Riemann integrability based optimality criteria for fractional optimization problems with fuzzy parameters

Document Type : Research Paper


1 Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, India

2 Department of Mathematics, G L Bajaj Institute of Technology and Management, Greater Noida, India


This paper aims to establish the Karush-Kuhn-Tucker type optimality criteria for linear fractional optimization problems with fuzzy parameters. To evolve the desired criteria first, the fractional optimization problem is transformed into the non-fractional optimization problem with fuzzy parameters. Then Hukuhara differentiability for the differentiation of functions with fuzzy parameters and Hausdorff metric to expound the distance between the fuzzy numbers is invoked. Optimality criteria are then elicited for the non-fractional optimization problems by introducing Lagrange multipliers and Riemann integration theory. In order to validate the developed theory, two numerical optimization problems are also verified.