基于模糊逻辑等价算子的直觉相似度
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摘要
首先,借助正则蕴涵算子,构造了4类不同的直觉模糊集之间的相似度,并在模式识别方面给出了简单应用。其次,证明了由Gdel,R_0,Lukasiewicz,Gougen蕴涵算子所确定的4个相似度可诱导直觉模糊集之集上的4个度量,并在相应的度量空间中分析了孤立点的分布情况。最后,将上述4个度量作为扰动参数,从鲁棒性分析的角度作了比较。
Firstly,four types of intuitionistic similarties are constructed by regular implication operators,and its application in pattern recognition are shown.Secondly,for similarities determined by Gdel,Ro,Lukasiewicz and Gougen implication operators are proved to be the metrics an IFSs(X).Also,the distributions of isolated points in corresponding metric spaces are studied.Finally,as the perturbation parameter,for metrics are compared form the view of robustness analysis.
Firstly,four types of intuitionistic similarties are constructed by regular implication operators,and its application in pattern recognition are shown.Secondly,for similarities determined by Gdel,Ro,Lukasiewicz and Gougen implication operators are proved to be the metrics an IFSs(X).Also,the distributions of isolated points in corresponding metric spaces are studied.Finally,as the perturbation parameter,for metrics are compared form the view of robustness analysis.
引文
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[11]D.F.Li,C.T.Cheng(2002)New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions.Pattern Recog ett 23:221~225.
[12]Pal SK,King RA(1981)Image enhancement using smoothing with fuzzy sets.IEEE Trans Syst Man Cybernet 11:495~501.
[13]J.H.Jin,Y.M.Li,C.Q.Li,Robustness of fuzzy reasoniog via logically Equivalence measure,Information Sciences,177(2007):5103~5117.
[14]C.Cornelis,G.Deschrijver,E.E.Kerre,Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:construction,classi?cation,application,Int.J.Approx.Reason.35(2004)55~95.
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[17]M.C.Zheng,Z.K.Shi,Y.Liu,Triple I method of approximate reasoning on Atanassov’s intuitionistic fuzzy sets,International Journal of Approximate Reasoning 55(2014)1369~1382.
[18]Y.M.Li,D.C.Li,W.Pedrycz,J.J.WU,An approach of measure the robustness of fuzzy reasoning,International Journal of Intelligent Systems,20(2005)393~413.
[19]Supriya Kumar De,Ranjit Biswas C,Akhil Ranjan Roy,Some operations on intuitionistic fuzzy sets,Fuzzy Sets and Systems 114(2000)477~484.
[20]Mitchell H.B.(2003)On the Dengfeng-Chuntian similarity measure and its application to pattern recognition.Pattern Recognit Lett.24:3101~3104.
[21]Y.H.Li,David L.Olson,Zheng Qin,Similarity measures between intuitionistic fuzzy(vague)sets:A comparative analysis,Pattern Recognition Letters 28(2007)278~285.
[22]D.H.Hong,Kim C.,(1999)A note on similarity measures between vague sets and between elements.Inf Sci 115:83~96.
[23]Y.Li,Z.Chi,D.Yan(2002)Similarity measures between vague sets and vague entropy.J Comput Sci 29:129~132.
[24]Fatih Emre Boran,Diyar Akay,A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition,Information Sciences,255(2014)45~57.
[25]Przemyslaw Grzegorzewski,Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,Fuzzy Sets and Systems 148(2004)319~328.
[26]W.L.Hung,M.S.Yang,Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance,Pattern Recognition Letters 25(2004)1603~1611.
[27]S.S.Dai,D.W.Pei,D.H.Guo,Robustness analysis of full implication inference method,International Journal of Approximate Reasoning,54(2013)653~666.
[28]G.J.Wang,H.J.Zhou,Introduction to Mathematical Logic and Resolution Principle,Science Press,Beijing,U.K.Alpha Science International Limited,Oxford,2009.
[29]熊金城.点集拓扑[M](第三版).北京:科学出版社,2003.
[30]E.P.Klement,R.Mesiar,E.Pap,Triangular Norms,Trangular norms,Kluwer Academic Publishers,Dordrecht,2000.
[31]G.J.Wang,J.Y.Duan,On robustness of the full implication triple I inference method with respect to finer measurements,International Journal of Approximate Reasoning.55(2014):787~796.
[32]王国俊.非经典数理逻辑与近似推理[M](第二版).北京:科学出版社,2008.
[33]W.Q.Wang,X.L.Xin,Distance measure between intuitionistic fuzzy sets,Pattern Recognition Letters 26(2005)2063~2069.
[34]Y.M.Li,Analysis of Fuzzy System,Science Press,Beijing,2005.
[35]K.Y.Cai,Robustness of fuzzy reasoning andδ-equalities of fuzzy sets,IEEE transactions on fuzzy systems[J],9(5)(2001)783~750.
[36]M.S.Ying,Perturbation of fuzzy reasoning,IEEE Trans.Fuzzy Syst.7(5)(1999)625~629.
[2]C.Y.Wang,B.Q.Hu,On fuzzy-valued operations and fuzzy-valued fuzzy sets,Fuzzy Sets and Systems,Volume 268,1June 2015,Pages 72~92.
[3]Glad Deschrijver,Triangular norms which are meet-morphisms in interval-valued fuzzy set theory,Fuzzy Sets and Systems,Volume 181,Issue 1,16October 2011,Pages 88~101.
[4]Kamal El-Saady,Lattice-valued fuzzy frames,Information Sciences,Volume 177,Issue 21,1November 2007,Pages4810~4819.
[5]Pan Haiyu,Li Yongming,Cao Yongzhi.Lattice-valued simulations for quantitative transition systems[J].International Journal of Approximate Reasoning,56(2015)28~42.
[6]Pan Haiyu,Cao Yongzhi,Zhang Min,Chen Yixiang.Simulation for lattice-valued doubly labeled transition systems[J].International Journal of Approximate Reasoning,55(2014)797~811.
[7]I.Couso,L.Garrido,L.Sánchez,Similarity and dissimilarity measures between fuzzy sets:A formal relational study,Information Sciences,229(2013)122~141.
[8]Szmidt E,Kacprzyk J,A new concept of a similarity measure for intuitionistic fuzzy sets and its use in group decision making.In:Torra V,Narukawa Y,Miyamoto S(eds)Modelling decision for artificial intelligence,LNAI 3558,Springer 272~282.
[9]Xu ZS,Chen J(2007)Approach to group decision making based on interval-valued intuitionistic judgement matrices.Syst Engi Theory Pract 27:126~133.
[10]G.W.Wei,G.Lan(2008)Grey relational analysis method for intervalvalued intuitionistic fuzzy multiple attribute decision making.In:Fifth international conference on fuzzy systems and knowledge discovery,pp 291~295.
[11]D.F.Li,C.T.Cheng(2002)New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions.Pattern Recog ett 23:221~225.
[12]Pal SK,King RA(1981)Image enhancement using smoothing with fuzzy sets.IEEE Trans Syst Man Cybernet 11:495~501.
[13]J.H.Jin,Y.M.Li,C.Q.Li,Robustness of fuzzy reasoniog via logically Equivalence measure,Information Sciences,177(2007):5103~5117.
[14]C.Cornelis,G.Deschrijver,E.E.Kerre,Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:construction,classi?cation,application,Int.J.Approx.Reason.35(2004)55~95.
[15]G.Deschrijver,C.Cornelis,E.E.Kerre,Class of intuitionistic fuzzy t-norms satisfying the residuation principle,Int.J.Uncertain.Fuzziness Knowl.Based Syst.11(6)(2003)691~709.
[16]G.Deschrijver,C.Cornelis,E.E.Kerre,On the representation of intuitionistic fuzzy t-norms and t-conorms,IEEE Trans.Fuzzy Syst.12(1)(2004)45~61.
[17]M.C.Zheng,Z.K.Shi,Y.Liu,Triple I method of approximate reasoning on Atanassov’s intuitionistic fuzzy sets,International Journal of Approximate Reasoning 55(2014)1369~1382.
[18]Y.M.Li,D.C.Li,W.Pedrycz,J.J.WU,An approach of measure the robustness of fuzzy reasoning,International Journal of Intelligent Systems,20(2005)393~413.
[19]Supriya Kumar De,Ranjit Biswas C,Akhil Ranjan Roy,Some operations on intuitionistic fuzzy sets,Fuzzy Sets and Systems 114(2000)477~484.
[20]Mitchell H.B.(2003)On the Dengfeng-Chuntian similarity measure and its application to pattern recognition.Pattern Recognit Lett.24:3101~3104.
[21]Y.H.Li,David L.Olson,Zheng Qin,Similarity measures between intuitionistic fuzzy(vague)sets:A comparative analysis,Pattern Recognition Letters 28(2007)278~285.
[22]D.H.Hong,Kim C.,(1999)A note on similarity measures between vague sets and between elements.Inf Sci 115:83~96.
[23]Y.Li,Z.Chi,D.Yan(2002)Similarity measures between vague sets and vague entropy.J Comput Sci 29:129~132.
[24]Fatih Emre Boran,Diyar Akay,A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition,Information Sciences,255(2014)45~57.
[25]Przemyslaw Grzegorzewski,Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,Fuzzy Sets and Systems 148(2004)319~328.
[26]W.L.Hung,M.S.Yang,Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance,Pattern Recognition Letters 25(2004)1603~1611.
[27]S.S.Dai,D.W.Pei,D.H.Guo,Robustness analysis of full implication inference method,International Journal of Approximate Reasoning,54(2013)653~666.
[28]G.J.Wang,H.J.Zhou,Introduction to Mathematical Logic and Resolution Principle,Science Press,Beijing,U.K.Alpha Science International Limited,Oxford,2009.
[29]熊金城.点集拓扑[M](第三版).北京:科学出版社,2003.
[30]E.P.Klement,R.Mesiar,E.Pap,Triangular Norms,Trangular norms,Kluwer Academic Publishers,Dordrecht,2000.
[31]G.J.Wang,J.Y.Duan,On robustness of the full implication triple I inference method with respect to finer measurements,International Journal of Approximate Reasoning.55(2014):787~796.
[32]王国俊.非经典数理逻辑与近似推理[M](第二版).北京:科学出版社,2008.
[33]W.Q.Wang,X.L.Xin,Distance measure between intuitionistic fuzzy sets,Pattern Recognition Letters 26(2005)2063~2069.
[34]Y.M.Li,Analysis of Fuzzy System,Science Press,Beijing,2005.
[35]K.Y.Cai,Robustness of fuzzy reasoning andδ-equalities of fuzzy sets,IEEE transactions on fuzzy systems[J],9(5)(2001)783~750.
[36]M.S.Ying,Perturbation of fuzzy reasoning,IEEE Trans.Fuzzy Syst.7(5)(1999)625~629.