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 1

 Deng entropy
 [期刊] , 2016, 91(): 549553 EI SCIE SCOPUS
 被引用 68 (Web of Science℠)

摘要DempsterShafer evidence theory has been widely used in many applications due to its advantages to handle uncertainty. However, how to measure uncertainty in evidence theory is still an open issue. The main contribution of this paper is that a new entropy, named as Deng entropy, is presented to measure the uncertainty of a basic probability assignment (BPA). Deng entropy is the generalization of Shannon entropy since the value of Deng entropy is identical to that of Shannon entropy when the BPA defines a probability measure. Numerical examples are illustrated to show the efficiency of Deng entropy. (C) 2016 Elsevier Ltd. All rights reserved.关键词DempsterShafer evidence theory , Uncertainty measure , Entropy , Shannon entropy , Deng entropy
 2

 Methods to determine generalized basic probability assignment in generalized evidence theory

[期刊]
,
2011, 45(2): 3438
EI
SCOPUS
CSCD
PKU

摘要Determination of the basic probability assignment (BPA) is the first step to use evidence theory. How to determine BPA is still an open issue. Two methods, namely strong constrain method and weak constrain method, are proposed to deal with open world and close world respectively. In the framework of the proposed generalized evidence theory, a strong constrain method for determination of generalized basic probability assignment (GBPA) is developed. Compared with the existing methods, the new method can generate GBPA without the constrain that the empty set should be set zero. In addition, the value of the empty illustrates the possibility degree that the frame of discernment is not complete. A weak constrain method is also presented to generate BPA in the close world. The weak constrain can determine the BPA even the sample does not cross with the representation model. Some numerical examples are used to illustrate the efficiency of the proposed methods.
 3

 A New Aggregating Operator for Linguistic Information Based on D Numbers
 [期刊] , 2016, 24(6): 831846 EI SCIE SCOPUS
 被引用 44 (Web of Science℠)

摘要How to efficiently make decision under uncertain is a hot research topic. In this paper, a new aggregating operator for linguistic decision making based on D numbers is proposed. D numbers is a new mathematic tool to model uncertainty, since it ignores the condition that elements on the frame must be mutually exclusive. Compared with these existing aggregating operators, the new method is clear, concise and less computational complexity. A numerical example is used to demonstrate the effectiveness of the proposed method.关键词Aggregating operator , linguistic information , belief function , DempsterShafer evidence theory , decision making , D numbers
 4

 A method to determine basic probability assignment in the open world and its application in data fusion and classification
 [期刊] , 2017, 46(4): 934951 EI SCOPUS SCIE
 被引用 6 (Web of Science℠)

摘要Under the circumstance of the complete frame of discernment, There are quantities sufficient researches applying the DempsterShafer evidence theory (DS theory) to process uncertain information. However, in most real cases, the frame of discernment is not complete, and the classic evidence theory is not applicable in some degree, including the basic probability assignment (BPA) generation method. In this paper, under the assumption of the open world, the BPA determination issue is focused originally, and a new method based on triangular fuzzy member is proposed to determine BPA. First, the mean value, standard deviation, extreme values as well as the triangular membership function of each attribute can be determined. Then, a nested structure BPA function with an assignment for the null set can be constructed, using the intersection point of one test sample and the models above. Experiments are conducted with the proposed method to determine BPA, through which the classification accuracy rates are computed, analyzed and compared with those generated by other BPA determination methods, which demonstrates the efficiency of the proposed method both in the open world and in the closed world. © 2016 Springer Science+Business Media New York关键词Data fusion , Fuzzy sets , Information fusion , Probability , Basic probability assignment , Classification accuracy , Dempster Shafer evidence theory , Determination methods , Evidence theories , Triangular fuzzy numbers , Triangular membership functions , Uncertain informations
 5

 A new evidential methodology of identifying influential nodes in complex networks
 [期刊] , 2017, 103(): 101110 EI SCOPUS SSCI SCIE
 被引用 3 (Web of Science℠)

摘要© 2017 Elsevier Ltd In the field of complex networks, how to identify influential nodes in complex networks is still an open research topic. In the existing evidential centrality (EVC), the global structure information in complex networks is not taken into consideration. In addition, EVC also has the limitation that only can be applied on weighted networks. In this paper, a New Evidential Centrality (NEC) is proposed by modifying the Basic Probability Assignment (BPA) strength generated by EVC. According to the shortest paths between the nodes in the network rather than just considering local information, some other BPAs are constructed. With a modified combination rule of Dempster–Shafer evidence theory, the new centrality measure is determined. Numerical examples are used to illustrate the efficiency of the proposed method.关键词Complex networks  Dempster–Shafer evidence theory  Evidential centrality  Influential nodes
 6

