A New Fuzzy Set Theory Satisfying All Classical Set Formulas

	A New Fuzzy Set Theory Satisfying All Classical Set Formulas
	Gao, Qing-Shi 1,2; Gao, Xiao-Yu 2; Hu, Yue 1,2
	2009-07-01
发表期刊	JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY
ISSN	1000-9000
卷号	24 期号:4 页码:798-804
摘要	A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be "non-uniform inclusive" to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z(0)-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh's fuzzy set system. Analysis shows that 1) Zadeh's fuzzy set system defines the relations A = B and A subset of B between two fuzzy sets A and B as "for all u is an element of U, (mu(A) is an element of (u) = mu(B)(u))" and "for all u is an element of U, (mu(A)(u) <= mu(B)(u))" respectively is inappropriate, because it makes all fuzzy sets be "non-uniformly inclusive"; 2) it is also inappropriate to define two fuzzy sets' union and intersection operations as the max and min of their grades of membership, because this prevents fuzzy set's ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min {a + b, 1} and max{a + b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3) it is incorrect to define the set complement as 1 - mu(A)(u), because it can be proved that set complement cannot exist in Zadeh's fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the classical set theory. It is consistent with normal, natural, and classical thinking, logic, and concepts.
关键词	fuzzy set Zadeh's fuzzy set classical set C-fuzzy set
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[60343010] ; National Basic Research 973 Program of China[2003 CB317000] ; Foundation of Institute of Computing Technology, Chinese Academy of Sciences[20056510]
WOS研究方向	Computer Science
WOS类目	Computer Science, Hardware & Architecture ; Computer Science, Software Engineering
WOS记录号	WOS:000268249500017
出版者	SCIENCE PRESS
引用统计	被引频次：3[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/11738
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Gao, Qing-Shi
作者单位	1.Univ Sci & Technol Beijing, Dept Comp Sci, Beijing 100083, Peoples R China 2.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gao, Qing-Shi,Gao, Xiao-Yu,Hu, Yue. A New Fuzzy Set Theory Satisfying All Classical Set Formulas[J]. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,2009,24(4):798-804.
APA	Gao, Qing-Shi,Gao, Xiao-Yu,&Hu, Yue.(2009).A New Fuzzy Set Theory Satisfying All Classical Set Formulas.JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,24(4),798-804.
MLA	Gao, Qing-Shi,et al."A New Fuzzy Set Theory Satisfying All Classical Set Formulas".JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY 24.4(2009):798-804.