D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

Deng, Xinyang; Jiang, Wen

doi:10.1016/j.ijar.2019.01.007

Cited by 113 publications

(58 citation statements)

References 94 publications

(94 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%

“…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%

“…In this paper, we put our attention on a special theory for uncertainty reasoning which is called D number theory (DNT). 8,9 This theory is a recently proposed theoretical framework that has generalized Dempster-Shafer theory (DST). 10,11 In DST, every piece of knowledge or information is abstracted as a mass function or basic probability assignment (BPA), and each BPA is defined on a mutually exclusive and collectively exhaustive set which is called frame of discernment (FOD).…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Number Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A total uncertainty measure for D numbers based on belief intervals

Deng

Jiang

2019

Int J Intell Syst

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“…Many math tools are presented to model uncertainty, such as Z numbers, [53][54][55] D numbers, [56][57][58][59][60][61] and entropy model. [62][63][64][65][66][67] Among then, evidence theory is widely used due to its efficiency to deal with uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

Int J Intell Syst

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Dempster‐Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision‐making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

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“…MCDM is a crucial research topic in decision theory. Because the objects to be expressed and handled are usually uncertain, the criteria involved in decision problems are not always represented as real numbers, so plenty of useful theories are proposed, such as Dempster-Shafer theory, 24,[27][28][29][30][31][32][33][34] D numbers theory, [35][36][37][38] Z-numbers theory, [39][40][41][42] etc. Given the advantages of PFS, the concept of soft likelihood function is combined in this paper to develop an MCDM method in Pythagorean fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

On Pythagorean fuzzy decision making using soft likelihood functions

2019

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Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)‐based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA‐based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.

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D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

Cited by 113 publications

References 94 publications

A total uncertainty measure for D numbers based on belief intervals

A total uncertainty measure for D numbers based on belief intervals

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

On Pythagorean fuzzy decision making using soft likelihood functions

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