Choquet积分的模糊化扩展II型

计算机科学 ›› 2013, Vol. 40 ›› Issue (Z11): 105-108.

Choquet积分的模糊化扩展II型

杨蓉,郑三元

深圳大学机电与控制工程学院深圳518000;深圳大学机电与控制工程学院深圳518000

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金项目(61105044)资助

Type II Fuzzification on Choquet Integral

YANG Rong and ZHENG San-yuan

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 重点讨论Choquet积分的II型模糊化扩展形式。相对于Choquet积分的模糊化扩展I型,II型扩展支持模糊数的被积函数,并给出精确数的积分结果。基于带符号的模糊测度,分别讨论了Choquet积分的模糊化扩展II型的计算方法和相关算法。并用实例说明:Choquet积分的模糊化扩展II型作为一种聚合工具在处理涉及非精确数的数据挖掘问题(例如:推理和回归问题)上的实用价值。

关键词: Choquet积分,模糊数,模糊测度,聚合

Abstract: This paper provided a detailed discussion on one fuzzification of Choquet integral which supports fuzzy-valued integrand and gave crisp-valued integration result．It is a generalized Choquet integral for fuzzy-valued integrand,interval-valued integrand,as well as the crisp-valued integrand．The presented generalized Choquet integral with respect to signed fuzzy measure can act as an aggregation tool which is especially useful in many information fusing and data mining problems (such as regression and decision making) where not only crisp data but also heterogeneous fuzzy data are involved.

Key words: Choquet integral,Fuzzy data,Fuzzy measure,Aggregation

杨蓉,郑三元. Choquet积分的模糊化扩展II型[J]. 计算机科学, 2013, 40(Z11): 105-108. https://doi.org/

YANG Rong and ZHENG San-yuan. Type II Fuzzification on Choquet Integral[J]. Computer Science, 2013, 40(Z11): 105-108. https://doi.org/

参考文献

[1] Choquet G．Theory of Capacities [J]．Annales de l’Institut Fourier,5:131-295
[2] Halmos P R．Measure Theory [M]．New York:Springer-Verlag New York Inc,1974:324
[3] Murofushi T,Sugeno M,Machida M．Non Monotonic FuzzyMeasures and the Choquet Integral [J]．Fuzzy Sets and Systems,1994,64:73-86
[4] Wang Z,Klir G J.Fuzzy Measure Theory [M]．New York:Springer-Verlag New York Inc,1992:363
[5] Leung K S,Wong M L,Lam W,et al．Learning Nonlinear Multiregression Networks Based on Evolutionary Computation [J]．IEEE Transaction on Systems,Man and Cybernetics,Part B,2002,32:630-644
[6] Xu K,Wang Z,Leung K S．Classification by Nonlinear Integral Projections [J]．IEEE Transaction on Fuzzy Systems,2003,11:187-201
[7] Wang Z．A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals[C]∥Proceedings on 12th IEEE International Conference on Fuzzy Systems,2003．2003,2:819-821
[8] Buckley J J,Eslami E．An Introduction to Fuzzy Logic and Fuzzy Sets[M]．Physica-Verlag Heidelberg,2002:296
[9] 陶长琪,凌和良．基于Choquet积分的模糊数直觉模糊数多属性决策方法[J]．控制与决策,2012,27(9):1381-1386
[10] 陈亚婷,吴博,张国春．基于一种推广的Choquet积分的回归模型[J]．河北大学学报:自然科学版,2010,30(4):353-355
[11] 安相华,冯毅雄,谭建荣．基于Choquet积分与证据理论的产品方案协同评价方法[J]．浙江大学学报:工学版,2012,46(1):163-169
[12] 张磊,樊治平,乐琦．基于Choquet积分的综合风险测评方法[J]．东北大学学报:自然科学版,2010,31(11):1665-1668
[13] 王坚强,聂荣荣．准则关联的直觉模糊多准则决策方法[J]．控制与决策,2011,26(9):1348-1352
[14] 郑三元,杨蓉．Choquet积分的模糊化扩展I型 [J]．深圳大学学报:理工版

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