模糊粗糙单调数据挖掘算法及在污水处理中应用研究
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摘要
随着社会发展的日益复杂化,信息的复杂化和海量化使得数据挖掘成为时代研究的一个主题,从而涌现出许多数据挖掘方法,而模糊和粗糙方法就是两个有力数据挖掘工具,粗糙集主要是通过属性的约简实现数据挖掘的功能,但由于它的主要数学基础是等价关系,所以在实际应用时受到许多限制,围绕等价关系,有些人提出相容关系、相邻关系、优势关系、模糊等价关系等拓展关系,同时不少人提出了许多属性约简的算法,但由于这些关系的局限性,还是经常存在数据的一致性问题、连续属性的离散化问题、受不完备数据影响的问题等。在这里,本文通过分析一些现象及以往数学定义的单调的局限性,认为世界是模糊单调的,结合模糊和粗糙的理论方法提出了模糊粗糙单调概念和关系,并提出一些数学模型,讨论了模糊单调关系的一些定义及粗糙性质,指出该关系与等价关系及以往的单调关系之间的关系,进行了相应的粗糙性质拓展。在模糊粗糙单调模型的基础上,结合序与映射的理论,提出区间划分的方法,并提出一些数据挖掘的算法,通过实验验证了算法的有效性,通过与其他属性约简算法的对比分析,体现了算法的优点。最后把模糊粗糙单调的方法和神经网络的方法结合应用。具体的创新点如下:
(1)提出并定义了模糊粗糙单调的关系及概念,提出了四种模糊单调的数学模型,参考粗糙集理论,给出模糊单调的粗糙定义,讨论分析了模糊单调关系和等价关系及一般单调关系的关系,参考粗糙理论,对模糊单调的粗糙性质进行一些拓展。
(2)在决策表和模糊单调模型的基础上,根据序和映射的理论,提出一种区间划分的方法,提出了基于区间最小值和区间平均值的模糊单调隶属函数,通过提出并证明一些命题构建了基于区间最小值和基于区间平均值的模糊单调关系,并讨论它们的参数性质,从而分别得出基于区间最小值的模糊粗糙单调的数据挖掘算法和基于区间平均值的模糊粗糙单调数据挖掘算法,采用UCI的国际污水数据验证了两种算法的有效性,通过分析和设计决策过滤规则进行属性约简从而达到数据挖掘的目的,对比分析了两种算法的知识精细程度和粗糙程度,通过与其他属性约简算法的比较,体现这两种算法的不同点和优点,并给出它们的时间复杂度。
(3)根据包含度的理论,结合模糊粗糙单调的模型方法,在模糊单调Ⅳ模型的基础上,把模糊包含单调的概念引入到决策表中,通过提出并证明一些命题,从而构建了输入的条件属性和输出决策属性之间的模糊包含单调关系,并推导出相应的模糊包含单调决策隶属函数,通过该隶属函数提出基于包含度的模糊粗糙单调数据挖掘算法,同样采样UCI的污水数据验证该算法有效性,通过与前面两种算法的对比分析,得出该算法的不同特点和效果,通过与其他基于包含度的属性约简算法的比较,得出它的不同点及优点,通过与其他属性约简算法的比较,体现了它的优点。
(4)通过对污水溶解氧控制模型的分析,提出了一种基于RBF神经网络的污水溶解氧预处理模型,采用某污水厂的数据结合遗传优化的方法对该模型方法进行验证,肯定了该模型方法在一定范围内的有效性,同时指出存在的一些问题,提出模糊粗糙单调的RBF神经网络预测模型,通过UCI的污水数据验证了该方法的有效性,并指出它改善了前一种方法存在的一些问题,提出了模糊粗糙单调的RBF神经网络溶解氧预测处理模型,是模糊粗糙单调方法与神经网络方法的结合应用。
With more and more complexity of society development, data mining becomes an era research topic because of the complexity and the magnitude of information, so many data mining methods appear, and fuzzy and rough methods are two important tools for data mining. Rough sets acts as the data mining function mainly through the attributes reduction, but because the base of its mathematic is equivalent relationship, so there is much limit in many applications, then some people present some extensive relationship around the equivalent relationship such as consistent relationship, adjacent relationship, dominance relationship, and fuzzy equivalent relationship etc, at the same time many people present many attributes reduction algorithms. But because of the limit of these relationships, there always exist some problems in those attributes reduction algorithms based on them for application such as data inconsistent, the disperse of continuum data, data imperfect etc. Here this paper presents an idea that the world is fuzzy monotone after analyzing some phenomenon and the limit of current monotone definition in math, and then presents fuzzy rough monotone concept with relationship and some mathematic models combining with fuzzy and rough methods. Then some definitions of fuzzy monotone relationship and rough property are discussed, and the relationship is pointed out among fuzzy monotone relationship, equivalence relationship and current mathematic monotone relationship, then some rough properties are developed in fuzzy monotone relationship. Some data mining methods are presented based on advance zone partition methods method and fuzzy rough monotone model, which is through adopting the order and map theory. After the experiment, effects of these algorithms are validated and their merit is shown through the comparisons with other attributes reduction algorithms. At last fuzzy rough monotone method are combined using with neural networks. Innovative points in this paper are as follows:
(1) Fuzzy rough monotone relationship and concept are presented and defined; four fuzzy monotone mathematic models and the rough definition of fuzzy monotone models are presented according to rough theory. The relationship among fuzzy monotone relationship, equivalent relationship and normal monotone relationship is discussed and analyzed; some rough properties of fuzzy monotone models are developed according to the rough theory.
