Fuzzy Sets and Systems 115 (2000) 11–33 www.elsevier.com/locate/fss Aggregation operators for soft decision making in water resources Ozren Despic a ; * , Slobodan P. Simonovic b a Department of Industrial & Mechanical Engineering, Center for Management of Technology & Entrepreneurship, University of Toronto, Toronto, Canada M5S 3G9 b Department of Civil and Geological Engineering and Natural Resources Institute, University of Manitoba, Winnipeg, Canada R3T 2N2 Received November 1998 Abstract This paper presents a general methodology for numerical evaluation of complex qualitative criteria based on the theory of fuzzy sets. A special emphasis is given to the criteria frequently used in water resources decision making. Water resources’ qualitative criteria are exhibiting a high level of complexity that does not allow for an easy and reliable straightforward evaluation. Due to this complexity, a satisfying evaluation is possible neither on numerical scale nor through a direct construction of suitable fuzzy membership function. The theoretical contribution of presented research consists of the analysis and development of appropriate mathematical techniques for modeling human reasoning. Analyzed techniques include exible decomposition methodology, construction of fuzzy sets and selection of aggregation operators that can perform justiable aggregation of fuzzy sets. Methodology presented in this paper provides precise and consistent evaluation tool for many qualitative criteria and therefore enables a successful inclusion of these criteria into qualitative decision making model. A special attention in this paper is given to the aggregation methods. An original aggregation method named polynomial composition under pseudomeasures is developed and presented along with the four well-known aggregation methods that seem to be appropriate for the implementation in water resources decision making. The new method has been developed as a suitable aggregation operator for the case study domain: qualitative evaluation of ood control. c  2000 Elsevier Science B.V. All rights reserved. Keywords: Membership functions; Aggregation operators; Decision making; Flood control 1. Introduction Historically, decision making process has been re- lated to data collection and information processing that satises all the parties interested in the prob- lem under consideration. Complexity of the decision making process is increasing with time. With the complexity of modern societies’ social structure and ever-expanding human knowledge about numerous * Corresponding author. connections among the components of a system, it is not surprising that we are not able or willing any more to include all the relevant information or to con- sider all the parties interested in a decision making process. However, the way we make decisions today has been considerably changed. The main change is certainly a shift from single-objective optimization toward multi-objective analysis, especially when the system analyzed is a part of a natural environment. In this report, we are addressing water resources’ systems. Although immense complexity is a natural 0165-0114/00/$ - see front matter c  2000 Elsevier Science B.V. All rights reserved. PII:S0165-0114(99)00030-5