The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems

• Published in: Mathematics and computers in simulation Vol. 205; pp. 861 - 877
• Main Authors: Agarwal, Deepika, Singh, Pitam, El Sayed, M.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2023
• Subjects: Fuzzy-valued functions; H-differentiability; Hausdorff metric; KKT conditions; Lagrange multipliers; H-differentiability; Lagrange multipliers; KKT conditions; Fuzzy-valued functions; Hausdorff metric
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2022.10.024

The Karush–Kuhn–Tucker (KKT) optimality conditions have a crucial role in finding the efficient solution of any optimization problem. Many researchers have been focussing on the establishment of KKT optimality conditions for deterministic fractional optimization problems (FOP). Also, solution algorithms for fuzzy-valued fractional optimization problem have been proposed by the researchers. However as far as authors are aware, there is no study available for the establishment of optimality conditions for the fuzzy-valued fractional optimization problem (FVFOP). In this paper, KKT optimality conditions are derived for FVFOP. Differentiation of fuzzy-valued functions is obtained using Hausdorff metric which find the distance of two fuzzy numbers and Hukuhara difference which is used to determine the difference between two fuzzy-valued functions. Considered FVFOP is transformed into non-fractional objective using the modified objective approach. The solution concept is developed using Lagrange multipliers, α-cuts and Dinkelbach algorithm. The proposed optimality conditions are verified by the numerical problems and the results are shown graphically for different values of α.