Author(s): Shaik Rehana; P. P Mujumdar
Linked Author(s): Pradeep P Mujumdar
Keywords: No Keywords
Abstract: Most Fuzzy Waste Load Allocation Models (FWLAM) developed earlier (Sasikumar and Mujumdar, 1998; Mujumdar and Sasikumar, 2002; Ghosh and Mujumdar, 2006) solve fuzzy multiobjective optimization problems using the max-min operator, which usually may not result in a unique solution. Existence of multiple solutions in the max-min formulation of fuzzy optimization model is common. A methodology is necessary to capture all the decision alternatives from a fuzzy multiobjective optimization model in a given problem setting. As the number of objectives and decision variables increases in the fuzzy multiobjective optimization model, the possibility of multiple solutions increases (Karmakar and Mujumdar 2007). It is therefore desirable to capture the multiple solutions of fuzzy multiobjective optimization model as parametric equation or equations that represent a subspace. In this paper a procedure to capture all solutions of an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) developed earlier by the authors is presented. To capture the solutions of optimal fractional removal levels in the river water quality management problem, two optimization models have been developed: One to maximize and another to minimize the summation of membership functions of the dischargers by keeping the maximum goal fulfillment level same as that obtained in IFWLAM to obtain a lower limit and an upper limit of fractional removal levels respectively. A range of upper and lower limits of fractional removal levels are obtained for each discharger. Within this range the discharger can select the fractional removal level so that the resulting fuzzy risk will be within specified bounds. The solutions obtained are in the form of interval numbers of fractional removal levels and will be more favorable to the decision makers compared to single valued optimal solutions. The proposed methodology is discussed with application to a case study of the Tunga-Bhadra river system in India.
Year: 2009