一种新型模糊映射  

A New Type of Fuzzy Mappings

作　　者：朱翔[1,2] 廖祖华[2] ZHU Xiang;LIAO Zu-hua(Division of General Courses, Wuxi Institute of Technology, Wuxi 214121, China;School of Science, Jiangnan University, Wuxi 214122, China)

机构地区：[1]无锡职业技术学院基础部,江苏无锡214121 [2]江南大学理学院,江苏无锡214122

出　　处：《模糊系统与数学》2018年第3期54-63,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61673193;61170121;11401259);江苏省自然科学基金资助项目(BK20151117);江苏省高等职业院校专业带头人高端研修资助项目(2016GRFX057)

摘　　要：模糊映射在模糊优化、模糊评判、模糊控制和模糊决策等领域有着大量的应用。通过对Zadeh扩展原理和极小扩展原理的研究,提出了一种新型模糊映射,它是极小扩展原理的推广。另外,对该新型模糊映射进行研究,得到了它在模糊集运算下的性质以及一个模糊集在该新型模糊映射下的像的分解定理。最后,讨论了模糊集与新型模糊映射的相容性问题,得到了模糊集在新型模糊映射下的最小原像定理。Fuzzy mapping has a lot of applications in the fields of fuzzy optimization,fuzzy evaluation,fuzzy control and fuzzy decision.Based on the study of Zadeh extension principle and minimal extension principle,a new fuzzy mapping is proposed,which is a generalization of minimal extension principle.In addition,the new fuzzy mapping is studied,and its properties under fuzzy set operation is given.And the decomposition theorem of a fuzzy set under the new fuzzy mapping is obtained.Finally,the compatibility of fuzzy sets with new fuzzy mappings is discussed,and the minimum theorem is obtained under the new fuzzy mappings.

关 键 词：模糊集 模糊映射 扩展原理 最小原像 

分 类 号：O159[理学—数学]