Abstract
This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear fractional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.
Highlights
While modeling practical problems in real world, it is observed that some parameters of the problem may not be known certainly
This paper introduces an interval valued linear fractional programming problem (IVLFP)
To introduce an interval-valued linear fractional programming problem, we can consider another kind of possible linear fractional programming problems as follows: IVLFP(1) minimize f x = f L x, f U x subject to: (8)
Summary
While modeling practical problems in real world, it is observed that some parameters of the problem may not be known certainly. For an optimization problem it is possible that the parameters of the model be inexact. For example in a linear programming problem we may have inexact right hand side values or the coefficients in objective function may be fuzzy We consider an optimization problem with interval valued objective function. Hsien-Chung Wu ([4,5]) proved and derived the Karush-Kuhn-Tucker (KKT) optimality conditions for an optimization problem with interval valued objective function. A fractional programming problem is the optimizing one or several ratios of functions First we introduce a linear fractional programming problem with interval valued parameters. We try to convert it to an optimization problem with interval valued objective function.
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