 A new method to identify influential nodes based on relative entropy
 [期刊] , 2017, 104(): 257267 EI SCOPUS SSCI SCIE
 被引用 5 (Web of Science℠)

摘要© 2017 Elsevier Ltd How to identify influential nodes is still an open and vital issue in complex networks. To address this problem, a lot of centrality measures have been developed, however, only single measure is focused on by the existing studies, which has its own shortcomings. In this paper, a novel method is proposed to identify influential nodes using relative entropy and TOPSIS method, which combines the advantages of existing centrality measures. Because information flow spreads in different ways in different networks. In the specific network, the appropriate centrality measures should be considered to sort the nodes. In addition, the remoteness between the alternative and the positive/negetive ideal solution is redefined based on relative entropy, which is proven to be more effective in TOPSIS method. To demonstrate the effectiveness of the proposed method, four real networks are selected to conduct several experiments for identifying influential nodes, and the advantages of the method can be illustrated based on the experimental results.关键词Centrality measure  Complex networks  Influential nodes  Relative entropy  TOPSIS
 7

 Evidential Supplier Selection Based on DEMATEL and Game Theory
 [期刊] , 2018, 20(4): 13211333 SCOPUS CPCIS SCIE
 被引用 33 (Web of Science℠)

摘要© 2017, Taiwan Fuzzy Systems Association and SpringerVerlag GmbH Germany. The supplier selection plays an important role in supplier chain management. How to evaluate the performance of suppliers is still an open issue. Multicriteria decisionmaking (MCDM), due to its ability of solving multisource information problem, has become a quite effective tool. Currently, the analytic network process (ANP) and Entropy weight are employed to solved MCDM problems. However, these techniques ignore the onesidedness of the single weighting method and cannot deal with the uncertainties of input data. In this paper, a new evidential ANP methodology based on game theory is proposed to efficiently address supplier management under uncertain environment. First, ANP and entropy weight are employed to obtain the subjective and objective weights of criteria. Second, based on decisionmaking trial and evaluation laboratory (DEMATEL) and game theory, the comprehensive weight of ANP and entropy weight can be determined. Game theory is employed to combine the merits of subjective weight and objective weight, and DEMATEL is adopted to adjust the weight of criteria to make the result more reasonable. Finally, evidence theory is adopted to deal with the uncertainties of input data and get the supplier selection result. A case study is given to demonstrate the proposed modeling process. By comparing with the existing methods, we demonstrate that the proposed model has many advantages and it shows the efficiency and rationality in supplier selection problem.关键词ANP  DEMATEL  Dempster–Shafer evidence theory  Entropy weight  Game theory  MCDM  Supplier selection
 8

 Basic frame of generalized evidence theory

[期刊]
,
2010, 44(12): 119124
EI
SCOPUS
CSCD
PKU

摘要The basic assumption of classical DempsterShafer theory of evidence is that the frame of discernment is complete. However, the frame of discernment is often incomplete in real data fusion application systems. A generalized evidence theory (GET) is proposed to solve this problem in this paper. The generalized basic probability assignment (GBPA) is defined. The value assigned to the empty set shows the support degree to incomplete frame of discernment. A new combination rule, called generalized combination rule (GCR), is proposed to handle evidence combination. It is shown that the proposed combination rule satisfies both commutative law and associative law. Another desirable property of the proposed GET is that it will be reduced as the classical evidence theory when the GBPA to empty set is zero. Some numerical examples are used to show the efficiency of the proposed GET.
 9

 Combining belief functions based on distance of evidence (vol 38, pg 489, 2004)
 [期刊] , 2010, 50(1): 360360 EI SCIE SCOPUS 2.135
 被引用 0 (Web of Science℠)

 10

 NOVEL APPROACHES FOR THE TRANSFORMATION OF FUZZY MEMBERSHIP FUNCTION INTO BASIC PROBABILITY ASSIGNMENT BASED ON UNCERTAINTY OPTIMIZATION
 [期刊] , 2013, 21(2): 289322 EI SCIE SCOPUS 0.619
 被引用 6 (Web of Science℠)

摘要With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, DempsterShafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.关键词Evidence theory , BPA , mass function , focal element , fuzzy membership function , optimization
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