Zadeh模糊集合理论的缺陷及其改进:C*-模糊集合理论  

Defects and overcoming of Zadeh's fuzzy set theory: C*-fuzzy set theory

作　　者：高庆狮[1] 

机构地区：[1]北京科技大学智能,语言与计算机科学研究所,北京100083

出　　处：《北京科技大学学报》2005年第5期513-519,共7页Journal of University of Science and Technology Beijing

基　　金：国家自然科学基金(No.GJZRJJ-60343010;GJZRJJ-60573014)"973"项目(No.2003CB317007)中国科学院计算技术研究所创新工程基金(No.20056510)

摘　　要：分析和证明了Zadeh模糊集合理论的三个缺点和两个错误,提出了一个考虑模糊集合之间关系,并且用相关系数来刻画这种关系的程度的新模糊集合理论(系统)——C*-模糊集合理论(系统).新理论(系统)能克服Zadeh模糊集合理论的三个缺点和两个错误;能正确地描绘客观世界的全部模糊现象;有补集;隶属度有统一的计算公式;并且是经典集合系统的特例,能满足全部经典集合的公式,与正常思维、逻辑和概念一致.Three shortcomings and two errors of Zadeh＇s fuzzy set theory were analyzed and proved, and a new fuzzy set theory, C^＊-fuzzy set theory, was proposed. The new C^＊-fuzzy set considers the relationship between fuzzy sets and represents the relationship with relativity. It overcomes all the errors and shortcomings of Zadeh＇s fuzzy set theory： it correctly reflects different kinds of fuzzy phenomena in the natural world; set complement exists on it; it has uniform calculating formulas for membership; it satisfies all formulas of the classical set theory and is consistent with classical and normal thinking, logic and concepts.

关 键 词：集合 模糊集合 Zadeh模糊集合理论:C^＊-模糊集合理论 

分 类 号：O159[理学—数学]