一致模的序关系
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摘要
三角模(三角余模)是一类重要的模糊算子,广泛应用于模糊控制、模糊聚类和人工智能中。作为三角模(三角余模)的推广,一致模广泛应用于多值逻辑、专家系统、图像处理、信息融合等领域。本文围绕一致模的序关系展开讨论,针对每一类一致模分析了相应的最大元和最小元,对一致模的应用具有一定的指导意义。
Triangle norm(triangle conorm) is a kind of important fuzzy operator which is widely used in fuzzy control, fuzzy clustering and artificial intelligence. As the extension of triangle norm(triangle conorm), uninorm is extensively used in multi-valued logic, expert system, image processing, information fusion and many other fields. In this paper, the order relations of uninorms are discussed, and the corresponding maximum and minimum elements are analyzed for each class of uninorms, which is of guiding significance for the application of uninorms.
Triangle norm(triangle conorm) is a kind of important fuzzy operator which is widely used in fuzzy control, fuzzy clustering and artificial intelligence. As the extension of triangle norm(triangle conorm), uninorm is extensively used in multi-valued logic, expert system, image processing, information fusion and many other fields. In this paper, the order relations of uninorms are discussed, and the corresponding maximum and minimum elements are analyzed for each class of uninorms, which is of guiding significance for the application of uninorms.
引文
[1] 王国俊.非经典数理逻辑与近似推理[M].北京:科学出版社,2000.
[2] 仇英辉,何霖.基于三角模算子的RPL协议路由优化算法[J].传感技术学报,2015,28(12):125-130.
[3] 连玉平,刘坤,史战红.一种由三角模所诱导的粗糙集间的相似性度量方法[J].兰州大学学报(自然科学版),2014,50(4):120-123,128.
[4] MAS M, MASSANET S, AGUILERA D R, et al. A survey on the existing classes of uninorms[J]. Journal of Intelligent & Fuzzy Systems, 2015,29(3):1021-1037.
[5] CALVO T, MESIAR R. Aggregation operators:ordering and bounds[J]. Fuzzy Sets and Systems, 2003,139(3):685-697.
[6] FODOR J C, YAGERR R, RYBALOV A. Structure of uninorms[J]. International Journal of Uncertainty, Fuzziness Knowledge-Based Systems,1997,5(4):411-427.
[7] KLEMENT E P, MESIAR R, PAP E. Triangular Norms [M]. London:Springer Science+Business Media Dordrecht, 2000.
[8] BAETS B D. Idempotent uninorms[J]. European Journal of Operational Research, 1999,118(3):631-642.
[9] LI G, LIU H W. Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous T-conorm[J]. Fuzzy Sets and Systems, 2016,287:154-171.
[10] LI G, LIU H W, FODOR J. Single-point characterization of uninorm with nilpotent underlying T-norm and T-conorm[J]. International Journal of Uncertainty, Fuzziness Knowledge-Based Systems, 2014,22(4):591-604.
[11] DRYGAS P. On the structure of continuous uninorms[J]. Kybernetika, 2007,43(2):183-196.
[2] 仇英辉,何霖.基于三角模算子的RPL协议路由优化算法[J].传感技术学报,2015,28(12):125-130.
[3] 连玉平,刘坤,史战红.一种由三角模所诱导的粗糙集间的相似性度量方法[J].兰州大学学报(自然科学版),2014,50(4):120-123,128.
[4] MAS M, MASSANET S, AGUILERA D R, et al. A survey on the existing classes of uninorms[J]. Journal of Intelligent & Fuzzy Systems, 2015,29(3):1021-1037.
[5] CALVO T, MESIAR R. Aggregation operators:ordering and bounds[J]. Fuzzy Sets and Systems, 2003,139(3):685-697.
[6] FODOR J C, YAGERR R, RYBALOV A. Structure of uninorms[J]. International Journal of Uncertainty, Fuzziness Knowledge-Based Systems,1997,5(4):411-427.
[7] KLEMENT E P, MESIAR R, PAP E. Triangular Norms [M]. London:Springer Science+Business Media Dordrecht, 2000.
[8] BAETS B D. Idempotent uninorms[J]. European Journal of Operational Research, 1999,118(3):631-642.
[9] LI G, LIU H W. Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous T-conorm[J]. Fuzzy Sets and Systems, 2016,287:154-171.
[10] LI G, LIU H W, FODOR J. Single-point characterization of uninorm with nilpotent underlying T-norm and T-conorm[J]. International Journal of Uncertainty, Fuzziness Knowledge-Based Systems, 2014,22(4):591-604.
[11] DRYGAS P. On the structure of continuous uninorms[J]. Kybernetika, 2007,43(2):183-196.