(G,N)蕴涵满足U-MP、U-MT、U-HS不等式的条件  

U-Modus ponens,U-Modus tollens and U-Hypothetical syllogism property of(G,N)-implication

作　　者：于鹏[1] 党思昱 李冉冉 YU Peng;DANG Si-yu;LI Ran-ran(School of Mathematics&Data Science,Shaanxi University of Science&Technology,Xi′an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《陕西科技大学学报》2024年第2期224-232,共9页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(12171294).

摘　　要：(G,N)-蕴涵是由不一定结合的二元分组函数G与模糊否定N生成的一类重要模糊蕴涵算子,深入研究(G,N)-蕴涵算子所满足的性质,对于推广(G,N)-蕴涵在模糊推理中的应用具有积极意义.本文针对(G,N)-蕴涵是否满足U-Modus Ponens,U-Modus Tollens与U-Hypothetical Syllogism不等式的问题展开讨论,给出了(G,N)-蕴涵在一致模U取幂等一致模,可表示一致模情形下,(G,N)-蕴涵满足上述不等式的条件.(G,N)-implication is an important kind of fuzzy implication operator which is generated by the non-necessarily associative binary grouping function G and the fuzzy negation N.It is of positive significance to further study the properties satisfied by the(G,N)-implication operator for promoting the application of(G,N)-implication in fuzzy reasoning.This paper discusses whether the(G,N)-implication satisfies the U-Modus Ponens,U-Modus Tollens and U-Hypothetical Syllogism inequalities,and gives the conditions under which the(G,N)-implication satisfies the above inequality in the case that the uninorm U is idempotent uninorms or representable uninorms.

关 键 词：一致模 (G N)-蕴涵 U-Modus Ponens推理规则 U-Modus Tollens推理规则 

分 类 号：O14[理学—数学]