(2) A zone partition method is presented according to the order and map theory based on decision table and fuzzy monotone models; two fuzzy monotone membership functions are presented based on minimum and average value of zone separately; two fuzzy monotone relationships are constructed and their parameters properties are discussed after some propositions are presented and proved; then two data mining algorithms based on minimum and average value of zone separately are presented; the UCI international wastewater data are used to validate the effect of two data mining algorithms after the decision rules being analyzed and designed; the rough and fine degree of these two data mining algorithms is compared and analyzed; the merits and different properties are shown thorough the comparison of other attributes reduction algorithms, and the time complexity is given too.
(3) Fuzzy inclusive monotone concept is introduced into decision table according to inclusion theory and fuzzy monotone model methods based on fuzzy monotoneⅣmodel; the fuzzy inclusive monotone relationship between input condition attributes and output decision attributes is constructed after some propositions are presented and proved; the fuzzy inclusive monotone decision membership function is deduced; the fuzzy rough monotone data mining algorithm based inclusion degree is presented based on the membership function; the different properties and the effect of the algorithm is shown by the comparison of above two algorithms; the merit of the algorithm is shown by the comparison of other attributes reduction and those based on inclusion degree too;
(4) A pretreatment model of wastewater dissolved oxygen based on RBF neural networks is presented through the analysis of wastewater dissolved oxygen control model; the model is effective in certain extension and exists some problems after the validation of the data of a guangzhou wastewater treatment factory combined with evolutionary optimized method, then a fuzzy rough monotone RBF neural networks forecast model is presented and its effect is validated by UCI wastewater data ,and some problems for former model method are improved in latter model method; then a fuzzy rough pretreatment model of wastewater dissolved oxygen based on RBF neural networks is presented, which is combined using fuzzy rough monotone method and neural networks method.
(1)提出并定义了模糊粗糙单调的关系及概念,提出了四种模糊单调的数学模型,参考粗糙集理论,给出模糊单调的粗糙定义,讨论分析了模糊单调关系和等价关系及一般单调关系的关系,参考粗糙理论,对模糊单调的粗糙性质进行一些拓展。
(2)在决策表和模糊单调模型的基础上,根据序和映射的理论,提出一种区间划分的方法,提出了基于区间最小值和区间平均值的模糊单调隶属函数,通过提出并证明一些命题构建了基于区间最小值和基于区间平均值的模糊单调关系,并讨论它们的参数性质,从而分别得出基于区间最小值的模糊粗糙单调的数据挖掘算法和基于区间平均值的模糊粗糙单调数据挖掘算法,采用UCI的国际污水数据验证了两种算法的有效性,通过分析和设计决策过滤规则进行属性约简从而达到数据挖掘的目的,对比分析了两种算法的知识精细程度和粗糙程度,通过与其他属性约简算法的比较,体现这两种算法的不同点和优点,并给出它们的时间复杂度。
(3)根据包含度的理论,结合模糊粗糙单调的模型方法,在模糊单调Ⅳ模型的基础上,把模糊包含单调的概念引入到决策表中,通过提出并证明一些命题,从而构建了输入的条件属性和输出决策属性之间的模糊包含单调关系,并推导出相应的模糊包含单调决策隶属函数,通过该隶属函数提出基于包含度的模糊粗糙单调数据挖掘算法,同样采样UCI的污水数据验证该算法有效性,通过与前面两种算法的对比分析,得出该算法的不同特点和效果,通过与其他基于包含度的属性约简算法的比较,得出它的不同点及优点,通过与其他属性约简算法的比较,体现了它的优点。
(4)通过对污水溶解氧控制模型的分析,提出了一种基于RBF神经网络的污水溶解氧预处理模型,采用某污水厂的数据结合遗传优化的方法对该模型方法进行验证,肯定了该模型方法在一定范围内的有效性,同时指出存在的一些问题,提出模糊粗糙单调的RBF神经网络预测模型,通过UCI的污水数据验证了该方法的有效性,并指出它改善了前一种方法存在的一些问题,提出了模糊粗糙单调的RBF神经网络溶解氧预测处理模型,是模糊粗糙单调方法与神经网络方法的结合应用。
With more and more complexity of society development, data mining becomes an era research topic because of the complexity and the magnitude of information, so many data mining methods appear, and fuzzy and rough methods are two important tools for data mining. Rough sets acts as the data mining function mainly through the attributes reduction, but because the base of its mathematic is equivalent relationship, so there is much limit in many applications, then some people present some extensive relationship around the equivalent relationship such as consistent relationship, adjacent relationship, dominance relationship, and fuzzy equivalent relationship etc, at the same time many people present many attributes reduction algorithms. But because of the limit of these relationships, there always exist some problems