A stepwise fuzzy linear programming model with possibility and necessity relations

  • Authors:

  • Adel Hatami-Marbini;Per J. Agrell;Madjid Tavana;Ali Emrouznejad

  • Affiliations:

  • Louvain School of Management, Center of Operations Research and Econometrics CORE, Université catholique de Louvain 34 Voie du Roman Pays, Louvain-la-Neuve, Belgium;Louvain School of Management, Center of Operations Research and Econometrics CORE, Université catholique de Louvain 34 Voie du Roman Pays, Louvain-la-Neuve, Belgium;Business Systems and Analytics Department, La Salle University, Philadelphia, PA, USA;Operations & Information Management Group, Aston Business School, Aston University, Birmingham, UK

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2013

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Abstract

Linear programming LP is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP FLP problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to 1 the decision variables; 2 the coefficients of the decision variables in the objective function; 3 the coefficients of the decision variables in the constraints; 4 the right-hand-side of the constraints; or 5 all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms.