基于直觉模糊推理的(1,2,1)-α型三Ⅰ算法
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摘要
本文研究了直觉模糊推理(1,2,1)-α型三Ⅰ算法,给出了IFMP、IFMT问题的直觉模糊推理(1,2,1)-α型三Ⅰ算法解的表达形式和分解形式,在此基础上,指出了模糊推理(1,2,1)-α型三Ⅰ算法是直觉模糊推理(1,2,1)-α型三Ⅰ算法的特例,并给出了相应的证明。
In this paper, intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods are discussed, the expression form and decomposition form of solutions in intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods based on IFMP and IFMT problems are given.On this basis,it is indicated that fuzzy inference(1,2,1)-α type triple Ⅰ methods are the exception of intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods,and the corresponding certification is provided.
In this paper, intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods are discussed, the expression form and decomposition form of solutions in intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods based on IFMP and IFMT problems are given.On this basis,it is indicated that fuzzy inference(1,2,1)-α type triple Ⅰ methods are the exception of intuitionistic fuzzy inference(1,2,1)-α type triple Ⅰ methods,and the corresponding certification is provided.
引文
[1]Zadeh L A.Fuzzy sets[J].Info Contr,1965,8:338~353.
[2]Wang X.A course in fuzzy systems and control[M].Upper Saddle River,NJ:Prentice Hall PTR,1997.
[3]Mamdani H,Gaines B R.Fuzzy reasoning and its applications[J].London:Academic Press,1981.
[4]Zadeh A.Outline of a new approach to the analysis of complex systems and decision and process[J].IEEE Trans Syst Man Cyber,1973,1:28~44.
[5]王国俊.模糊推理全蕴涵三I算法[J].中国科学(E辑),1999,29(1):43~53.
[6]Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets Syst,1986,20:87~96.
[7]Deschrijver G,Cornelis C,Kerre E.Class of intuitionistic fuzzy t-norms satisfying the residuation principle[J].Int Uncert Fuzz Knowl-Bas Syst,2003,11:691~709.
[8]Iakovidis D.K,Papageorgiou E.Intuitionistic fuzzy cognitive maps for medical decision making[J].IEEE Transactions on Information Technology in Biomedicine(United States),2011,15(1):100~107.
[9]徐泽水.直觉模糊信息集成理论及其应用[M].北京:科学出版社,2008.
[10]Przemyslaw G.On possible and necessy inclusion of intuitioni-stic fuzzy sets[J].Info Sci,2011,181:342~350.
[11]Deschrijver G,Cornelis C,Kerre E.On the representation of Intuitionistic fuzzy t-norms and t-conorms[J].IEEE Trans Fuzzy Syst,2004,12:45~61.
[12]Cornelis C,Deschrijver G,Keer E.Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:Construction,classification,application[J].Int Approx Reas,2004,35:55~95.
[13]郑慕聪.剩余型直觉蕴涵算子的统一形式[J].模糊系统与数学,2013,27(2):15~22.
[14]郑慕聪.剩余型直觉模糊推理的三I方法[J].中国科学(信息科学),2013,43(6):810~820.
[15]Zheng C,Shi Z K,Liu Y.Triple I methods of approximate reasoning on Atanassov’s intuitionistic fuzzy sets[J].International Journal of Approximate Reasoning,2014,55(6):1369~1382.
[16]李洪兴.Fuzzy系统的概率表示[J].中国科学(E辑),2006,36(4):359~366.
[17]Tang M,Liu X.Differently implicational universal triple I methods of(1,2,2)type[J].Computers and Mathematics with Applications,2010,59(6):1965~1984.
[18]Luo X,Sang N,Zhang K.Differently implicational universal triple I algorithms of(1,2,1)type[J].Journal of Computational Iformationn Systems,2013,9(2):765~772.
[19]Luo X,Sang N,Zhang K.Unified Differently Implicational(1,2,1)Type Algorithms of Fuzzy Reasoning[J].Journal of Computational Information Systems,2013,9(4):1669~1677.
[20]Klement P,Mesiar R,Pap E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
[2]Wang X.A course in fuzzy systems and control[M].Upper Saddle River,NJ:Prentice Hall PTR,1997.
[3]Mamdani H,Gaines B R.Fuzzy reasoning and its applications[J].London:Academic Press,1981.
[4]Zadeh A.Outline of a new approach to the analysis of complex systems and decision and process[J].IEEE Trans Syst Man Cyber,1973,1:28~44.
[5]王国俊.模糊推理全蕴涵三I算法[J].中国科学(E辑),1999,29(1):43~53.
[6]Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets Syst,1986,20:87~96.
[7]Deschrijver G,Cornelis C,Kerre E.Class of intuitionistic fuzzy t-norms satisfying the residuation principle[J].Int Uncert Fuzz Knowl-Bas Syst,2003,11:691~709.
[8]Iakovidis D.K,Papageorgiou E.Intuitionistic fuzzy cognitive maps for medical decision making[J].IEEE Transactions on Information Technology in Biomedicine(United States),2011,15(1):100~107.
[9]徐泽水.直觉模糊信息集成理论及其应用[M].北京:科学出版社,2008.
[10]Przemyslaw G.On possible and necessy inclusion of intuitioni-stic fuzzy sets[J].Info Sci,2011,181:342~350.
[11]Deschrijver G,Cornelis C,Kerre E.On the representation of Intuitionistic fuzzy t-norms and t-conorms[J].IEEE Trans Fuzzy Syst,2004,12:45~61.
[12]Cornelis C,Deschrijver G,Keer E.Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:Construction,classification,application[J].Int Approx Reas,2004,35:55~95.
[13]郑慕聪.剩余型直觉蕴涵算子的统一形式[J].模糊系统与数学,2013,27(2):15~22.
[14]郑慕聪.剩余型直觉模糊推理的三I方法[J].中国科学(信息科学),2013,43(6):810~820.
[15]Zheng C,Shi Z K,Liu Y.Triple I methods of approximate reasoning on Atanassov’s intuitionistic fuzzy sets[J].International Journal of Approximate Reasoning,2014,55(6):1369~1382.
[16]李洪兴.Fuzzy系统的概率表示[J].中国科学(E辑),2006,36(4):359~366.
[17]Tang M,Liu X.Differently implicational universal triple I methods of(1,2,2)type[J].Computers and Mathematics with Applications,2010,59(6):1965~1984.
[18]Luo X,Sang N,Zhang K.Differently implicational universal triple I algorithms of(1,2,1)type[J].Journal of Computational Iformationn Systems,2013,9(2):765~772.
[19]Luo X,Sang N,Zhang K.Unified Differently Implicational(1,2,1)Type Algorithms of Fuzzy Reasoning[J].Journal of Computational Information Systems,2013,9(4):1669~1677.
[20]Klement P,Mesiar R,Pap E.Triangular norms[M].Dordrecht:Kluwer Academic Publishers,2000.
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