Multi-Criteria Decision Making under Uncertainty in Rainfall-Runoff Calibration: A Fuzzy Compromise Programming Approach Based on Alpha Level Sets

This paper involves a methodology developed for multi-criteria decision making and to reduce the number of Pareto optimal solutions. The technique is a Fuzzy Compromise Programming (FCP) coupled to a Genetic Algorithm (GA) applied for a case study on multi-objective rainfall-runoff calibration. The uncertainty associated with probable preferences of decision-makers has also been dealt with by the fuzzy extension principle and alpha-cut levels (i.e. considering the importance of the criteria by triangular fuzzy weights). The problem, therefore, becomes to solve a set of non-linear programming problems using GA, which results in ranking the alternatives based on a distance metrics. The obtained results show that the proposed hybrid FCP-GA approach performs well as a means to sieve among the Pareto optimal parameter sets of the problem. It would also help to choose the most preferable solutions, especially in cases where one is obliged to give a limited number of best solutions.