区间值模糊推理的CRI方法
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摘要
讨论了区间值上的三角模及伴随性质,获得了几个重要的结果.利用区间值上的三角模和蕴涵算子,分别给出了FMP与FMT问题的区间值模糊推理的CRI算法解的计算公式.针对区间值上的三角模和蕴涵算子,特别是剩余型伴随对,讨论了FMP、FMT问题的区间值模糊推理的CRI算法的还原性.
The triangular norms and their adjoint properties on the interval-valued set are discussed,and some important results are obtained.By using the triangular norms and implication operators on the interval-valued set,the formulas of solutions of CRI algorithms for interval-valued fuzzy reasoning of FMP and FMT problems are worked out respectively.Aiming at the triangular modules and implication operators on interval-valued set,particularly the residual adjoint pair,the reductive properties of CRI algorithm for interval-valued fuzzy reasoning of FMP and FMT are discussed.
The triangular norms and their adjoint properties on the interval-valued set are discussed,and some important results are obtained.By using the triangular norms and implication operators on the interval-valued set,the formulas of solutions of CRI algorithms for interval-valued fuzzy reasoning of FMP and FMT problems are worked out respectively.Aiming at the triangular modules and implication operators on interval-valued set,particularly the residual adjoint pair,the reductive properties of CRI algorithm for interval-valued fuzzy reasoning of FMP and FMT are discussed.
引文
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[2]ZADEH L A.Outline of a new approach to the analysis of complex systems and decision processes[J].IEEE Transactions on Systems Man&Cybernetics,1973,3(1):28-44.
[3]MAMDANI E H.Application of fuzzy logic to approximate reasoning using linguistic synthesis[J].IEEE Transactions on Computers,1977,26(12):1182-1191.
[4]DUBOIS D,PRADE H.Fuzzy sets in approximate reasoning,Part 1:Inference with possibility distributions[J].Fuzzy Sets and Systems,1991,40(1):143-202.
[5]吴望名.关于模糊逻辑的一场争论[J].模糊系统与数学,1995(2):1-9.
[6]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.
[7]WANG G J.On the logic foundation of fuzzy reasoning[J].Information Sciences,1999,117(1/2):47-88.
[8]李洪兴.模糊控制的插值机理[J].中国科学:技术科学,1998,28(3):259-267.
[9]SONG S,FENG C,LEE E S.Triple I method of fuzzy reasoning[J].Computers and Mathematics with Applications,2002,44:1567-1579.
[10]WANG G J,FU L.Unified forms of Triple I method[M].Pergamon Press,Inc.2005.
[11]LIU H W,WANG G J.A Note on the Unified Forms of Triple I Method[J].Computers&Mathematics with Applications,2006,52(10):1609-1613.
[12]PEI D W.Full implication triple I algorithms and their consistency in fuzzy reasoning[J].Journal of Mathematical Research&Exposition,2004,24(2):359-368.
[13]彭家寅,李洪兴,侯健,等.基于逐点优化模糊推理的模糊控制器及其插值机理[J].系统科学与数学,2005,25(3):311-322.
[14]李洪兴.变论域自适应模糊控制器[J].中国科学:E辑,1999,29(1):32-42.
[15]李洪兴,彭家寅,王加银,等.基于三I算法的模糊系统及其响应性能[J].系统科学与数学,2006,26(5):578-590.
[16]彭家寅.FMP与FMT问题的模糊熵三I算法及其还原性[J].系统工程理论与实践,2005,25(4):76-82.
[17]彭家寅.基于POFI方法的模糊系统及其响应性能[J].模式识别与人工智能,2008,21(2):129-135.
[18]宋士吉,吴从火斤.关于模糊推理的全蕴涵三I算法的约束度理论[J].自然科学进展,2000,10(10):884-889.
[19]宋士吉,吴澄.模糊推理的反向三I算法[J].中国科学:E辑,2002,32(2):230-246.
[20]ALBRYCHT J,WISNIEWSKI H.Proceedings polish symposium on interval and fuzzy mathmatics[C].Poznan,Poland,1983.
[21]WANG G.TRIPLE I method and interval valued fuzzy reasoning[J].Science China Technological Sciences,2000,43(3):242-253.
[22]王向云.区间值模糊推理的三Ⅰ算法[J].高校应用数学学报,2003,18(4):467-472.
[23]秦娟.基于区间值模糊推理三I算法的研究[D].西安:西北大学,2008.
[24]李莹芳,秦克云,何星星.基于S蕴涵算子的区间值模糊推理的三I算法[J].模糊系统与数学,2011,25(4):1-7.
[25]吴望名.模糊推理的原理和方法[M].贵阳:贵州科技出版社,1994.