in those attributes reduction algorithms based on them for application such as data inconsistent, the disperse of continuum data, data imperfect etc. Here this paper presents an idea that the world is fuzzy monotone after analyzing some phenomenon and the limit of current monotone definition in math, and then presents fuzzy rough monotone concept with relationship and some mathematic models combining with fuzzy and rough methods. Then some definitions of fuzzy monotone relationship and rough property are discussed, and the relationship is pointed out among fuzzy monotone relationship, equivalence relationship and current mathematic monotone relationship, then some rough properties are developed in fuzzy monotone relationship. Some data mining methods are presented based on advance zone partition methods method and fuzzy rough monotone model, which is through adopting the order and map theory. After the experiment, effects of these algorithms are validated and their merit is shown through the comparisons with other attributes reduction algorithms. At last fuzzy rough monotone method are combined using with neural networks. Innovative points in this paper are as follows:
(1) Fuzzy rough monotone relationship and concept are presented and defined; four fuzzy monotone mathematic models and the rough definition of fuzzy monotone models are presented according to rough theory. The relationship among fuzzy monotone relationship, equivalent relationship and normal monotone relationship is discussed and analyzed; some rough properties of fuzzy monotone models are developed according to the rough theory.
(2) A zone partition method is presented according to the order and map theory based on decision table and fuzzy monotone models; two fuzzy monotone membership functions are presented based on minimum and average value of zone separately; two fuzzy monotone relationships are constructed and their parameters properties are discussed after some propositions are presented and proved; then two data mining algorithms based on minimum and average value of zone separately are presented; the UCI international wastewater data are used to validate the effect of two data mining algorithms after the decision rules being analyzed and designed; the rough and fine degree of these two data mining algorithms is compared and analyzed; the merits and different properties are shown thorough the comparison of other attributes reduction algorithms, and the time complexity is given too.
(3) Fuzzy inclusive monotone concept is introduced into decision table according to inclusion theory and fuzzy monotone model methods based on fuzzy monotoneⅣmodel; the fuzzy inclusive monotone relationship between input condition attributes and output decision attributes is constructed after some propositions are presented and proved; the fuzzy inclusive monotone decision membership function is deduced; the fuzzy rough monotone data mining algorithm based inclusion degree is presented based on the membership function; the different properties and the effect of the algorithm is shown by the comparison of above two algorithms; the merit of the algorithm is shown by the comparison of other attributes reduction and those based on inclusion degree too;
(4) A pretreatment model of wastewater dissolved oxygen based on RBF neural networks is presented through the analysis of wastewater dissolved oxygen control model; the model is effective in certain extension and exists some problems after the validation of the data of a guangzhou wastewater treatment factory combined with evolutionary optimized method, then a fuzzy rough monotone RBF neural networks forecast model is presented and its effect is validated by UCI wastewater data ,and some problems for former model method are improved in latter model method; then a fuzzy rough pretreatment model of wastewater dissolved oxygen based on RBF neural networks is presented, which is combined using fuzzy rough monotone method and neural networks method.
引文
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