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Aggregation operators for soft decision making in water resources. (English) Zbl 0978.90059

Summary: 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 flexible decomposition methodology, construction of fuzzy sets and selection of aggregation operators that can perform justifiable 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 flood control.

MSC:

90B50 Management decision making, including multiple objectives
03E72 Theory of fuzzy sets, etc.
49M27 Decomposition methods
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