An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades

Fu, Chao; Wang, Ying‐Ming

doi:10.1016/j.cie.2014.12.031

Cited by 57 publications

(28 citation statements)

References 42 publications

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“…Dempster-Shafer (D-S) evidence theory [48,49] is a powerful tool to handle the uncertainty. It has been widely used in many fields, like risk analysis [52][53][54], controller design [55,56], pattern recognition [57][58][59], fault diagnosis [60][61][62], multiple attribute decision making [63,64] and so on.…”

Section: Introductionmentioning

confidence: 99%

An evidential Markov decision making model

Jiang

2018

Information Sciences

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The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical laws. In this paper, an Evidential Markov (EM) decision making model based on Dempster-Shafer (D-S) evidence theory and Markov modelling is proposed to address this issue and model the real human decision-making process. In an evidential framework, the states are extended by introducing an uncertain state which represents the hesitance of a decision maker. The classical Markov model can not produce the disjunction effect, which assumes that a decision has to be certain at one time. However, the state is allowed to be uncertain in the EM model before the final decision is made. An extra uncertainty degree parameter is defined by a belief entropy, named Deng entropy, to assignment the basic probability assignment of the uncertain state, which is the key to predict the disjunction effect. A classical categorization decision-making experiment is used to illustrate the effectiveness and validity of EM model. The disjunction effect can be well predicted and the free parameters are less compared with the existing models.Keywords: Evidential Markov model; Markov decision making model;Dempster-Shafer evidence theory; the sure thing principle; the law of total probability; disjunction effect

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Section: Introductionmentioning

confidence: 99%

An evidential Markov decision making model

Jiang

2018

Information Sciences

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“…It is easy to see that the belief structure can flexibly model uncertain attribute values. Information concerning attribute weights is unknown or partially known. Without loss of generality, our study divides restrictions on attribute weights into the following four forms: (a) no weight information (Wei, Song, Jiao, & Yang, ; Yang, Sheng, Xia, & Yang, ), (b) ordinal preference information (Bao et al, ; Chin et al, ), (c) uniform weight distribution with interval constraints (Fu & Wang, ; Xu, Wang, & Palacios‐Marqués, ), and (d) normal weight distribution with interval constraints (Zhu et al, ).…”

Section: Preliminariesmentioning

confidence: 99%

“…We use data from a case study by Fu and Wang () to assess the performance of the proposed method. All calculations in this numerical example were performed using MATLAB R2016a, and the simulation had 10,000 iterations.…”

Section: Numerical Examplementioning

confidence: 99%

“…Table also lists the results obtained using the IDER approach proposed by Fu and Wang (). Clearly, the optimal alternative to our proposed method was identical to that obtained by IDER.…”

Section: Numerical Examplementioning

confidence: 99%

“…Chin and Fu () subsequently proposed an integrated ER approach to handle imprecise attribute weights. Fu and Wang () used an interval difference‐based ER (IDER) approach to generate optimized intervals of attribute weights, which involves constructing three optimization models to rank alternatives in three scenarios. Chen, Wang, Shi, Zhang, and Lin () provided a way to determine the weights of items of discrete evidence by using the pignistic probability distance.…”

Section: Introductionmentioning

confidence: 99%

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A stochastic multicriteria acceptability analysis–evidential reasoning method for uncertain multiattribute decision‐making problems

et al. 2019

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Evidential reasoning (ER) is an effective approach for assessing alternatives with uncertain attribute values in the context of decision making. For the ER approach to be able to handle variations in the weights of uncertain attributes in an appropriate manner, this paper proposes a method to solve problems of uncertain multiattribute decision making that involve both uncertain attribute values and uncertain attribute weights, which this method does by combining the ER approach and stochastic multicriteria acceptability analysis‐2 (SMAA‐2). First, the uncertainty in attribute values is described by using a belief decision matrix as in the ER approach. The analytical ER algorithm is then used to create the utility function in the SMAA‐2 model, and that function is used to calculate the probability of different sorting positions of the decision units under weight‐related restrictions. Finally, the results of ranking are obtained by combining the sorting weights. An example is provided to verify the effectiveness of the proposed method.

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A new probability transformation method based on a correlation coefficient of belief functions

2019

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The Dempster‐Shafer evidence theory is widely used in many fields of information fusion because of its advantage in handling uncertain information. One of the key issues in this theory is how to make decision based on a basic probability assignment (BPA). Currently, a feasible scheme is transforming a BPA to a distribution of probabilities. However, little attention was paid to the correlation between BPA and probability distribution. In this paper, a novel method about the probability transformation based on a correlation coefficient of belief functions is proposed. The correlation coefficient is a new measurement, which can effectively measure the correlation between BPAs. The proposed method aims at maximizing the correlation coefficient between the given BPA and the transformed probability distribution. On the basis of this idea, the corresponding probability distribution can be obtained and could reflect the original information of the given BPA to the maximum extent. It is valid to consider that the proposed probability transformation method is reasonable and effective. Numerical examples are given to show the effectiveness of the proposed method.

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An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades

Cited by 57 publications

References 42 publications

An evidential Markov decision making model

An evidential Markov decision making model

A stochastic multicriteria acceptability analysis–evidential reasoning method for uncertain multiattribute decision‐making problems

A new probability transformation method based on a correlation coefficient of belief functions

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