云模型理论研究及云进化策略的马尔可夫链分析

With more and more in-depth research of cloud model theory, cloud model has been successfully used in many areas such as optimization, system evaluation, data mining, decision support, intelligent control, network security and digital watermarking. But there are still some fundamental problems need to be solved. This project aims at further promoting theoretical research of cloud model and studying the asymptotic behavior of cloud evolution strategies based on Markov chain. The research results will have important theoretical significance and application value.The project focuses specifically on the following four aspects: Firstly, probe into inherent formation mechanisms and mathematical properties of the normal cloud model which is a special heavy-tailed distribution with mean value, and make a comparative analysis with other heavy-tailed distribution. Secondly, study the algorithm and properties of the multivariate normal cloud considering correlation, and then present a multivariate reverse normal cloud algorithm accordingly. Thirdly, explore the mathematical properties of statistical algorithm of algebraic operation of cloud model. Fourthly, prove the convergence of the cloud evolution strategies based on Markov chain theory , estimate the convergence speed, then do some simulation experiments.

随着云模型理论研究的深入发展，在优化计算、系统评测、数据挖掘、决策支持、智能控制、网络安全和数字水印等诸多领域中也得到了越来越广泛的应用，但是还有一些基础性理论问题亟待解决。本项目旨在继续深入研究云模型理论，及基于马尔可夫链建模分析云进化策略的渐近行为，研究成果将具有重要的理论意义和应用价值。本项目具体围绕如下四个方面展开： 1、研究正态云模型这类有平均值的重尾分布的内在形成机制和数学性质，并与其他重尾分布作深入地比较分析；2、研究具有相关性的多维正态云的算法和性质，相应提出一种多维逆向正态云算法；3、研究云模型的代数运算的统计算法的数学性质；4、基于马尔可夫链理论证明云进化策略的收敛性，分析估计其收敛速度，并通过仿真实验进行验证。

云模型是一种可以有效实现语言值表示的定性概念与其定量表示之间不确定性转换的认知计算模型。本项目解决了云模型存在的几个基础理论问题，进一步探讨了其在进化计算、定性评价中的应用，主要包括以下三个方面：①基于概率论与实变函数理论研究了广义正态云模型和多维正态云模型；②探索了云模型在进化计算领域的应用，对云进化策略作了统计分析和改进，提出了两种基于贪心思想和云模型的进化算法，并分别应用于求解旅行商问题和背包问题；③研究了基于云模型的定性评价方法在软件可靠性、教师技能、病房护理满意度、网购风险和满意度等方面的应用。