A Modified D Numbers’ Integration for Multiple Attributes Decision Making

Wang, Ningkui; Liu, Xianming; Wei, Daijun

doi:10.1007/s40815-017-0323-0

Cited by 22 publications

(17 citation statements)

References 62 publications

(67 reference statements)

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“…DNT is a new theoretical framework for uncertainty reasoning which generalizes the DST from two aspects: on one hand, the elements within FOD are not required to be mutually exclusive in DNT; on the other hand, the providing information in DNT can be incomplete in contrast to

\sum m (\cdot) = 1

in DST. For more theoretical details about DNT and its recent advances, refer to literatures Furthermore, some applications of DNT can be found in references . A few of basic concepts in DNT are introduced as follows …”

Section: Number Theorymentioning

confidence: 99%

A total uncertainty measure for D numbers based on belief intervals

Deng

Jiang

2019

Int J Intell Syst

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Uncertainty quantification is very important in many applications. As a generalization of Dempster‐Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that theory. In this paper, inspired by distance‐based uncertainty measures for Dempster‐Shafer theory, a total uncertainty measure for a D number is proposed based on its belief intervals. The proposed total uncertainty measure can simultaneously capture the discord, and nonspecificity, and nonexclusiveness involved in D numbers. And some basic properties of this total uncertainty measure, including range, monotonicity, generalized set consistency, are also presented. At last, an illustrative application about feature evaluation is given to verify the effectiveness of the proposed uncertainty measure.

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\sum m (\cdot) = 1

Section: Number Theorymentioning

confidence: 99%

A total uncertainty measure for D numbers based on belief intervals

Deng

Jiang

2019

Int J Intell Syst

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“…For another, the sum of basic probabilities of a mass function must be equal to 1, which is called completeness constraint. To overcome these existing shortcomings in D-S theory and enhance its capability in expressing uncertain information, a novel model, named as D numbers, has been proposed recently [ 30 , 31 , 32 , 33 , 58 ]. D numbers relax mass function’s exclusiveness hypothesis and BPA’s completeness constraint.…”

Section: Preliminariesmentioning

confidence: 99%

Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method

Deng

Jiang

2017

Sensors

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Failure mode and effect analysis (FMEA) is a useful tool to define, identify, and eliminate potential failures or errors so as to improve the reliability of systems, designs, and products. Risk evaluation is an important issue in FMEA to determine the risk priorities of failure modes. There are some shortcomings in the traditional risk priority number (RPN) approach for risk evaluation in FMEA, and fuzzy risk evaluation has become an important research direction that attracts increasing attention. In this paper, the fuzzy risk evaluation in FMEA is studied from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA. An illustrative example is provided and examined using the proposed model and other existing method to show the effectiveness of the proposed model.

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“…Aiming to overcome the above mentioned deficiencies of evidence theory, D number theory has emerged in 2012, which provides a more flexible way to deal with uncertain information, and the above mentioned limitations are well addressed. Since the advantage of D number theory, it has been widely carried out to solve these problems, such as decision making [65][66][67], location selection [68], risk assessment [69], supply chain management [70], target recognition [71], environmental impact assessment [72,73], curtain grouting efficiency assessment [74] and so forth [75][76][77]. Besides, D number thoery can be together used with other measures, such as intuitionistic hesitant fuzzy set [78], decision-making trial and evaluation laboratory method (DEMATEL) [79], failure mode and effect analysis (FMEA) [80], to generate new measures for some real-life problems.…”

Section: Introductionmentioning

confidence: 99%

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

2020

Information

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Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

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A Modified D Numbers’ Integration for Multiple Attributes Decision Making

Cited by 22 publications

References 62 publications

A total uncertainty measure for D numbers based on belief intervals

A total uncertainty measure for D numbers based on belief intervals

Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

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