Optimality, duality and saddle point analysis for interval-valued nondifferentiable multiobjective fractional programming problems

Abstract

This paper is developed to discuss the theoretical aspects of multiobjective fractional problems under interval uncertainty. For this, we have formulated an interval multiobjective fractional model (IVMFP) in which the numerator and denominator of objective functions are assumed to be interval valued functions. Partial ordering is invoked to define LU-Pareto optimal solutions to the problem. Thereafter, necessary optimality conditions of the Fritz John type and Kuhn Tucker type are derived in the classical way. LU-convexity and LU-concavity are used to establish the sufficient optimality criteria and with the same assumptions, the parametric duality theory is discussed. Also, interval valued vector Lagrangian is proposed and the corresponding results are established to locate the saddle point.