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[1]赵森烽,赵克勤.几何概型的联系概率（复概率）与概率的补数定理[J].智能系统学报,2013,8(1):11-15.[doi:10.3969/j.issn.1673-4785.201208025]
　ZHAO Senfeng,ZHAO Keqin.Contact probability (complex probability) of the geometry probability and the complement number theorem of probability[J].CAAI Transactions on Intelligent Systems,2013,8(1):11-15.[doi:10.3969/j.issn.1673-4785.201208025]

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几何概型的联系概率（复概率）与概率的补数定理

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《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷: 8 期数: 2013年第1期页码: 11-15 栏目: 学术论文—人工智能基础出版日期: 2013-03-25

Title:: Contact probability (complex probability) of the geometry probability and the complement number theorem of probability

文章编号:: 1673-4785(2013)01-0011-05

作者:: 赵森烽¹，赵克勤^2，3; 1.浙江工业大学之江学院理学系，浙江杭州 310024；
2.诸暨市联系数学研究所，浙江诸暨 311811；
3.浙江大学非传统安全与和平发展中心，浙江杭州 310058

Author(s):: ZHAO Senfeng¹, ZHAO Keqin^2,3; 1.Department of Science， Zhijiang College of Zhejiang University of Technology, Hangzhou 310024, China;
2.Zhuji Institute of Connection Mathematics, Zhuji 311811, China;
3.Center for Nontraditional Security and Peaceful Development Studies, Zhejiang University, Hangzhou 310058, China

关键词:: 随机试验; 几何概型; 联系概率（复概率）; 概率; 表现定理; 补数定理

Keywords:: random test; geometry probability; contact probability (complex probability); probability; representation theorem; inverse theorem

分类号:: TP18

DOI:: 10.3969/j.issn.1673-4785.201208025

文献标志码:: A

摘要:: 为研究等可能随机试验结果为无穷多时的联系概率计算和应用，借助简单的“均匀投针”随机试验，导出几何概型的联系概率(复概率).该联系概率中的主概率和伴随概率依次对应于主事件的大数概率（主概率）和主事件的即或概率（伴随事件的大数概率）.在此基础上给出了随机事件的表现定理和概率的补数定理，利用后者可以在已知一个随机事件概率的基础上方便地得到该事件的联系概率.通过实例说明了几何概型的联系概率与古典概型的联系概率具有同样的形式和性质.

Abstract:: In order to research the calculation and application of contact probability when the result of equally likely random trial is infinite, the researcher utilized the simple “uniform needle” random test to derive contact probability (complex probability) of geometry probability. The main probability and the concomitant probability of the contact probability respectively correspond to the great number probability (main probability) of the main event and the even if probability (great number probability of concomitant event) of the main event. And on this basis, the representation theorem of the random event and complement number theorem of probability were provided in the study. The complement number theorem was used to conveniently find the contact probability of the event based on the premise of knowing the probability of a random event. The results illustrated that the contact probability of geometry probability had the same form and property with the contact probability of typical probability.

参考文献/References:: ［1］赵森烽，赵克勤．概率联系数化的原理与联系概率在概率推理中的应用［J］．智能系统学报, 2012, 7(3): 200-205. 
ZHAO Senfeng, ZHAO Keqin. The principle of the probability of connection number and application in probabilistic reasoning［J］. CAAI Transactions on Intelligent Systems, 2012, 7(3): 200-205.
［2］赵克勤．集对分析的不确定性理论在AI中的应用［J］．智能系统学报, 2006, 1(2): 16-25. 
ZHAO Keqin. The application of uncertainty systems theory of set pair analysis (SPA) in the artificial intelligence［J］. CAAI Transactions on Intelligent Systems, 2006, 1(2): 16-25.
［3］赵克勤．二元联系数A+Bi的理论基础与基本算法及在人工智能中的应用［J］．智能系统学报, 2008, 3(6): 476-486. 
ZHAO Keqin. The theoretical basis and basic algorithm of binary connection A+Bi and its application in AI［J］. CAAI Transactions on Intelligent Systems, 2008, 3(6): 476-486.
［4］赵克勤．集对分析及其初步应用［M］．杭州：浙江科技出版社, 2000: 44-64.
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ZHAO Keqin, XUAN Aili. Set pair theory—a new theory method of non define and its applications［J］. Systems Engineering, 1996, 14(1): 18-23.
［6］赵克勤．试论集对分析与概率论的关系［C］//中南模糊系统与数学论文集．长沙：湖南科技出版社, 1995: 253.
［7］王梓坤．概率论基础及其应用［M］．北京：科学出版社, 1979: 1-219.
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相似文献/References:: [1]赵森烽,赵克勤.频率型联系概率与随机事件转化定理[J].智能系统学报,2014,9(1):53.[doi:10.3969/j.issn.1673-4785.201305003]
　ZHAO Senfeng,ZHAO Keqin.Frequency-type contact probability and random events transformation theorem[J].CAAI Transactions on Intelligent Systems,2014,9():53.[doi:10.3969/j.issn.1673-4785.201305003]

备注/Memo

收稿日期：2012-08-18.
网络出版日期：2013-01-25.
基金项目：国家社会科学基金重点资助项目(08ASH006)；教育部哲学社会科学研究重大课题攻关项目(08JZD0021D).
通信作者：赵克勤.
E-mail: zjzhaok@sohu.com.
作者简介：
赵森烽，男，1993年生，主要研究方向为信息与计算、集对分析、联系概率等，发表学术论文1篇.
赵克勤，男，1950年生，研究员，中国人工智能学会理事、人工智能基础专业委员会副主任、集对分析联系数学专业筹备委员会主任.主要研究方向为联系数学，1989年提出集对分析（联系数学），发表学术论文90余篇，出版专著1部.

更新日期/Last Update: 2013-04-12

几何概型的联系概率（复概率）与概率的补数定理 PDF下载HTML

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几何概型的联系概率（复概率）与概率的补数定理

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