论文标题:必然性理论与模糊数的排序及其应用
论文作者
论文导师 袁学海,论文学位 硕士,论文专业 应用数学
论文单位 辽宁师范大学,点击次数 183,论文页数 46页File Size295k
2005-05-01论文网 http://www.lw23.com/lunwen_98397942/
Necessity measure; fuzzy infintegral; fuzzy variables; lead; fuzzy numbers; rank; subfuzzy bases; fuzzy interpolation; nonlinear programming
本文共四章.在第一章中,从本文的需要和预备知识的角度出发,简要概述了可能性理论、模糊数、模糊基及模糊插值映射中的某些基本内容;正文分三部分,即第二、三、四章.第二章在可能性理论的基础上,首先,提出了必然性测度的概念及性质.其次,给出了基于必然性测度的模糊下积分的定义,证明了函数为模糊下可积函数当且仅当它为模糊上可积函数,进而给出模糊可积函数的定义及性质. 最后,证明了由模糊变量ξ诱导的必然性测度与由ξ导出的可能性测度Π_ξ诱导的必然性测度一致,统称为标准必然性测度,从而使可能性理论进一步完善.第三章,通过几种不同的方式给模糊数赋值,给出了模糊数的排序问题的新的方法.第四章,对于一类特殊的模糊基,本文提出了次模糊基的概念,讨论了次模糊基的性质,给出了基于次模糊基的模糊插值映射的定义,并运用模糊插值映射研究了一类非线性规划问题.
This paper has four chapters .The emphasis in the first chapter is mainly on possibility theory ,fuzzy numbers,fuzzy bases and fuzzy interpolation. The main results in this chapter are well-known. For this reason, this chapter can be omitted by the readers who are familiar with the basic concepts and theories of them. The main b ody has three parts, namely the second, the third and the fourth chapter. In chapter two, first, we have put forward the concept of necessity measure on the basis of possibility theory. Second, we have put forward the concept of fuzzy infintegral, proved the function is fuzzy infintegral if and only if it is fuzzy supintegral, then put forward the concept and the characters of the fuzzy integral. Third, we have proved the necessity measure leaded by fuzzy variable ξ is equal to which leaded by Π_ξ. So we call the two kind of necessity measure normal necessity measure. Therefore the possibility theory is made better. In the third chapter, sequencing problem can be solved to a certain extent, by introducing several methods to rank fuzzy numbers. A special class of fuzzy bases , called subfuzzy bases ,have introduced in chapter four ,and we have considered the characters of subfuzzy bases and fuzzy interpolation .We have shown that the nonlinear programming problems can be simplied by means of fuzzy interpolation.
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