概率论基本部分与模糊集合理论的统一定义  

A uniform definition of fuzzy set theory and fundamental of probability theory

作　　者：高庆狮[1] 高小宇[1] 胡月[1] 

机构地区：[1]北京科技大学

出　　处：《大连理工大学学报》2006年第1期141-150,共10页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(6034301060573014);"973"国家重点基础研究资助项目(2003CB317007);中国科学院计算技术研究所创新工程资助项目(20056510)

摘　　要：提出一个概率论的基本部分与模糊集合理论的统一理论,称为W-理论.它可以解释为概率论,也可以解释为新模糊集合理论(称做P-模糊集合理论,它与C-模糊集合理论等价),而Zadeh-模糊集合理论是新模糊集合理论的一个有三个缺点和两个错误的子系统.这里,模糊集合对应于(带概率的)事件,隶属度对应于概率,关系系数对应于条件概率,等等.模糊集合之间关系与概率论的事件之间关系一样,不仅有不相交,非一致包含,相交而不非一致包含,而且还有相互独立,等等.新模糊集合理论与概率论的基本部分是同构的.A uniform definition of fuzzy set theory and probability theory, called W-theory, is proposed. W-theory can be considered as both the fuzzy set theory （called P-fuzzy set theory, it is equivalent to C-fuzzy set theory） and the fundamental part of the probability theory. And the Zadeh＇s fuzzy set theory is a sub-system with two mistakes and three shortcomings of new fuzzy set theory. Here the fuzzy set corresponds to the event （with probability）, the membership corresponds to probability, and the relation-coefficient corresponds to the conditional probability, etc.. The relation between two fuzzy sets has mutual disjoint, mutual nonLuniformly inclusive, mutual interceptive but not non-uniformly inclusive, and independent, as the same as in probability theory. New fuzzy set theory is isomorphic to the fundamental part of probability theory.

关 键 词：概率论 P-模糊集合理论 C-模糊集合理论 Zadeh-模糊集合理论 

分 类 号：O159[理学—数学]