A new matrix game with payoffs of generalized Dempster‐Shafer structures

Zhou, Lian; Xiao, Fuyuan

doi:10.1002/int.22164

Cited by 10 publications

(5 citation statements)

References 78 publications

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“…respectively. e SVTNNs payoff matrices of the two players are given by C � 〈(6, 7, 9, 1); 0.9, 0.2, 0.4〉 〈(3.5, 5, 7, 9); 0.5, 0.4, 0.2〉 〈 (3,5,6,8); 0.6, 0.5, 0.1〉 〈(5, 6.5, 8, 10); 0.7, 0.3, 0.5〉 , D � 〈(5, 6.5, 8, 9); 0.8, 0.2, 0.3〉 〈(4, 5, 7, 8.5); 0.8, 0.3, 0.1〉 〈(3.5, 4.5, 6, 7.5); 0.6, 0.4, 0.2〉 〈(6, 7, 8, 9); 0.9, 0.1, 0.4〉 . (28) e vectors of the constraints and the coefficient matrices are given by…”

Section: 1mentioning

confidence: 99%

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Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Gaber

Alharbi

Dagestani

et al. 2021

Journal of Mathematics

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Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.

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Section: 1mentioning

confidence: 99%

“…Singh et al [7] established 2-tuple linguistic matrix games. Zhou et al [8] constructed novel matrix game with generalized Dempster-Shafer payoffs. Seikh et al [9] solved matrix games with payoffs of hesitant fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Gaber

Alharbi

Dagestani

et al. 2021

Journal of Mathematics

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“…Similarly, Zhou and Xiao 54 present a new matrix game with payoffs of generalised D‐S structures. Their generalised D‐S structures mean to present probability nonspecificity and inaccuracy as interval‐values and then payoffs in such a game are determined by linear programming.…”

Section: Related Workmentioning

confidence: 99%

A decision support framework for security resource allocation under ambiguity

Liu

McAreavey

et al. 2020

Int J Intell Syst

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There has been increasing interest in using Stackelberg game (known as a security game) to allocate limited security resources against different attacker types with a specific probability distribution. However, real problems of this kind often face ambiguous information, such as imprecise, unreliable and absent payoffs, and ambiguous assignments of these payoffs. To this end, based on decision theory and the Dempster-Shafer theory of evidence, this paper proposes a novel framework that can handle these common types of ambiguity. More specifically, this paper deploys the underlying principles of existing rules from decision theory, as a way to characterise different attitudes to ambiguity, during the transformation of ambiguous payoffs into point-valued payoffs. Hence, our framework holds some good properties: (i) it subsumes traditional security games without ambiguous payoffs, (ii) a uniform margin of error will not affect the results and (iii) the influence

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“…Matrix game theory is an effective tool for portraying two-person non-cooperation competitions and has been applied to some fields such as advertising, biology, emergency and military issues [3][4][5]. Matrix game theory considers the characteristics of players' non-cooperative behaviors and aims to solve the conflict of interests between players.…”

Section: Introductionmentioning

confidence: 99%

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

Yang

Ding

2021

Complex Intell. Syst.

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How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.

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A new matrix game with payoffs of generalized Dempster‐Shafer structures

Cited by 10 publications

References 78 publications

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers

A decision support framework for security resource allocation under ambiguity

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

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