一种基于二型模糊的广义模糊软集  

A Generalized Fuzzy Soft Set Based on Type-2 Fuzziness

作　　者：祖璇 汪峰[2] ZU Xuan;WANG Feng(Wanjiang College,Anhui Normal University, Anhui Wuhu 241008, China;School of Mathematical Sciences, Anhui University, Hefei 230601, China)

机构地区：[1]安徽师范大学皖江学院,安徽芜湖241008 [2]安徽大学数学科学学院,合肥230601

出　　处：《重庆工商大学学报（自然科学版）》2018年第3期10-17,共8页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金资助项目(71371011);安徽省高等学校省级自然科学研究重点项目(KJ2013A033);安徽大学研究生创新项目资助

摘　　要：针对普通模糊子集隶属度的模糊性,介绍了二型模糊集及现实刻画的合理性,然后从实际问题出发,提出了广义模糊软集的概念;在此基础上,研究广义模糊软集的包含关系,交、并、补运算和有关性质,并讨论基于广义模糊软集下的模糊软关系和模糊软矩阵,且进一步探讨与广义模糊软集平行的运算及性质;最后将广义模糊软集应用到医疗诊断中,通过解模糊,构造得分函数判断病人的患病类型,从而验证了它的可行性与有效性.For the fuzziness of the membership degree of fuzzy subsets,the concept of a type-2 fuzzy set and the rationality of describing the reality with it are introduced. Beginning with the practical problems,the concept of generalized fuzzy soft sets is proposed. On that basis,the inclusion relation,intersection,union,complement operations and related properties of generalized fuzzy soft sets are studied. Besides,this paper discusses fuzzy soft relation and fuzzy soft matrix based on generalized fuzzy soft sets,and further explores the operations and properties as generalized fuzzy soft sets. Finally,the generalized fuzzy soft sets are applied to medical diagnosis,a patient＇s type of his or her disease is judged by defuzzification and construction of score function,and the feasibility and validity of the generalized fuzzy soft set are verified.

关 键 词：二型模糊集 广义模糊软集 模糊软关系 模糊软矩阵 解模糊 得分函数 

分 类 号：O159[理学—数学]