Abstract
Recently fuzzy interval flexible linear programs have attracted many interests. These models are an extension of the classical linear programming which deal with crisp parameters. However, in most of the real-world applications, the nature of the parameters of the decision-making problems is generally imprecise. Such uncertainties can lead to increased complexities in the related optimisation efforts. Simply ignoring these uncertainties is considered undesired as it may result in inferior or wrong decisions. Therefore, inexact linear programming methods are desired under uncertainty. In this paper, we concentrate a fuzzy flexible linear programming model with flexible constraints and the interval objective function and then propose a new solving approach based on solving an associated multi-objective model. Finally, numerical example is included to illustrate the mentioned solving process.
Highlights
Fuzzy sets theory has been extensively employed in linear programming
The research on fuzzy linear programming has risen highly since Bellman and Zadeh proposed the concept of decision making in fuzzy environment
Zimmermann [1] introduced the first formulation of fuzzy linear programming to address the impreciseness and vagueness of the parameters in linear programming problems with fuzzy constraints and objective functions
Summary
Fuzzy sets theory has been extensively employed in linear programming. The main objective in fuzzy linear programming is to find the best solution possible with imprecise, vague, uncertain or incomplete information. Mahdavi-Amiri and Nasseri [9] developed some methods for solving fuzzy linear programming problems by introducing and solving certain auxiliary problems They apply a linear ranking function to order trapezoidal fuzzy numbers and deduce some duality results by establishing the dual problem of the linear programming problem with trapezoidal fuzzy variables. To ensure that solutions are absolutely feasible, Zhou et al exhibited Modified Interval Linear Programming (MILP) method, by adding an extra constraint to the second sub-model. We give a generalised form of these problems in two ways: in first way, we consider the flexibility condition for the constraints, and in second way we consider the multi-objective case for the objective In this sense, we introduce a new extended model and propose a method for solving the proposed model.
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