剩余型区间值直觉模糊差算子的统一形式
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摘要
研究区间值直觉三角模和区间值直觉三角余模的性质,提出区间值直觉模糊差算子和区间值直觉余伴随对的概念,证明它们可以由左连续的三角模生成,讨论它们在区间值直觉模糊区域上的结合性和分配性,给出由左连续三角模生成的区间值直觉三角余模所伴随的剩余型区间值直觉模糊差算子的统一形式.根据区间值直觉模糊算子与模糊算子的关系,给出4类区间值直觉模糊差算子的具体形式.
In this paper,properties of interval-valued intuitionistic t-norms and t-conorms are investigated in this paper. Notions of interval-valued intuitionistic fuzzy difference operator and co-adjoint pairs are introduced,which are proved to be induced by the leftcontinuous t-norm,and their algebraic properties for associativity and distributivity on interval-valued intuitionistic fuzzy domain are discussed. Then the unified form of residual interval-valued intuitionistic fuzzy difference operators adjoint to interval-valued intuitionistic t-conorm derived from the left-continuous t-norm are presented. Moreover,the explicit formulas of four interval-valued intuitionistic fuzzy difference operators are provided according to the relation between interval-valued intuitionistic fuzzy operator and fuzzy operator.
In this paper,properties of interval-valued intuitionistic t-norms and t-conorms are investigated in this paper. Notions of interval-valued intuitionistic fuzzy difference operator and co-adjoint pairs are introduced,which are proved to be induced by the leftcontinuous t-norm,and their algebraic properties for associativity and distributivity on interval-valued intuitionistic fuzzy domain are discussed. Then the unified form of residual interval-valued intuitionistic fuzzy difference operators adjoint to interval-valued intuitionistic t-conorm derived from the left-continuous t-norm are presented. Moreover,the explicit formulas of four interval-valued intuitionistic fuzzy difference operators are provided according to the relation between interval-valued intuitionistic fuzzy operator and fuzzy operator.
引文
[1]CHANG C C. Algebraic analysis of many valued logic[J]. Transactions of the American Mathematical Society,1958,88(2):467-490.
[2]王国俊.数理逻辑引论与归结原理[M]. 2版.北京:科学出版社,2006.
[3]HAJEK P. Mathematics of Fuzzy Logic[M]. Dordrecht:Kluwer Academic Publishers,1998.
[4]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.
[5]CIGNOLI R,DOTTAVIANO I,MUNDICI D. Algebraic Foundations of Many-Valued Reasoning[M]. Dordrecht:Kluwer Academic Publishers,2000.
[6]KLEMENT E P,MESIAR R,PAP E. Triangular Norms[M]. Dordrecht:Kluwer Academic Publishers,2000.
[7]裴道武.剩余格与正则剩余格的特征定理[J].数学学报,2002,45(2):271-278.
[8]裴道武. MTL代数的特征定理[J].数学学报,2007,50(6):1201-1206.
[9]郑慕聪,王国俊.正则余剩余格的特征及其应用[J].自然科学进展,2005,15(5):617-620.
[10]郑慕聪,王国俊.余剩余格及其应用[J].模糊系统与数学,2005,19(4):7-12.
[11]王国俊,郑慕聪,刘艳.余剩余格的理想和嵌入定理[J].陕西师范大学学报(自然科学版),2006,34(4):1-6.
[12]DESCHRIJVER G,CORNELIS C,KERRE E E. On the representation of intuitionistic fuzzy t-norms and t-conorms[J]. IEEE Transactions on Fuzzy Systems,2004,12(1):45-61.
[13]DESCHRIJVER G,CORNELIS C,KERRE E E. Class of intuitionistic fuzzy t-norms satisfying the residuation principle[J]. International J Uncertainty Fuzziness Knowledge-Based Systems,2003,11(6):691-709.
[14]CORNELIS C,DESCHRIJVER G,KERRE E E. Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:construction,classification,application[J]. International J Approximate Reasoning,2004,35(1):55-95.
[15]郑慕聪,史忠科.剩余型直觉模糊蕴涵算子的统一形式[J].模糊系统与数学,2013,27(2):15-22.
[16]ZHENG M C,SHI Z K,LIU Y. Triple I method of approximate reasoning on Atanassov’s intuitionistic fuzzy sets[J]. International J Approximate Reasoning,2014,55(6):1369-1382.
[17]郑慕聪,史忠科,刘艳.剩余型直觉模糊差算子的统一形式[J].陕西师范大学学报(自然科学版),2013,41(4):12-15.
[18]LIU Y,ZHENG M C. The dual triple I methods of FMT and IFMT[J]. Mathematical Problems in Engineering,2014,2014(3):1-8.
[19]朱怡权.关于正则余剩余格与对合BCK-格[J].模糊系统与数学,2010,24(1):23-28.
[20]DUBOIS D,PRADE D. Gradualness,uncertainty and bipolarity:making sense of fuzzy sets[J]. Fuzzy Sets and Systems,2012,192(1):3-24.
[21]徐泽水.直觉模糊信息集成理论及应用[M].北京:科学出版社,2008.
[22]WEI M,DAI Q X. A prediction model for traffic emission based on interval-valued intuitionistic fuzzy sets and case-based reasoning theory[J]. J Intelligent and Fuzzy Systems,2016,31(6):3039-3046.
