剩余型直觉模糊推理的反向三Ⅰ方法
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摘要
提出直觉模糊取式(IFMP)和直觉模糊拒取式(IFMT)问题的直觉模糊推理的反向三Ⅰ原则、反向α-三Ⅰ原则和反向三Ⅰ约束原则.针对剩余型直觉模糊蕴涵算子,给出IFMP、IFMT问题的直觉模糊推理的反向三Ⅰ算法、反向α-三Ⅰ算法及反向三Ⅰ约束算法求解的计算公式和分解形式,指出这些算法都是相应模糊集情形下的推广,讨论IFMP、IFMT问题的直觉模糊推理的反向三Ⅰ算法的还原性.
The reverse triple Ⅰ principle,reverse α-triple Ⅰ principle and reverse triple Ⅰ restriction principle of intuitionistic fuzzy reasoning for intuitionistic fuzzy modus ponens( IFMP) and intuitionistic fuzzy modus tollens( IFMT) problems are proposed. Aiming at the residual intuitionistic fuzzy implicator,the formulas and decomposition forms of solutions of intuitionistic fuzzy reasoning reverse triple Ⅰ methods,reverse α-triple Ⅰ methods and reverse triple Ⅰ restriction methods for IFMP and IFMT problems are given.It is pointed out that these methods are all generalized in the case of the corresponding fuzzy sets.Moreover,the reductive properties of intuitionistic fuzzy reasoning reverse triple Ⅰ methods for IFMP and IFMT problems are discussed.
The reverse triple Ⅰ principle,reverse α-triple Ⅰ principle and reverse triple Ⅰ restriction principle of intuitionistic fuzzy reasoning for intuitionistic fuzzy modus ponens( IFMP) and intuitionistic fuzzy modus tollens( IFMT) problems are proposed. Aiming at the residual intuitionistic fuzzy implicator,the formulas and decomposition forms of solutions of intuitionistic fuzzy reasoning reverse triple Ⅰ methods,reverse α-triple Ⅰ methods and reverse triple Ⅰ restriction methods for IFMP and IFMT problems are given.It is pointed out that these methods are all generalized in the case of the corresponding fuzzy sets.Moreover,the reductive properties of intuitionistic fuzzy reasoning reverse triple Ⅰ methods for IFMP and IFMT problems are discussed.
引文
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[2]ATANASSOV K.Intuitionistic Fuzzy Sets.Fuzzy Sets and Systems,1986,20(1):87-96.
[3]LI D F,CHENG C T.New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognitions.Pattern Recognition Letters,2002,23(1/2/3):221-225.
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[5]LIU H W,WANG G J.Multi-criteria Decision-Making Methods Based on Intuitionistic Fuzzy Sets.European Journal of Operational Research,2007,179(1):220-233.
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[7]MAMDANI E H.Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Systems.IEEE Transactions on Computers,1977,26(12):1182-1191.
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[10]ELKAN C.The Paradoxical Success of Fuzzy Logic.IEEE Expert,1994,9(4):3-8.
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[17]LIU H W,WANG G J.A Note on the Unified Forms of Triple I Method.Computers and Mathematics with Applications,2006,52(10/11):1609-1613.
[18]PEI D W.Full Implication Triple I Algorithms and Theirs Consistency in Fuzzy Reasoning.Journal of Mathematical Research and Exposition,2004,24(2):359-368.
[19]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.系统科学与数学,2005,25(3):311-322.(PENG J Y,LI H X,HOU J,et al.Fuzzy Controllers Based on Pointwise Optimization Fuzzy Inference and Its Interpolation Mechanism.Journal of Systems Science and Mathematical Sciences,2005,25(3):311-322.)
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[21]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.系统科学与数学,2005,25(5):578-590.(LI H X,PENG J Y,WANG J Y,et al.Fuzzy Systems Based on Triple I Algorithm and Their Response Ability.Journal of Systems Science and Mathematical Sciences,2005,25(5):578-590.)
[22]李洪兴,彭家寅,王加银.常见模糊蕴涵算子的模糊系统及其响应函数.控制理论与应用,2005,22(3):341-347.(LI H X,PENG J Y,WANG J Y.Fuzzy Systems and Their Response Functions Based on Commonly Used Fuzzy Implication Operators.Control Theory and Application,2005,22(3):341-347.)
[23]彭家寅.FMP与FMT问题的模糊熵三I算法及其还原性.系统工程理论与实践,2005,25(4):76-82.(PENG J Y.Fuzzy Entropy Triple I Algorithm for FMP and FMT Problems and Their Reductivity.System Engineering-Theory and Practice,2005,25(4):76-82.)
