Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Seikh, Mijanur Rahaman; Dutta, Shibaji

doi:10.1007/s00500-021-06559-7

Cited by 17 publications

(16 citation statements)

References 36 publications

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“…According to second comparing approach, to find an optimal solution of the SVTN MPP (P5) is equivalent to find an optimal solution of the crisp MPP (P9) and to find an optimal solution of the SVTN MPP (P6) is equivalent to find an optimal solution of the crisp MPP (P10). Seikh and Dutta (2022) shown that to find an optimal solution of (i) The interval MPPs (P7) and (P8) is equivalent to find an optimal solution of the CLPPs (P11) and (P12) respectively.…”

Section: Second Comparing Approachmentioning

confidence: 99%

“…Brikaa (2022) pointed out that as Seikh and Dutta (2022) have considered a mathematically incorrect result to transform the interval MPP (P7) into the CLPP (P11) as well as to transform the interval MPP (P8) into the CLPP (P12). So, the crisp MPPs (P11) and (P12) are not equivalent to interval MPPs (P7) and (P8) respectively.…”

Section: /3mentioning

confidence: 99%

“…It is obvious that to find an optimal solution of the SVTN MPPs (P5) and (P6), there is a need to compare SVTN numbers. Keeping the same in mind, Seikh and Dutta (2022) considered the following two approaches for comparing two SVTN numbers ̃ 〈( ) 〉…”

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confidence: 99%

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Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Kirti,

Verma,

Kumar

2023

Preprint

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Seikh and Dutta (Soft Computing (2022) 26:921–936) pointed out that there does not exist any approach to solve single-valued trapezoidal neutrosophic (SVTN) matrix games (matrix games in which each payoff is represented by a SVTN number). To fill this gap, Seikh and Dutta proposed two approaches to solve SVTN matrix games. Brikaa (Soft Computing (2022) 26:9137–9139) pointed out that it is inappropriate to use Seikh and Dutta’s first approach as a mathematically incorrect result is considered in it. Brikaa also modified Seikh and Dutta’s first approach to resolve its inappropriateness. In this paper, it is pointed out that it is also inappropriate to use Brikaa’s approach as some mathematically incorrect results are considered in it. Also, it is pointed out that it is inappropriate to use Seikh and Dutta’s second approach as a mathematically incorrect result is considered in it. Furthermore, Brikaa’s approach and Seikh and Dutta’s second approach are modified to resolve their inappropriateness. Finally, the correct results of a SVTN matrix game, considered by Seikh and Dutta to illustrate their proposed approaches, are obtained by the modified approaches.

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Section: Second Comparing Approachmentioning

confidence: 99%

Section: /3mentioning

confidence: 99%

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Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Kirti,

Verma,

Kumar

2023

Preprint

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“…Benchmarks Applications Certain novel concepts of neutrosophic sets, neutrosophic logic, and neutrosophic probability were explored in [31]. Seikh and Dutta [32] developed a matrix games model based on SVNSs. Saha and Paul [33] proposed generalized weighted exponential similarity measures for SVNSs.…”

Section: Researchersmentioning

confidence: 99%

Topological Structure of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Data Analysis for Uncertain Supply Chains

et al. 2022

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From production to retail, the food supply chain (FSC) encompasses all stages of food production. Food is now transmitted across continents over long ranges. People depend on supply chains for basic necessities such as food, water, drinks, etc. Any disruption in these shipment pipelines poses a serious threat to human life. Supplier selection (SS) has been identified as a crucial component of FSC, which has been contemplated as a multi-criteria decision-making (MCDM) problem in many studies. The failure of some specific MCDM problems is due to failure in contemplating the relationships between alternatives under uncertain circumstances. To address such challenges, we present a contemporary method for designating green suppliers based on single-valued neutrosophic hesitant fuzzy (SVNHF) information, in which the input assessment is taken into account using single-valued neutrosophic hesitant fuzzy numbers (SVNHFNs). The foremost purpose of this analysis is to construct a topological structure on single-valued neutrosophic hesitant fuzzy sets (SVNHFSs) as well as to validate several key properties with examples. We discuss certain properties of SVNHF topology such as the SVNHF closure, SVNHF interior, SVNHF exterior, and SVNHF frontier. We also examine the conceptualization of the SVNHF dense set and SVNHF base in SVNHF topology using comprehensive examples. Eventually, to demonstrate and validate the superiority and inferiority ranking (SIR) method and choice value (CV) method in terms of their rationality and scientific basis, a real-world example of supplier selection in a food supply chain is provided. A comparative analysis is also performed to discuss the symmetry, validity and advantage of the proposed techniques.

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“…Furthermore, some researchers [15][16][17] also proposed trapezoidal or triangular neutrosophic number programming methods to solve single-objective or multiobjective linear programming problems in indeterminate environments. Certain researchers [18] further proposed a nonlinear programming model to perform matrix games in the setting of singlevalued neutrosophic numbers. However, these optimal crisp feasible solutions of decision variables and objective functions obtained in uncertain optimization/planning problems are not really meaningful complete solutions but are actually special solutions in uncertain problems.…”

Section: Introductionmentioning

confidence: 99%

Confidence Neutrosophic Number Linear Programming Methods Based on Probability Distributions and Their Applications in Production Planning Problems

2022

Mathematical Problems in Engineering

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A neutrosophic number linear programming (NN-LP) method reveals a useful tool for solving optimal production planning problems in an indeterminate environment. The optimal feasible solutions of the decision variables and the objective function in the NN-LP method are obtained only depending on the subjectively specified uncertain range of neutrosophic numbers without considering some distribution and confidence level of product sample data. Due to the lack of some probability distribution and confidence level/interval in indeterminate situations, existing indeterminate optimization methods are difficult to guarantee the reliability and credibility of the optimal interval feasible solutions. To solve these problems, this study proposes confidence neutrosophic number linear programming methods based on some probability distributions to objectively determine the confidence level/interval of a sample dataset/multivalued set in the NN-LP problems and strengthen the reliability and credibility of the optimal interval feasible solutions. Therefore, this article first introduces a transformation method from product sample datasets (multivalued sets) with normal and log-normal distributions to confidence neutrosophic numbers (CNNs) (confidence intervals) from a probabilistic point of view. Then, CNN linear programming (CNN-LP) models and solution methods are proposed according to the normal and log-normal distributions and confidence levels of product sample datasets to obtain the optimal interval feasible solutions. Furthermore, the proposed CNN-LP methods are applied to two real cases in a manufacturing company of Shaoxing City in China to perform the production planning problems under normal and log-normal distributions and 95% CNN/confidence interval of the product sample datasets. Compared with existing related linear programming methods, the proposed CNN-LP methods can make the optimal interval feasible solutions more reasonable and credible/reliable than the existing linear programming methods and overcome the defects of the existing linear programming methods in indeterminate situations.

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Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Cited by 17 publications

References 36 publications

Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Topological Structure of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Data Analysis for Uncertain Supply Chains

Confidence Neutrosophic Number Linear Programming Methods Based on Probability Distributions and Their Applications in Production Planning Problems

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