Document Type : Original Article


1 Department of Mathematics, Faculty of Mathematics Science, University of Mazandaran, Babolsar, Iran.

2 Mazandaran University of Science and Technology, Babolsar, Iran.


This paper describes an application of fuzzy multi-objective quadratic model with flexible constraints for optimal allocation of limited available water resources among different water-user sectors. Due to the fact that, water resource allocation problem is one of the practical and essential subjects in real world and many of the parameters may be faced by uncertainty. In this paper, we present α - cut approach for transforming fuzzy multi-objective quadratic programming model with flexible constraints into a crisp form. By using this approach a multi-parametric multi-objective programming model corresponding to α and parameters of flexible constraints is obtained. One of the advantages of this model is that the α - cut level is not determined by the decision makers. Actually, this model itself can calculate the α - cut level. In order to achieve a desired Pareto optimal value of multi-parametric multi-objective model, we use goal programming method for illustration of water resource allocation with sensitivity analysis of lower bound of parameters in flexible constraints. To illustrate the efficiency of the proposed approach, we apply it for a real case problem of water resource allocation.


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