Attribute reduction based on evidence theory in incomplete decision systems

Wu, Wei

doi:10.1016/j.ins.2007.10.006

Cited by 178 publications

(53 citation statements)

References 59 publications

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“…• Various types of uncertainty are taken into account (Youn, 2005;Wu, 2008;Wu et al, 2002;Huang et al, 2012b;Zhang et al, 2010b) Science Publications…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

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“…• Various types of uncertainty are taken into account (Youn, 2005;Wu, 2008;Wu et al, 2002;Huang et al, 2012b;Zhang et al, 2010b) Science Publications…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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“…We need a method that can handle the classification with some degree of uncertainty. In this paper, we focus on applying belief functions to representing partial knowledge of incomplete information tables [7], [8]. In what follows, we set up the notations and recall lower and upper approximations in Variable Precision of Generalized Rough Sets (VPGRS) [9]-[12].…”

Section: Introductionmentioning

confidence: 99%

Evidence Theory in Incomplete Information Tables

Syau¹,

Lin²

2015

IJMLC

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(the power set of the universe of discourse) to itself, we show that they are mutually dual, and that both of them are order-preserving. We then introduce the belief and plausibility functions, respectively, over U, based on the -lower and -upper approximations, respectively, in VPGRS model, and we incorporate the concepts of evidence theory and VPGRS model to examine incomplete information tables.Index Terms-Rough sets, belief functions, reflexive relations, variable precision rough set models, lower and upper approximations. I. INTRODUCTIONEvidence theory is a useful tool in knowledge representation which plays an important role in dealing with many aspects of problem solving. This includes handling incomplete information tables [1]. One of the most important concepts an intelligent system needs to understand is the concept of knowledge. It may or may not be perfect. Also, one wants to know what knowledge is needed to achieve particular goals, and how that knowledge can be obtained. So, one of the important problems along this line is to seek an appropriate approach to analyze imperfect knowledge. The problem related to imperfect knowledge or an incomplete information table has been investigated by many researchers in different areas. Our approach is to apply evidence theory which is essentially Dempster-Shafer theory [2]. This theory is a generalization of the Bayesian theory of subjective probability, also known as the theory of belief functions. Some important features of Dempster-Shafer theory are that it has the capability to cope with varying levels of precision regarding the information and allows for direct representation of uncertainty of system responses where an imperfect information can be characterized by a set or an interval. With these features, we consider the concept of variable precision rough set model [3] certain. We need a method that can handle the classification with some degree of uncertainty. In this paper, we focus on applying belief functions to representing partial knowledge of incomplete information tables [7], [8]. In what follows, we set up the notations and recall lower and upper approximations in Variable Precision of Generalized Rough Sets (VPGRS) [9]-[12]. We then define belief functions and incomplete information tables. We establish several relationships on incomplete information tables by analyzing lower and upper approximations in VPGRS models. We also connect evidence theory and VPGRS models. II. PRELIMINARIESLet U be a nonempty finite set, referred as the universe of discourse (in short, the universe). The power set of U, denoted by 2 , is the collection of all subsets of U, including the whole set U and the empty set Ø. That is,The Cartesian product × is the set of all ordered pairs of elements of U. A binary relation on U is a subset of × .For a relation ⊆ × , we often write to represent ( , ) ∈ . In case R is an equivalence relation, we say that objects x and y are equivalent.Let ⊆ × . For each ∈ , the image of x under a relation R is defined as ( ) = { ∈ | }. Notic...

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“…An evaluation measure is used to measure the significance of features. A number of measures have been developed so far, such as dependency 28,41,46 , consistency 6,32 , fuzzy dependency 12 and mutual information 1 . Mutual information was firstly introduced to measure relevance between discrete variables.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Mutual Information Based min-Redundancy and Max-Relevance Heterogeneous Feature Selection

Yu¹,

An²,

Hu³

2011

IJCIS

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Feature selection is an important preprocessing step in pattern classification and machine learning, and mutual information is widely used to measure relevance between features and decision. However, it is difficult to directly calculate relevance between continuous or fuzzy features using mutual information. In this paper we introduce the fuzzy information entropy and fuzzy mutual information for computing relevance between numerical or fuzzy features and decision. The relationship between fuzzy information entropy and differential entropy is also discussed. Moreover, we combine fuzzy mutual information with "min-Redundancy-Max-Relevance", "Max-Dependency" and "min-Redundancy-Max-Dependency" algorithms. The performance and stability of the proposed algorithms are tested on benchmark data sets. Experimental results show the proposed algorithms are effective and stable.

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Attribute reduction based on evidence theory in incomplete decision systems

Cited by 178 publications

References 59 publications

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Evidence Theory in Incomplete Information Tables

Fuzzy Mutual Information Based min-Redundancy and Max-Relevance Heterogeneous Feature Selection

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