[23] WEI C P,WANG P,ZHANG Y Z. Entropy,similarity measure of interval-valued intuitionistic fuzzy sets and their applications[J]. Information Sciences,2011,181(19):4273-4286.
[24]NAYAGAM V L G,MURALIKRISHNAN S,SIVARAMAN G. Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets[J]. Expert Systems with Applications,2011,38(3):1464-1467.
[25]ANANTHI V P,BALASUBRAMANIAM P. A new image denoising method using interval-valued intuitionistic fuzzy sets for the removal of impulse noise[J]. Signal Processing,2016,121(4):81-93.
[26]JENEI S. A more efficient method for defining fuzzy connectives[J]. Fuzzy Sets and Systems,1997,90(1):25-35.
[27]ATANASSOV K. Intuitionstic fuzzy sets[J]. Fuzzy Sets and Systems,1986,20(1):87-96.
[28]ATANASSOV K. Interval valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1989,31(3):343-349.
[2]王国俊.数理逻辑引论与归结原理[M]. 2版.北京:科学出版社,2006.
[3]HAJEK P. Mathematics of Fuzzy Logic[M]. Dordrecht:Kluwer Academic Publishers,1998.
[4]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.
[5]CIGNOLI R,DOTTAVIANO I,MUNDICI D. Algebraic Foundations of Many-Valued Reasoning[M]. Dordrecht:Kluwer Academic Publishers,2000.
[6]KLEMENT E P,MESIAR R,PAP E. Triangular Norms[M]. Dordrecht:Kluwer Academic Publishers,2000.
[7]裴道武.剩余格与正则剩余格的特征定理[J].数学学报,2002,45(2):271-278.
[8]裴道武. MTL代数的特征定理[J].数学学报,2007,50(6):1201-1206.
[9]郑慕聪,王国俊.正则余剩余格的特征及其应用[J].自然科学进展,2005,15(5):617-620.
[10]郑慕聪,王国俊.余剩余格及其应用[J].模糊系统与数学,2005,19(4):7-12.
[11]王国俊,郑慕聪,刘艳.余剩余格的理想和嵌入定理[J].陕西师范大学学报(自然科学版),2006,34(4):1-6.
[12]DESCHRIJVER G,CORNELIS C,KERRE E E. On the representation of intuitionistic fuzzy t-norms and t-conorms[J]. IEEE Transactions on Fuzzy Systems,2004,12(1):45-61.
[13]DESCHRIJVER G,CORNELIS C,KERRE E E. Class of intuitionistic fuzzy t-norms satisfying the residuation principle[J]. International J Uncertainty Fuzziness Knowledge-Based Systems,2003,11(6):691-709.
[14]CORNELIS C,DESCHRIJVER G,KERRE E E. Implication in intuitionistic fuzzy and interval-valued fuzzy set theory:construction,classification,application[J]. International J Approximate Reasoning,2004,35(1):55-95.
[15]郑慕聪,史忠科.剩余型直觉模糊蕴涵算子的统一形式[J].模糊系统与数学,2013,27(2):15-22.
[16]ZHENG M C,SHI Z K,LIU Y. Triple I method of approximate reasoning on Atanassov’s intuitionistic fuzzy sets[J]. International J Approximate Reasoning,2014,55(6):1369-1382.
[17]郑慕聪,史忠科,刘艳.剩余型直觉模糊差算子的统一形式[J].陕西师范大学学报(自然科学版),2013,41(4):12-15.
[18]LIU Y,ZHENG M C. The dual triple I methods of FMT and IFMT[J]. Mathematical Problems in Engineering,2014,2014(3):1-8.
[19]朱怡权.关于正则余剩余格与对合BCK-格[J].模糊系统与数学,2010,24(1):23-28.
[20]DUBOIS D,PRADE D. Gradualness,uncertainty and bipolarity:making sense of fuzzy sets[J]. Fuzzy Sets and Systems,2012,192(1):3-24.
[21]徐泽水.直觉模糊信息集成理论及应用[M].北京:科学出版社,2008.
[22]WEI M,DAI Q X. A prediction model for traffic emission based on interval-valued intuitionistic fuzzy sets and case-based reasoning theory[J]. J Intelligent and Fuzzy Systems,2016,31(6):3039-3046.
[23] WEI C P,WANG P,ZHANG Y Z. Entropy,similarity measure of interval-valued intuitionistic fuzzy sets and their applications[J]. Information Sciences,2011,181(19):4273-4286.
[24]NAYAGAM V L G,MURALIKRISHNAN S,SIVARAMAN G. Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets[J]. Expert Systems with Applications,2011,38(3):1464-1467.
[25]ANANTHI V P,BALASUBRAMANIAM P. A new image denoising method using interval-valued intuitionistic fuzzy sets for the removal of impulse noise[J]. Signal Processing,2016,121(4):81-93.
[26]JENEI S. A more efficient method for defining fuzzy connectives[J]. Fuzzy Sets and Systems,1997,90(1):25-35.
[27]ATANASSOV K. Intuitionstic fuzzy sets[J]. Fuzzy Sets and Systems,1986,20(1):87-96.
[28]ATANASSOV K. Interval valued intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1989,31(3):343-349.