复模糊集值函数的积分及其应用研究

发布时间：2018-12-16 13:49

【摘要】：本文对模糊测度和模糊积分理论进行了推广,建立了基于复模糊集值测度的复模糊集值函数的积分.首先给出了复模糊集值测度及其性质以及复模糊集值测度空间上的可测函数及其性质.其次研究了基于复模糊集值测度的复模糊集值函数的积分理论,最后以复模糊集值函数的积分作为融合算子,给出了常用的几种复模糊集值积分分类器融合的方法,验证了这种融合方法的可行性、有效性及优越性.具体内容如下：第一章主要介绍了经典测度、模糊测度、模糊积分等概念.第二章建立了复模糊集值测度理论.给出了复模糊集值测度的定义并对其性质进行了探讨.第三章给出了基于复模糊集值测度的复模糊集值可测函数的概念并对其性质进行了研究.第四章基于复模糊集值测度,给出了复模糊集值函数的复模糊积分的概念并研究了其性质.类似于经典的积分理论,给出了复模糊集值函数的复模糊积分的单调收敛定理、法都引理和控制收敛定理.同时建立(S)型复模糊积分和(C)型复模糊积分并对其性质进行了研究.第五章复模糊积分理论在分类器分类技术中的应用.利用复模糊积分的特有性质设计的分类器模型具有较好的融合效果,精度更高、性能更好,而且降低了分类的不确定性.
[Abstract]:In this paper, the theory of fuzzy measure and fuzzy integral is generalized, and the integral of complex fuzzy set-valued function based on complex fuzzy set-valued measure is established. Firstly, the properties of complex fuzzy set-valued measures and the measurable functions and their properties on the space of complex fuzzy set-valued measures are given. Secondly, the integration theory of complex fuzzy set-valued function based on complex fuzzy set-valued measure is studied. Finally, the integration of complex fuzzy set-valued function is taken as the fusion operator, and several common methods of fusion of complex fuzzy set-valued integral classifier are given. The feasibility, effectiveness and superiority of this fusion method are verified. The main contents are as follows: in the first chapter, the concepts of classical measure and fuzzy integral are introduced. In chapter 2, the theory of complex fuzzy set-valued measure is established. The definition of complex fuzzy set-valued measure is given and its properties are discussed. In chapter 3, the concept of complex fuzzy set-valued measurable function based on complex fuzzy set-valued measure is given and its properties are studied. In chapter 4, based on the complex fuzzy set-valued measure, the concept of complex fuzzy integral of complex fuzzy set-valued function is given and its properties are studied. Similar to the classical integral theory, the monotone convergence theorems of complex fuzzy integrals for complex fuzzy set-valued functions, the Lemma of methods and the control convergence theorems are given. At the same time, (S) type complex fuzzy integral and (C) type complex fuzzy integral are established and their properties are studied. Chapter 5 the application of complex fuzzy integral theory in classifier classification technology. The classifier model designed by using the unique property of complex fuzzy integral has better fusion effect, higher precision and better performance, and reduces the uncertainty of classification.
【学位授予单位】：陕西师范大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O159

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