Mehar approach to solve neutrosophic linear programming problems using possibilistic mean

Abstract

Khatter (Soft Computing 24 (2020) 16847–16867) pointed out that although several approaches are proposed in the literature to solve single-valued neutrosophic linear programming problems (SVNLPPS) (linear programming problems in which all the parameters except decision variables are either represented by single-valued triangular neutrosophic numbers (SVTNNS) or single-valued trapezoidal neutrosophic numbers (SVTrNNS)). However, all the methods for comparing single-valued neutrosophic numbers (SVNNS), used in existing approaches, are independent from the attitude of the decision maker towards the risk. To fill this gap, Khatter (2020), firstly, proposed a method for comparing two SVNNS by considering the attitude of the decision maker towards the risk. Then, using the proposed comparing method, Khatter (2020) proposed an approach to solve SVNLPPS. In this paper, it is pointed out that a mathematical incorrect result is considered in Khatter’s approach. Hence, it is inappropriate to use Khatter’s approach. Also, it is pointed out that some mathematical incorrect results are considered in other existing approaches for solving SVNLPPS. Hence, it is inappropriate to use other existing approaches for solving SVNLPPS. Furthermore, to resolve the inappropriateness of Khatter’s approach and other existing approaches, a new approach (named as Mehar approach) is proposed to solve SVNLPPS. Finally, correct optimal solution of some existing SVNLPPS is obtained by the proposed Mehar approach.

A note on “An improved solution for the neutrosophic linear programming problems based on Mellin’s transform”

“…Then, the obtained results are better than the existing results (Khatter 2020). Bhatia et al (2022) pointed out that a mathematical incorrect result is considered in Khatter's approach (2020). Hence, it is inappropriate to use Khatter's approach (2020).…”

“…) , 𝜆 ∈ [0,1] then 𝑉(𝑎 ̃1 ⊕ 𝑎 ̃2, 𝜆) ≠ 𝑉(𝑎 ̃1, 𝜆) + 𝑉(𝑎 ̃2, 𝜆). Hence, Bhatia et al (2022) pointed out that Khatter's approach (2020) is not valid.…”

“…In this note, it is shown that a mathematical incorrect result, pointed out by Bhatia et al (2022) in Khatter's approach (2020, is also considered in Tamilarasi and Paulraj's approach (2022). Hence it is inappropriate to use Tamilarasi and Paulraj's (2022) approach to solve neutrosophic linear programming problems.…”

“…Hence, it is inappropriate to use Khatter's approach (2020). Bhatia et al (2022) also proposed a new approach (named as Mehar approach) to solve neutrosophic linear programming problems.…”

“…It is obvious that in Step 2 of Khatter's approach (2020) as well as in Tamilarasi and Paulraj's approach (2022), the relation 𝑉(𝑎 ̃1 ⊕ 𝑎 ̃2, 𝜆) = 𝑉(𝑎 ̃1, 𝜆) + 𝑉(𝑎 ̃2, 𝜆) is used to transform crisp linear programming problem (𝑃 2 ) into the crisp linear programming problem (𝑃 3 ) Bhatia et al (2022). considered an example to show that if 𝑉((𝑎 1 , 𝑎 2 , 𝑎 3…”