Abstract
In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand. Based on the (α,β)-cut concept a parametric (α,β)-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain (α,β)-Pareto optimal solution. We investigated the stability set of the first kind (SSFK) corresponding to the solution by extending the Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to crystalize the progressing SSFK for PIF-MOFTP as well as an illustrative numerical example is presented.
Highlights
Transportation issues (TP) have been studied in various writings [1,2,3,4,5,6,7]
This might involve thinking about vagueness, or specifying the fundamental parameters of the model, which are the coefficients of the objective function and the constrains [4,8]
The primary commitments are concerned with two unique viewpoints: one is to find a (α, β)-Pareto optimal solution for the PIFMOFTP, and another is to investigate the stability set of the first kind (SSFK) for PIF-multi-objective fractional transportation problem (MOFTP)
Summary
Transportation issues (TP) have been studied in various writings [1,2,3,4,5,6,7]. One of the significant issues looked at by specialists is that involving the exact values of parameters [7]. In this way, this might involve thinking about vagueness, or specifying the fundamental parameters of the model, which are the coefficients of the objective function and the constrains [4,8]. In this study the main hypotheses are that the transportation charge has a parametric nature, and the supply and the demand parameters are intuitionistic. The main hypotheses have not been presented in the literature, and the basic question is how we can get the SSFK for such PIF-MOFTP
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