[24]彭家寅.基于POFI方法的模糊系统及其响应性能.模式识别与人工智能,2008,21(2):129-135.(PENG J Y.Fuzzy Systems Based on POFI Method and Their Response Ability.Pattern Recognition and Artificial Intelligence,2008,21(2):129-135.)
[25]宋士吉,吴澄.模糊推理的反向三I算法.中国科学(E辑),2002,32(2):230-246.(SONG S J,WU D.Inverse Triple I Algorithm for Fuzzy Reasoning.Science in China(Series E),2002,32(2):230-246.)
[26]DESCHRIJVER G,KEER E E.Class of Intuitionistic Fuzzy tNorms Satisfying the Residuation Principle.International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2003,11(6):691-709.
[27]GRZEGORZEWISKI P.On Possible and Necessary Inclusion of Intuitionistic Fuzzy Sets.Information Sciences,2011,181(2):342-350.
[28]CORNELIS C,DESCHRIJVER G,KEER E E.Implication in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory:Construction,Classification,Application.International Journal of Approximate Reasoning,2004,35(1):55-95.
[29]郑慕聪,史忠科.剩余型直觉模糊蕴涵算子的统一形式.模糊系统与数学,2013,27(2):15-22.(ZHENG M C,SHI Z K.Unified Form of Residual Intuitionistic Fuzzy Implicators.Fuzzy Systems and Mathematics,2013,27(2):15-22.)
[30]郑慕聪,史忠科,刘艳.剩余型直觉模糊推理的三I方法.中国科学(信息科学),2013,43(6):810-820.(ZHENG M C,SHI Z K,LIU Y.Triple I Method of Intuitionistic Fuzzy Reasoning Based on Residual Implication.Science in China(Information Science),2013,43(6):810-820.)
[31]KLEMENT E P,MESIAR R,PAP E.Triangular Norms.Dordrecht,The Netherlands:Kluwer Academic Publishers,2000.
[32]宋士吉,冯纯伯,吴从炘.关于模糊推理的全蕴涵三I算法的约束度理论.自然科学进展,2000,10(10):884-889.(SONG S J,FENG C B,WU C X.Theory of Constraint Degree of the Triple I Algorithm for Fuzzy Reasoning.Progress in Natural Science,2000,10(10):884-889.)
[2]ATANASSOV K.Intuitionistic Fuzzy Sets.Fuzzy Sets and Systems,1986,20(1):87-96.
[3]LI D F,CHENG C T.New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognitions.Pattern Recognition Letters,2002,23(1/2/3):221-225.
[4]徐泽水.直觉模糊信息集成理论及应用.北京:科学出版社,2008.(XU Z S.Theory and Application of Intuitionistic Fuzzy Information Integration.Beijing,China:Science Press,2008.)
[5]LIU H W,WANG G J.Multi-criteria Decision-Making Methods Based on Intuitionistic Fuzzy Sets.European Journal of Operational Research,2007,179(1):220-233.
[6]ZADEH L A.Outline of a New Approach to the Analysis of Complex Systems and Decision Processes.IEEE Transactions on Systems,Man and Cybernetics,1973,3(1):28-44.
[7]MAMDANI E H.Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Systems.IEEE Transactions on Computers,1977,26(12):1182-1191.
[8]DUBOIS D,PRADE H.Fuzzy Sets in Approximate Reasoning,Part1:Inference with Possibility Distributions.Fuzzy Sets and Systems,1991,40(1):143-202.
[9]DUBOIS D,LANG J,PRADE H.Fuzzy Sets in Approximate Reasoning,Part 2:Logical Approaches.Fuzzy Sets and Systems,1991,40(1):203-244.
[10]ELKAN C.The Paradoxical Success of Fuzzy Logic.IEEE Expert,1994,9(4):3-8.
[11]王国俊.模糊推理的全蕴涵三I算法.中国科学(E辑),1999,29(1):43-53.(WANG G J.The Full Implication Triple I Method in Fuzzy Reasoning.Sciences in China(Series E),1999,29(1):43-53.)
[12]李洪兴.从模糊控制的数学本质看模糊逻辑的成功——关于“关于模糊逻辑似是而非的争论”的似是而非的介入.模糊系统与数学,1995,9(4):1-14.(LI H X.To See the Success of Fuzzy Logic from Mathematical Essence of Fuzzy Control-On“the Paradoxical Success of Fuzzy Logic”.Fuzzy System and Mathematics,1995,9(4):1-14.)
[13]李洪兴.模糊控制的插值机理.中国科学(E辑),1998,28(3):259-267.(LI H X.The Interpolation Mechanism of Fuzzy Control.Sciences in China(Series E),1998,28(3):259-267.)
