一类基于坐标变换的带参数直觉模糊距离构造方法

南京大学学报(自然科学版) ›› 2017, Vol. 53 ›› Issue (3): 462–.

一类基于坐标变换的带参数直觉模糊距离构造方法

张振华1*，胡　勇2，严玉清3

出版日期:2017-05-30 发布日期:2017-05-30
作者简介:1.广东外语外贸大学经济贸易学院，广州，510006；2.暨南大学大数据决策研究所，广州，510632；3．广东外语外贸大学金融学院，广州，510006
基金资助:
基金项目：国家自然科学基金(71271061)，广东省自然科学基金(2014A030313575，2016A030313688)，广东省软科学项目(2015A070704051)，广东省哲学社科项目(GD12XGL14)，广州市哲学社科项目(14G41)，广东省教育厅科技创新项目(2013KJCX0072)，全国统计科研重点项目(2016LZ18)，广东外语外贸大学重点创新团队项目(TD1605，15T21) 收稿日期：2016－11－28 *通讯联系人，Email：zhangzhenhua@gdufs.edu.cn

A construction approach of the distance measure with parameter between intuitionistic fuzzy sets based on the coordinates transformation

Zhang Zhenhua1*，Hu Yong2，Yan Yuqing3

Online:2017-05-30 Published:2017-05-30
About author:1.School of Economics and Trade，Guangdong University of Foreign Studies，Guangzhou，510006，China；2．Institute of Big Data and Decision Making，Jinan University，Guangzhou，510632，China；3．School of Finance，Guangdong University of Foreign Studies，Guangzhou，510006，China

摘要/Abstract

摘要： 1986年Atanassov提出直觉模糊集后，提出了多种直觉模糊集的距离公式，然而鲜有分析各种距离公式之间的差异．基于此，提出一种基于直觉模糊集三维坐标下的空间变换模型(隶属度、非隶属度、犹豫度)，并证明了在坐标变换下，变换前后向量空间具备相同的代数性质和代数结构．在此基础上，构建了一系列新的直觉模糊集空间模型及其上的距离．尤其重要的是，提出了两类带参数的距离公式，而且该两类距离公式的排序能力都随着参数的变化而变化，现有经典直觉模糊集距离公式都是新距离公式的特例．因此，将所有距离公式依据其排序能力分成两大类：强序距离和弱序距离．仿真实验结果表明，强序距离在聚类、分类和模式识别中的表现明显优于弱序距离，公开数据库的手写体图像识别实验也证明强序距离在模式识别中的优势．

Abstract: Since Atanassov introduced the concept of the intuitionistic fuzzy sets(IFS)in 1986，increasing distance measures between IFSs were presented by other researchers.However，few articles analyze the difference among these measuring distances.This paper first proposes a method based on the space transformation about all the three vectors(the membership，nonmembership and hesitation degree)．Then it is shown that the transformed space has the same algebra structure and properties as the original.Considering this characteristic，we present a series of new spaces of the IFS and new measuring distances.Particularly，two sorts of special measuring distances with parameter are proposed and their ordering capability changes with their parameter values，and all of the classic measuring distances are their special cases.Therefore，all these measuring distances can be classified to be two classes according to their ordering capability：one is strong order distance，and the other weak order one.Results show that the strong order distance is superior to the weak one when applied to clustering，classification，and pattern recognition.The experiment of image recognition for handwritten words also proved the superiority of strong order distance in pattern recognition.

张振华1*，胡　勇2，严玉清3. 一类基于坐标变换的带参数直觉模糊距离构造方法[J]. 南京大学学报(自然科学版), 2017, 53(3): 462–.

Zhang Zhenhua1*，Hu Yong2，Yan Yuqing3. A construction approach of the distance measure with parameter between intuitionistic fuzzy sets based on the coordinates transformation[J]. Journal of Nanjing University(Natural Sciences), 2017, 53(3): 462–.

