基于集对分析和模糊集合论的水体营养化评价模型的应用研究

尝试在水环境评价领域引入并应用集对分析和模糊集合论，结合水体营养化等水环境评价中模式识别、等级评价问题的实际应用，将相关的概念和理论进行拓广，定义了广义联系熵和广义相对隶属度。分别建立了基于集对分析的水体营养化评价一级模型和基于集对分析一模糊集合论的水体营养化评价二级模型。我国12个有代表性的湖库营养化程度评价的应用实例表明：所建模型的评价结果与调查结果相符，与单一模糊模式识别结果基本相符；二级模型与一级模型和单一模糊模式相比，评价结果相对全面，更符合用水障碍调查结果的实际情况；而且从广义联系熵判断，二级模型的广义联系熵较一级模型和单一模糊模式大一些，即更好地反映了待评价水样与评价标准两个集合的确定不确定关系和联系程度，从而在一定程度上验证了所建模型的有效性和简便性。文中所用理论方法和所建模型也可推广应用于其他领域。

Research and Application of Model Based on Set Pair Analysis and Fuzzy Set Theory for Evaluation of Water Eutrophication

The basic concept and theory of Set Pair Analysis (SPA) as well as Fuzzy Set Theory (FST) were attempted to apply and develop in the evaluation of water environment. The generalized connexion entropy and the generalized relative membership degree were defined, in order to establish the one-level model based on SPA, and the two-level model based on SPA and FST for evaluation of water eutrophication. The validity and simplicity of the models were proved out by the evaluation results of the eutrophication situations of 12 representative lakes (reservoirs) in China. The results of two founded models are consistent with the survey outcome, and identical approximately to the model in which just the fuzziness is taken into account (simplex fuzzy model). Contrasting the one-level model and the simplex fuzzy model, results of two-level model are more detailed, and possess bigger generalized connexion entropy, which means better reflection on the certain and uncertain relationship and connexion degree between the water samples and the evaluation standard. The theory developed and the model proposed here can be extended and applied to other fields.