| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-cut concept a parametric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-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.
|
|---|