Two fuzzy and optimal models of water resources ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Two fuzzy and optimal models of water resources evaluation based on the Principle of Maximum Entropy (POME) and Engineering Fuzzy Set Theory
Paper
Author:WANG Dong <wangdong@nju.edu.cn> (Nanjing University)
Presenter:WANG Dong <wangdong@nju.edu.cn> (Nanjing University)
Date: 2006-06-18     Track: Special Sessions     Session: Boltzmann Methods in Water Resources
DOI:10.4122/1.1000000612
DOI:10.4122/1.1000000613

The randomness of characteristic value of water resources evaluation is inevitable during its monitoring, experimenting, and data analyzing, as a result of the physical process, the chemical process and biological process of water contamination are all stochastic process. On the other hand, the fuzziness of water resources evaluation is also inevitable, for the classification standard, the evaluation class and pollution degree is impersonal fuzzy concept and phenomenon. Entropy is a very important scientific conception. The entropy of a system was first defined by Boltzmann in 1872. Shannon (1948) developed a mathematical theory of entropy. Jaynes (1957) formulated the Principle of Maximum Entropy (POME), which makes good winning in solution the ill-posed problem. Zadeh (1965)’s Fuzzy Sets has been widely used in many fields. In 1998, Chen made a great progress, which was named Engineering Fuzzy Set Theory. This new developed theory provides a new way to ascertain membership degree and membership function. Now it is clear that studies with the use of entropy, the Principle of Maximum Entropy (POME) and Engineering Fuzzy Set Theory in water resources have been relatively few. Nevertheless, they are promising and justify further research. It is the former studies that provided motivation for our following work. The objective here is to consider both the randomness and the fuzziness of water resources evaluation, based on the Principle of Maximum Entropy (POME), and used the concept and method of Engineering Fuzzy Set Theory. Two weighting generalized distances are defined respectively to build up two fuzzy and optimal models for water resources evaluation. The validity and reliability of modelⅠand modelⅡare proved by the results of eutrophication evaluation of 12 representative lakes and reservoirs in China. The results of these two models are basically identical, and consistent with the survey outcome. Contrasting the fuzzy model in which only the fuzziness is taken into account, the results of two models constructed here are more detailed, and possess lesser Shannon entropy, which means the smaller uncertainty and more reliability. The theory used and the models constructed here can be extended and applied to other fields.