Zadeh模糊集合理论存在问题证明及其改进——一个满足全部经典集合公式的C-模糊集合系统  

Testification for bug of Zadeh-fuzzy set theory and improvement — C-fuzzy set theory that satisfies all classical set formulas

作　　者：高庆狮[1] 

机构地区：[1]北京科技大学

出　　处：《大连理工大学学报》2005年第5期772-780,共9页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(60343010);"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：Zadeh模糊集合理论具有不能正确描绘客观世界的全部模糊现象,特别是不能描绘相交而不“包含或者分散包含”的情况,不可能存在反集等两个严重缺点;定义了不存在的反集这一严重错误,导致了思维、逻辑和概念混乱.但是,Zadeh等把错误缺点说成为“对传统的挑战”、“摆脱传统的约束”[2-序]的先进成果.企图用“算子”拼盘(不是像概率论那样各种公式有统一的解释)来掩盖缺点,导致了系统混乱(不清楚什么时候需要使用什么算子),误导人们以为模糊集合理论必然与常规思维、逻辑和概念相悖.为此,分析和证明了Zadeh模糊集合的错误.介绍了一个新模糊集合系统:C-模糊集合系统,它能克服Zadeh模糊集合理论的全部错误和缺点,能正确地描绘客观世界的全部模糊现象,有反集.它是经典集合系统的特例而不是推广,能满足全部经典集合的公式,与正常思维、逻辑和概念一致.The shortcomings of Zadeh＇s fuzzy set theory, which can not correctly reflect different kinds of fuzzy phenomena in the natural world, especialy can not depict the phenomenon of cutting without “covering or dispersly covering”, are discussed. In addition, the proof of the error of Zadeh＇s fuzzy set theory, which incorrectly defined the set complement and which cannot exist in Zadeh＇s fuzzy set theory, is proposed. This error of Zadeh＇s fuzzy set theory causes confusion in thinking, logic and conception. Zadeh mistook the shortcomings of [-2-order-] for “challenge to tradition” and as “the advanced results of getting rid of traditional constraints”. He used “operator” （no general explanation as probability theory for different equations） to conceal shortcomings. This idea induced system confusion （no one knows when and what kind of operator is used）, and causes serious mistake of the belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. To solve this problem, a new fuzzy set theory, C-fuzzy set theory is proposed. It has complement, and it can overcome the error and the shortcoming of Zadeh＇s fuzzy set theory, and it is consistent with normal, natural and classical thinking, logic and concepts.

关 键 词：经典集合 Zadeh模糊集合 集合 反集 C-模糊集合 

分 类 号：O159[理学—数学]