gλ模糊测度和模糊积分的进一步分析及应用word论文.docxVIP

g??模糊测度和模糊积分的进一步研究及应用 摘要模糊数学作为一门新兴的学科，是经典数学的重要推广，具有很重要的理 论意义。经过几十年的短暂发展，模糊数学与经典数学相互渗透，形成了很多 新的学科，如模糊拓扑学、模糊随机数学、模糊分析学以及模糊逻辑理论等几 大分支，每一个分支内涵都十分的丰富。自从 1974 年 Sugeno M 首次引入模糊测度和模糊积分的概念以来，国内外 众多学者研究了许多关于模糊测度和模糊积分的问题，得到了一些很好的结论。 近年来，模糊测度及由其定义的模糊积分已经在模式识别、信息融合、计算机 视觉中得到了成功的应用。因此，研究特殊结构的模糊测度和模糊积分是十分 必要的。本文所研究的问题有以下几个方面： 首先，介绍了模糊测度和模糊积分的相关内容，然后又介绍了 g??模糊测度的定义和相关性质，为文章的后续内容奠定了基础。其次，研究了 g??模糊测度无穷级数敛散性，在引入广义可加的概念下，讨???论了 g 模糊测度与 g??概率测度的转化定理。同时对 g 模糊积分的相关性质加 以证明，并讨论了其收敛定理。最后，利用模糊数学的相关知识给出了一级和多级模糊综合评判模型，讨论了结合交互作用的综合评判，给出了 g??模糊测度表示交互作用的能力。并把 模糊综合评判和结合交互作用的综合评判简单应用于教学质量评价和学生评价 等方面。关键词 g??模糊测度； g??模糊积分；广义可加性；模糊综合评价Further Research of theg??Fuzzy Measure and Fuzzy Integral and Its ApplicationAbstractAs an newly emerging discipline, fuzzy mathematics with important theoretical significance is a important popularity of classical mathematics. After decades of brief development, by interpenetrating with classical mathematics it has formed many new subjects, such as fuzzy topology, random fuzzy mathematics, fuzzy analysis and fuzzy logic theory and so on. And each branch is with rich connotation.Many domestic and foreign scholars have achieved many good conclusions by doing research on Fuzzy measure and Fuzzy integral since the concept of fuzzy measure and fuzzy integral was first introduced by Sugeno M in 1974. In recent years, fuzzy measure and fuzzy integral has been successfully applied to pattern recognition, computer vision, information fusion. Therefore, the research of special structure of fuzzy measure and fuzzy integral is very necessary.In this paper, the research problems are as follows:First, this paper introduces the related contents of fuzzy measure and fuzzy integral, and then introduces the definition and related properties of g??fuzzy measure, which laid a foundation for the subsequent content.?Secondly, studied the convergence or divergence of g??fuzzy measure infinite series, with the introduction of the concept of generalized additive, discussed the transformation