

Granular Computing Based Data Mining in the Views of Rough Set and Fuzzy Set

2010 ◽  
pp. 148-178 ◽  
Author(s):  
Guoyin Wang ◽  
Jun Hu ◽  
Qinghua Zhang ◽  
Xianquan Liu ◽  
Jiaqing Zhou
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Rule Sets ◽  
Incomplete Information Systems

Granular computing (GrC) is a label of theories, methodologies, techniques, and tools that make use of granules in the process of problem solving. The philosophy of granular computing has appeared in many fields, and it is likely playing a more and more important role in data mining. Rough set theory and fuzzy set theory, as two very important paradigms of granular computing, are often used to process vague information in data mining. In this chapter, based on the opinion of data is also a format for knowledge representation, a new understanding for data mining, domain-oriented data-driven data mining (3DM), is introduced at first. Its key idea is that data mining is a process of knowledge transformation. Then, the relationship of 3DM and GrC, especially from the view of rough set and fuzzy set, is discussed. Finally, some examples are used to illustrate how to solve real problems in data mining using granular computing. Combining rough set theory and fuzzy set theory, a flexible way for processing incomplete information systems is introduced firstly. Then, the uncertainty measure of covering based rough set is studied by converting a covering into a partition using an equivalence domain relation. Thirdly, a high efficient attribute reduction algorithm is developed by translating set operation of granules into logical operation of bit strings with bitmap technology. Finally, two rule generation algorithms are introduced, and experiment results show that the rule sets generated by these two algorithms are simpler than other similar algorithms.

Comparative Analysis of Hybrid Soft Set Methods

2014 ◽  
pp. 360-383
Author(s):  
Debadutta Mohanty
Keyword(s):  
Information System ◽  
Comparative Analysis ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Rough Set ◽  
Definition Of ◽  
The Relationship

The whole mathematical scenario has changed with the advent of the Rough Set Theory, a powerful tool to deal with uncertainty and incompleteness of knowledge in information system. With the advancement of research, the Soft Set Theory has emerged as an advanced mathematical tool to deal with data associated with uncertainty. The present chapter endeavors to forge a connection between soft set and rough set and maps a new model rough soft set to address the challenges of vagueness and impreciseness. Although the research contribution of M. Irfan Ali, Dan Meng, et al. and Feng Feng et al. had given distinct definition of rough soft set and soft rough set, the analysis explaining the genesis of these sets is not appropriate. This chapter is a new attempt to construct the relationship between a rough set, soft set, and fuzzy set to form a hybrid soft set giving a concrete comprehensive definition of rough soft set in border perspective.

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