L_n*系统中α-反向FMP和α-反向FMT问题的解
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摘要
提出了α-反向FMP、多重α-反向FMP,以及α-反向FMT和多重α-反向FMT问题。通过在F(S)中引入一个预序,在L_n~*系统中,给出了上述问题的解。并说明了这些解从形式上和α-反向三I算法的结果一致,从而在逻辑系统L_n~*中建立了反向三I算法的形式化推理机制。
It proposes problems of α- reverse FMP,collective α- reverse FMP,as well as α-reverse FMT, collective α-reverse FMT. By introducing a preorder in F(S), the solutions for these problems are given in propositional logical system L_n~*. And it clarifies that these solutions can be brought into line with the solutions of methods of α- reverse triple-I.Therefore, formal reasoning system of α-reverse triple-I problems is provided in propositional logical system L_n~*.
It proposes problems of α- reverse FMP,collective α- reverse FMP,as well as α-reverse FMT, collective α-reverse FMT. By introducing a preorder in F(S), the solutions for these problems are given in propositional logical system L_n~*. And it clarifies that these solutions can be brought into line with the solutions of methods of α- reverse triple-I.Therefore, formal reasoning system of α-reverse triple-I problems is provided in propositional logical system L_n~*.
引文
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[2]王国俊.模糊推理的全蕴涵三I算法[J].中国科学:E辑,1999,29(1):43-53.
[3]Wang G J.On the logic of fuzzy reasoning[J].Inform Sci,1999,117(1):47-88.
[4]Wang Guojun,Wang Wei.Partial valuations and fuzzy reasoning[M]//Fuzzy logic and soft computing.[S.l.]:Kluwer Academic Publishers,1999:213-220.
[5]Wang G J.Non-fuzzy versions of reasoning in classical logics[J].Information Sciences,2001,138.
[6]裴道武.模糊推理全蕴涵三I算法及其还原性[J].数学研究与评论,2004(2):359-368.
[7]王国俊.三I算法与区间值模糊推理[J].中国科学:E辑,2000,30(4):331-340.
[8]刘东利,王国俊.多值逻辑系统Wn中α-三I问题的形式解[J].计算机工程与应用,2005,41(25):51-53.
[9]Liu H W,Wang G J.A note on the unified forms of triple I method[J].Comput Math Appl,2006,52:1609-1613.
[10]Wang G J,Fu L.Unified forms of triple I method[J].Comput Math Appl,2005,49:923-932.
[11]李骏,王国俊.基于支持度理论的广义MP问题的形式化解[J].电子学报,2008,36(11):2190-2194.
[12]宋士吉.模糊推理的反向三I算法[J].中国科学:E辑,2002,32(2):230-246.
[13]彭家寅,侯健,李洪兴.基于某些常见蕴涵算子的反向三I算法[J].自然科学进展,2005,15(4):404-410.
[14]秦克云,裴峥.基于?ukasiewicz蕴涵算子的反向三I算法[J].模糊系统与数学,2005,19(2):1-5.
[15]刘东利.模糊推理反向三I问题的真度形式解[J].模糊系统与数学,2012,26(6):1-6.
[16]刘东利,吴棋滢.基于真度理论的α-反向三I问题的形式解[J].模糊系统与数学,2014,28(4):6-10.
[17]王国俊.非经典数理逻辑与近似推理[M].2版.北京:科学出版社,2008.