满足广义假言推理的模糊蕴涵类  

Families of Fuzzy Implications Satisfying Generalized Hypothetical Syllogism

作　　者：陈斐 覃锋[1] 赵元元 CHEN Fei;QIN Feng;ZHAO Yuan-yuan(College of Mathematics ＆ Information Science,Jiangxi Normal University,Nanchang 330063,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330063

出　　处：《模糊系统与数学》2018年第4期42-57,共16页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61563020);江西省自然科学基金重点资助项目(20171ACB20010)

摘　　要：在模糊推理中,由于广义假言推理(GHS)在模糊蕴涵的选择方面扮演着重要的角色。因此,本文将研究满足(GHS)性质的模糊蕴涵类。但由于模糊蕴涵类太多,其函数方程过于复杂,故本文仅在熟悉的模糊蕴涵(即(S,N)-蕴涵,R-蕴涵,QL-蕴涵,f-蕴涵和g-蕴涵)类中讨论这一问题。另一方面,在一般三角模下研究满足(GHS)的模糊蕴涵并不容易,所以本文假定*=TP,即乘积三角模。研究结论表明在这些模糊蕴涵类中满足(GHS)的模糊蕴涵不多,但是对于文[10]中提出的几类模糊蕴涵都满足(GHS)。最后,我们还检查了几种常见模糊蕴涵的构成方法对(GHS)性质的保持性。In fuzzy reasoning, generalized hypothetical syllogism （GHS） plays a central role in the selection of suitable fuzzy implications for a specific task. Therefore, in this paper, we attempt to investigate the fuzzy implications that do satisfy （GHS）. The variety of fuzzy implications and the equation are so complex that we restrict our investigations of fuzzy implications only for those which come from several well-known families of fuzzy implications, such as （S, N）-,R-, QL- and f-, g-implications of Yager＇s families. On the other hand, it is very difficult to study fuzzy implications satisfying GHS for common t-norms,so we assume ＊=TP in the whole paper. Since these families of well-known fuzzy implications hardly satisfy （GHS）, we investigate some classes of fuzzy implications suggested by [10] and show that every element from these classes satisfies （GHS）. Finally, we check the preservation of （GHS） by some important generating methods of fuzzy implication that exist in the literature.

关 键 词：模糊蕴涵 假言推理 构成方法 

分 类 号：O159[理学—数学]