二型模糊熵研究现状
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摘要
二型模糊熵用于衡量二型模糊集合的模糊程度与信息量,综述其研究现状。简单回顾了二型模糊集合的基本定义,论述了二型模糊熵的发展现状,重点研究了几种典型区间二型模糊熵的公理化定义及其计算公式,最后指出了未来的发展方向。
The entropy of a type-2 fuzzy set is used to measure the fuzziness degree and information quantity of the set,this paper summarizes the research status quo of this index.The basic knowledge of type-2 fuzzy sets is reviewed in brief,the development status of the index is dissertated,several typical axiomatic definitions and formulae of entropies of interval type-2 fuzzy sets are researched as the key.The future development is finally pointed out.
The entropy of a type-2 fuzzy set is used to measure the fuzziness degree and information quantity of the set,this paper summarizes the research status quo of this index.The basic knowledge of type-2 fuzzy sets is reviewed in brief,the development status of the index is dissertated,several typical axiomatic definitions and formulae of entropies of interval type-2 fuzzy sets are researched as the key.The future development is finally pointed out.
引文
[1]王玲,秦克云,刘雅雅.区间值模糊软集的相似度及距离和熵[J].济南大学学报(自然科学版),2015,29(5):361-366
[2]张丽波.基于三角模糊熵的信息安全风险评估研究[D].哈尔滨:黑龙江大学,2013
[3]徐翀.基于直觉模糊熵权法的智能变电站建设项目风险评价[J].华东电力,2014,42(7):1449-1451
[4]郑毅,郑苹.结合模糊熵和遗传算法的双阈值图像分割[J].应用科学学报,2014,32(4):427-433
[5]杨望灿,张培林,任国全,等.基于模糊熵与LS-SVM的轴承故障诊断[J].机械强度,2014,36(5):666-670
[6]郑近德,陈敏均,程军胜,等.多尺度模糊熵及其在滚动轴承故障诊断中的应用[J].振动工程学报,2014,27(1):145-151
[7]Sadeghian A, Mendel J M, Tahayori H. Advances in Type-2Fuzzy Sets and Systems:Theory and Applications[M]. Germany, Berlin:Springer, 2013
[8]Zhang H,Zhang W,Mei C.Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure[J].Knowledge-Based Systems,2009,22(6):449-454
[9]Liu X.Entropy,distance measure and similarity measure of fuzzy sets and their relations[J].Fuzzy Sets and Systems,1992, 52(3):305-318
[10]Bustince H,Burillo P.Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J].Fuzzy Sets and Systems,1996, 78(3):305-316
[11]Wang G, Li X. On the IV-fuzzy degree and the IV-similarity degree of IVFS and their integral representation[J].Journal of Engineering Mathematics, 2004, 21:195-201
[12]Zeng W,Li H.Relationship between similarity measure and entropy of interval-valued fuzzy sets[J].Fuzzy Sets and Systems,2006,157(11):1477-1484
[13]Wu D,Mendel J M.Uncertainty measures for interval type-2fuzzy sets[J].Information Sciences,2007,177(23):5378-5393
[14]Zeng W,Guo P.Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship[J].Information Sciences,2008,178(5):1334-1342
[15]邓廷权,王占江,汪培培,等.二型模糊集的模糊熵研究[J].控制与决策,2012,27(3):408-412
[2]张丽波.基于三角模糊熵的信息安全风险评估研究[D].哈尔滨:黑龙江大学,2013
[3]徐翀.基于直觉模糊熵权法的智能变电站建设项目风险评价[J].华东电力,2014,42(7):1449-1451
[4]郑毅,郑苹.结合模糊熵和遗传算法的双阈值图像分割[J].应用科学学报,2014,32(4):427-433
[5]杨望灿,张培林,任国全,等.基于模糊熵与LS-SVM的轴承故障诊断[J].机械强度,2014,36(5):666-670
[6]郑近德,陈敏均,程军胜,等.多尺度模糊熵及其在滚动轴承故障诊断中的应用[J].振动工程学报,2014,27(1):145-151
[7]Sadeghian A, Mendel J M, Tahayori H. Advances in Type-2Fuzzy Sets and Systems:Theory and Applications[M]. Germany, Berlin:Springer, 2013
[8]Zhang H,Zhang W,Mei C.Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure[J].Knowledge-Based Systems,2009,22(6):449-454
[9]Liu X.Entropy,distance measure and similarity measure of fuzzy sets and their relations[J].Fuzzy Sets and Systems,1992, 52(3):305-318
[10]Bustince H,Burillo P.Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets[J].Fuzzy Sets and Systems,1996, 78(3):305-316
[11]Wang G, Li X. On the IV-fuzzy degree and the IV-similarity degree of IVFS and their integral representation[J].Journal of Engineering Mathematics, 2004, 21:195-201
[12]Zeng W,Li H.Relationship between similarity measure and entropy of interval-valued fuzzy sets[J].Fuzzy Sets and Systems,2006,157(11):1477-1484
[13]Wu D,Mendel J M.Uncertainty measures for interval type-2fuzzy sets[J].Information Sciences,2007,177(23):5378-5393
[14]Zeng W,Guo P.Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship[J].Information Sciences,2008,178(5):1334-1342
[15]邓廷权,王占江,汪培培,等.二型模糊集的模糊熵研究[J].控制与决策,2012,27(3):408-412