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Neutrosophic linear programming problems (NLPPs) are uniquely defined linear programming problems under neutrosophic environment in which coefficients or parameters are either neutrosophic numbers or neutrosophic set values. Bhatia et al. (Soft Computing, 26:8479–8495, 2022) pointed out some mathematical inappropriateness in the neutrosophic linear programming problem (NLPP) solution approaches in particular given by Khatter (Soft Computing, 24, 16847–16867, 2020) and Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) for solving single valued triangular neutrosophic linear programming problems (SVTrNLPPs) and single-valued trapezoidal neutrosophic linear programming problems (SVTNLPPs) respectively. Khatter (Soft Computing, 24, 16847–16867, 2020) proposed solution approach to convert SVTrNLPP into an equivalent crisp programming problem using the possibilistic mean value of each neutrosophic coefficient of the problem. Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) proposed solution approach with the conversion of SVTrNLPP into equivalent crisp programming problem using ranking function value of each neutrosophic coefficient of the problem. Bhatia et al. (Soft Computing, 26:8479–8495, 2022) pointed out inappropriateness in the approaches by Khatter (Soft Comput, 24, 16847–16867, 2020) and Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) on the interpretation that the property of ranking function i.e. \( R\left({\tilde{A}}_{i1}+{\tilde{A}}_{i2}\right)=R\left({\tilde{A}}_{i1}\right)+R\left({\tilde{A}}_{i2}\right) \) and property of possibilistic mean of NNs i.e. \( V\left({\tilde{A}}_{i1}+{\tilde{A}}_{i2}\right)=V\left({\tilde{A}}_{i1}\right)+V\left({\tilde{A}}_{i2}\right) \) do not hold on the constraint part of the problems with N coefficients. Bhatia et al. (Soft Comput, 26:8479–8495, 2022) claimed that these approaches as well as other existing approaches are mathematically incorrect and should not be used for solving SVNLPPs, SVTrNLPPs and other neutrosophic linear programming problems. In this paper, we propose a rebuttal note on the points raised by Bhatia et al. (Soft Comput, 26:8479–8495, 2022) related to the inappropriateness of the approaches particularly Khatter (Soft Comput, 24, 16847–16867, 2020), Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) and prove that these approaches as well as all other built on approaches are mathematically correct and appropriate methods for solving NLPPs. The aim of this rebuttal note to clarify the correctness of existing approaches and bring back the faith of researchers on these approaches on neutrosophic linear programming problems.

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Defending NLPP Solution Approaches: A Rebuttal to Bhatia et al. (2022) “Mehar Approach to Solve Neutrosophic Linear Programming Problems Using Possibilistic Mean”

  • 会议论文

  • 发表日期：

    2026年

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  • Kailash Lachhwani

摘要

Neutrosophic linear programming problems (NLPPs) are uniquely defined linear programming problems under neutrosophic environment in which coefficients or parameters are either neutrosophic numbers or neutrosophic set values. Bhatia et al. (Soft Computing, 26:8479–8495, 2022) pointed out some mathematical inappropriateness in the neutrosophic linear programming problem (NLPP) solution approaches in particular given by Khatter (Soft Computing, 24, 16847–16867, 2020) and Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) for solving single valued triangular neutrosophic linear programming problems (SVTrNLPPs) and single-valued trapezoidal neutrosophic linear programming problems (SVTNLPPs) respectively. Khatter (Soft Computing, 24, 16847–16867, 2020) proposed solution approach to convert SVTrNLPP into an equivalent crisp programming problem using the possibilistic mean value of each neutrosophic coefficient of the problem. Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) proposed solution approach with the conversion of SVTrNLPP into equivalent crisp programming problem using ranking function value of each neutrosophic coefficient of the problem. Bhatia et al. (Soft Computing, 26:8479–8495, 2022) pointed out inappropriateness in the approaches by Khatter (Soft Comput, 24, 16847–16867, 2020) and Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) on the interpretation that the property of ranking function i.e. \( R\left({\tilde{A}}_{i1}+{\tilde{A}}_{i2}\right)=R\left({\tilde{A}}_{i1}\right)+R\left({\tilde{A}}_{i2}\right) \) and property of possibilistic mean of NNs i.e. \( V\left({\tilde{A}}_{i1}+{\tilde{A}}_{i2}\right)=V\left({\tilde{A}}_{i1}\right)+V\left({\tilde{A}}_{i2}\right) \) do not hold on the constraint part of the problems with N coefficients. Bhatia et al. (Soft Comput, 26:8479–8495, 2022) claimed that these approaches as well as other existing approaches are mathematically incorrect and should not be used for solving SVNLPPs, SVTrNLPPs and other neutrosophic linear programming problems. In this paper, we propose a rebuttal note on the points raised by Bhatia et al. (Soft Comput, 26:8479–8495, 2022) related to the inappropriateness of the approaches particularly Khatter (Soft Comput, 24, 16847–16867, 2020), Singh et al. (J Intell Fuzzy Syst, 37, 885–895, 2019) and prove that these approaches as well as all other built on approaches are mathematically correct and appropriate methods for solving NLPPs. The aim of this rebuttal note to clarify the correctness of existing approaches and bring back the faith of researchers on these approaches on neutrosophic linear programming problems.