14 - Fuzzy compromise approach to water resources systems planning under uncertainty

Summary

ABSTRACT

A fuzzy compromise approach is applied to two water resources systems planning examples, for the purpose of allowing various sources of uncertainty and facilitating a flexible form of group decision support. The examples compare the ELECTRE method, and Compromise Programming, with the fuzzy approach. The fuzzy compromise approach allows a family of possible conditions to be reviewed, and supports group decisions through fuzzy sets designed to reflect collective opinions and conflicting judgments. Evaluating alternatives to produce rank orderings are accomplished with two ranking measures for fuzzy sets. The ranking measures are also shown to indicate the impact of different levels of decision-maker risk aversion. Two distinct ranking measures are used – a centroid measure and a fuzzy comparison measure based on a fuzzy goal.

INTRODUCTION

Multicriteria decision analysis (MCDA) has been moving from optimization methods to more interactive decision support tools. Some areas of interest have been identified by Dyer et al. (1992) as:

Sensitivity analysis and the incorporation of vague or imprecise judgements of preferences. Development of improved interactive software for multicriterion decision support systems.

Uncertainty is a source of complexity in decision making that can be found in many forms. Typical ones include uncertainty in model assumptions and uncertainty in data or parameter values. There may also be uncertainty in the interpretation of results. While some uncertainties can be modeled as stochastic variables in a Monte Carlo simulation, for example, other forms of uncertainty may simply be vague or imprecise.

Traditional techniques for evaluating discrete alternatives such as ELECTRE (Benayoun, Roy, and Sussmann 1966), AHP (Saaty 1980), Compromise Programming (Zeleny 1973, 1982), and others normally do not consider uncertainties involved in procuring criteria values.