【摘要】：本文對模糊測度和模糊積分理論進行了推廣,建立了基于復模糊集值測度的復模糊集值函數(shù)的積分.首先給出了復模糊集值測度及其性質(zhì)以及復模糊集值測度空間上的可測函數(shù)及其性質(zhì).其次研究了基于復模糊集值測度的復模糊集值函數(shù)的積分理論,最后以復模糊集值函數(shù)的積分作為融合算子,給出了常用的幾種復模糊集值積分分類器融合的方法,驗證了這種融合方法的可行性、有效性及優(yōu)越性.具體內(nèi)容如下：第一章主要介紹了經(jīng)典測度、模糊測度、模糊積分等概念.第二章建立了復模糊集值測度理論.給出了復模糊集值測度的定義并對其性質(zhì)進行了探討.第三章給出了基于復模糊集值測度的復模糊集值可測函數(shù)的概念并對其性質(zhì)進行了研究.第四章基于復模糊集值測度,給出了復模糊集值函數(shù)的復模糊積分的概念并研究了其性質(zhì).類似于經(jīng)典的積分理論,給出了復模糊集值函數(shù)的復模糊積分的單調(diào)收斂定理、法都引理和控制收斂定理.同時建立(S)型復模糊積分和(C)型復模糊積分并對其性質(zhì)進行了研究.第五章復模糊積分理論在分類器分類技術中的應用.利用復模糊積分的特有性質(zhì)設計的分類器模型具有較好的融合效果,精度更高、性能更好,而且降低了分類的不確定性.
[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.
【學位授予單位】：陜西師范大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O159

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