Planning Regional Water Resources System Using an Interval Fuzzy Bi-Level Programming Method

Abstract

An interval fuzzy bi-level programming (IFBP) approach is developed for planning water resources management system. The developed IFBP improves upon the existing bi-level programming by introducing interval mathematical programming (IMP) into its framework. The IFBP can handle uncertainties expressed as interval values in the constraints' left- and right-hand sides, as well as in the upper- and lower-level objective functions. Moreover, the decision dimensions of objective functions can be addressed through setting different tolerance levels based on the fuzzy set theory, such that tradeoffs corresponding to different upper- and lower-level objectives as well as varied system optimality and reliability can be generated. A case study is provided for an application to planning a water resources management system, where a number of scenarios are analyzed. For all scenarios under consideration, the IFBP method has advantages over the conventional programming methods with single decision maker in reflecting the interactions among multi-level objectives and strategies as well as encouraging co-operations among multiple parties under uncertainty.

Keywords: bi-level programming, decision making, fuzzy, interval, planning, uncertainty water resources