载入中....
设为首页 收藏本站 联系我们 网站地图
论文网
您现在的位置: 免费毕业论文网 >> 理学论文 >> 数学 >> 正文
搜索: 论文

随机模糊集与概率模糊集的研究

更新时间 2009-9-20 10:13:28 点击数:

随机模糊集与概率模糊集的研究
The Study of Probabilistic Fuzzy Sets and R-fuzzy Sets
【中文摘要】 模糊集理论是1965年由控制论专家L.A.Zadeh第一个引入的。之后,模糊集和模糊系统理论被广泛应用到许多领域,在模糊数学领域逐渐形成了模糊拓扑学、模糊分析学、模糊代数学和非经典逻辑等系统的理论。为了建立模糊集的理论基础,人们做了许多工作,形成了如:集合套理论、模糊集和随机集落影理论及γ-模糊集理论。这些研究成果显示,模糊集理论与概率论有着密切的联系。1975年,Hirota引入了模糊概率集的概念。之后,Gerstenkorn和Manko提出了双模糊概率集的概念,这些研究工作在模糊集和概率论之间建立了联系。然而,迄今为之,随机模糊集和概率模糊集之间的联系还没有被讨论过。本文的目的就是在随机模糊集和概率模糊集之间建立联系。首先,讨论模糊概率集和γ-模糊集之间的联系。给出了一个新的概念γ-模糊集合套,指出模糊概率集可看作是γ-模糊集合套的等价类。其次,对γ-模糊集的概念在直觉模糊集理论上作了推广,给出了γ-直觉模糊集的概念及γ-直觉集合套的概念,并讨论了其性质。最后,利用γ-直觉集合套讨论了由Gerstenkorn提出的双模糊概率集和γ-直慌模糊集之间的联系。

【英文摘要】 Content:The theory of fuzzy sets was first introduced by control theory professor L.A.Zadeh.Since then,the theory of fuzzy sets and fuzzy systems was applied in many fields.In the field of fuzzy mathematics, many mathematical theory such as fuzzy topology,fuzzy analysis, fuzzy algebra and fuzzy logic,etc.,are obtained.In order to build the theory base of fuzzy sets,people presented many works such as the theory of nested sets,the theory of fuzzy sets and falling shadows of random sets and the theory of r-fuzzy sets.Their works have shown that the theory of fuzzy sets has intimate connection with probability theory.In 1975,Hirota introduced the concept of fuzzy probabilistic sets.Then,Gerstenkorn and Manko introduced the concept of bifuzzy probabilistic sets.Those works built a connection between fuzzy sets and probability theory,However,the relations between r-fuzzy sets and probabilistic fuzzy sets have not been described so far.The aim of this paper is to build a connection between probabilistic fuzzy sets and r-fuzzy sets.Firstly,The relations between fuzzy probabilistic sets and r-fuzzy sets are discussed.A new concept of r-fuzzy nested set is presented and it is pointed a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set.Secondly,we generalize the concept of r-fuzzy set on r-fuzzy set theory,and the concept of r-bifuzzy set and r-bifuzzy nested set is presented.Then the properties of it are studied.Finally,by the use of r-bifuzzy nested set,the relations between r-bifuzzy set and bifuzzy probabilistic set presented by Gerstenkorn are discussed.

【中文关键词】 模糊概率集; r-模糊集; r-模糊集合套; 双模糊概率集; r-直觉模糊集; r-直觉集合套
【英文关键词】 fuzzy probabilistic set; r-fuzzy set; r-fuzzy nested set; bifuzzy probabilistic set; r-bifuzzy set; r-bifuzzy nested set
毕业论文目录】
摘要 2-3
Abstract 3
1.引言 6-7
2.预备知识 7-13
3.模糊概率集和r-模糊集 13-17
4.双模糊概率集和r-直觉模糊集 17-27
5.结论 27-28
参考文献 28-29
致谢 29-30

返回栏目页:数学论文

设为主页】【收藏论文】【保存论文】【打印论文】【回到顶部】【关闭此页