[14]WANG G J.Triple I Method and Interval-Valued Fuzzy Reasoning.Sciences in China(Series E),2000,43(3):331-340.
[15]SONG S J,FENG C B,LEE E S.Triple I Method of Fuzzy Reasoning.Computers and Mathematics with Applications,2002,44(12):1567-1579.
[16]WANG G J,FU L.Unified Forms of Triple I Method.Computers and Mathematics with Applications,2005,49(5/6):923-932.
[17]LIU H W,WANG G J.A Note on the Unified Forms of Triple I Method.Computers and Mathematics with Applications,2006,52(10/11):1609-1613.
[18]PEI D W.Full Implication Triple I Algorithms and Theirs Consistency in Fuzzy Reasoning.Journal of Mathematical Research and Exposition,2004,24(2):359-368.
[19]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.系统科学与数学,2005,25(3):311-322.(PENG J Y,LI H X,HOU J,et al.Fuzzy Controllers Based on Pointwise Optimization Fuzzy Inference and Its Interpolation Mechanism.Journal of Systems Science and Mathematical Sciences,2005,25(3):311-322.)
[20]李洪兴.变论域自适应模糊控制器.中国科学(E辑),1999,29(1):32-42.(LI H X.Variable Domain Adaptive Fuzzy Controller.Science in China(Series E),1999,29(1):32-42.)
[21]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.系统科学与数学,2005,25(5):578-590.(LI H X,PENG J Y,WANG J Y,et al.Fuzzy Systems Based on Triple I Algorithm and Their Response Ability.Journal of Systems Science and Mathematical Sciences,2005,25(5):578-590.)
[22]李洪兴,彭家寅,王加银.常见模糊蕴涵算子的模糊系统及其响应函数.控制理论与应用,2005,22(3):341-347.(LI H X,PENG J Y,WANG J Y.Fuzzy Systems and Their Response Functions Based on Commonly Used Fuzzy Implication Operators.Control Theory and Application,2005,22(3):341-347.)
[23]彭家寅.FMP与FMT问题的模糊熵三I算法及其还原性.系统工程理论与实践,2005,25(4):76-82.(PENG J Y.Fuzzy Entropy Triple I Algorithm for FMP and FMT Problems and Their Reductivity.System Engineering-Theory and Practice,2005,25(4):76-82.)
[24]彭家寅.基于POFI方法的模糊系统及其响应性能.模式识别与人工智能,2008,21(2):129-135.(PENG J Y.Fuzzy Systems Based on POFI Method and Their Response Ability.Pattern Recognition and Artificial Intelligence,2008,21(2):129-135.)
[25]宋士吉,吴澄.模糊推理的反向三I算法.中国科学(E辑),2002,32(2):230-246.(SONG S J,WU D.Inverse Triple I Algorithm for Fuzzy Reasoning.Science in China(Series E),2002,32(2):230-246.)
[26]DESCHRIJVER G,KEER E E.Class of Intuitionistic Fuzzy tNorms Satisfying the Residuation Principle.International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2003,11(6):691-709.
[27]GRZEGORZEWISKI P.On Possible and Necessary Inclusion of Intuitionistic Fuzzy Sets.Information Sciences,2011,181(2):342-350.
[28]CORNELIS C,DESCHRIJVER G,KEER E E.Implication in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory:Construction,Classification,Application.International Journal of Approximate Reasoning,2004,35(1):55-95.
[29]郑慕聪,史忠科.剩余型直觉模糊蕴涵算子的统一形式.模糊系统与数学,2013,27(2):15-22.(ZHENG M C,SHI Z K.Unified Form of Residual Intuitionistic Fuzzy Implicators.Fuzzy Systems and Mathematics,2013,27(2):15-22.)
[30]郑慕聪,史忠科,刘艳.剩余型直觉模糊推理的三I方法.中国科学(信息科学),2013,43(6):810-820.(ZHENG M C,SHI Z K,LIU Y.Triple I Method of Intuitionistic Fuzzy Reasoning Based on Residual Implication.Science in China(Information Science),2013,43(6):810-820.)
[31]KLEMENT E P,MESIAR R,PAP E.Triangular Norms.Dordrecht,The Netherlands:Kluwer Academic Publishers,2000.
[32]宋士吉,冯纯伯,吴从炘.关于模糊推理的全蕴涵三I算法的约束度理论.自然科学进展,2000,10(10):884-889.(SONG S J,FENG C B,WU C X.Theory of Constraint Degree of the Triple I Algorithm for Fuzzy Reasoning.Progress in Natural Science,2000,10(10):884-889.)