参考文献

[1]　Zadeh L A．Fuzzy sets.Information and Control，1965，8：338－353. [2] Atanassov K．Intuitionistic fuzzy sets.Fuzzy Sets and Systems，1986，20(1)：87－96. [3] Atanassov K．Intuitionistic fuzzy sets.Theory and applications.Heidelberg，New York，USA：Physica Verlag，1999，324. [4] Szmidt E，Kacprzyk J．Distances between inituitionistic fuzzy sets.Fuzzy Sets and Systems，2000，114(3)：505－518. [5] Szmidt E，Kacprzyk J．Dilemmas with distances between intuitionstic fuzzy sets：Straightforward approaches may not work.Studies in Computational Intelligence，2008，109：415－430. [6] Wang W Q，Xin X L．Distance measures between intuitionstic fuzzy sets.Pattern Recognition Letters，2005，26(13)：2063－2069. [7] Li Y H，Olson D L，Qin Z．Similarity between intuitionstic fuzzy(vague)sets：A comparative analysis.Pattern Recognition Letters，2007，28(2)：278－285. [8] Xu Z S．Some similarity measures of intuitionstic fuzzy sets and their applications to multiple attribute decision making.Fuzzy Optimization and Decision Making，2007，6(2)：109－121. [9] Xu Z S，Yager R R．Intuitionistic and intervalvalued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group.Fuzzy Optimization and Decision Making，2009，8(2)：123－139. [10] Chen S M．Measures of similarity between vague sets.Fuzzy Sets and Systems，1995，74(2)：217－223. [11] Chen S M．Similarity measures between vague sets and between elements.IEEE Transactions on Systems，Man，and Cybernetics，1997，27(1)：153－157. [12] Hong D H，Kim C．A note on similarity measures between vague sets and between elements.Information Sciences，1999，115(1)：83－96. [13] Li D F，Chen C T．New similarity measures between intuitionistic fuzzy sets and application to pattern recognitions.Pattern Recognition Letters，2002，23(1－3)：221－225. [14] 李　凡，徐章艳．Vague集之间的相似度量．软件学报，2001，12(6)：922－927.(Li F，Xu Z Y．Measures of similarity between vague sets.Journal of Software，2001，12(6)：922－927.) [15] 周晓光，谭春桥，张　强．基于Vague集的决策理论与方法．北京：科学出版社，2009，200.(Zhou X G，Tan C Q，Zhang Q．Decision theory and method based on vague sets.Beijing：Science Press，2009，200.) [16] 申晓勇，雷英杰，蔡　茹等．基于加权Minkowski距离的IFS相异度度量方法．系统工程与电子技术，2009，31(6)：1358－1361.(Shen X Y，Lei Y J，Cai R，et al.Method for dissimilarity measure among intuitionistic fuzzy sets based on weighted Minkowski distance.Systems Engineering and Electronics，2009，31(6)：1358－1361.) [17] 王　毅，刘三阳，程月蒙等．基于倾向性的直觉模糊相似度量方法．系统工程与电子技术，2015，37(4)：863－867.(Wang Y，Liu S Y，Cheng Y M，et al.Intuitionistic fuzzy similarity measure approach based on orientation.Systems Engineering and Electronics，2015，37(4)：863－867.) [18] 李宝萍，陈华友．直觉模糊面集的相似度及其在模式识别中的应用．模糊系统与数学，2015，29(1)：134－141.(Li B P，Chen H Y．Intuitionistic fuzzy area set and its application in pattern recognition.Fuzzy Systems and Mathematics，2015，29(1)：134－141.) [19] 廖建平，王卫民．基于新直觉模糊相似度量的直觉模糊谱聚类算法．科技通报，2015，31(4)：222－226.(Liao J P，Wang W M．Intuitionistic fuzzy spectral clustering algorithm based on new intuitionistic fuzzy similarity measurement.Bulletin of Science and Technology，2015，31(4)：222－226.) [20] 陈　岩，张　宁．基于直觉模糊相似度量的群决策专家水平评判方法．数学的实践与认识，2016，46(2)：183－189.(Chen Y，Zhang N．Expert judgment method of group decision making based on intuitionistic fuzzy similarity measure.Mathematics in Practice and Theory，2016，46(2)：183－189.) [21] 单玉莹，裴道武．直觉模糊数排序方法的合理性．模糊系统与数学，2014，28(5)：170－177.(Shan Y Y，Pei D W．Rationality of ordering methods of intuitionistic fuzzy numbers.Fuzzy Systems and Mathematics，2014，28(5)：170－177.) [22] 邓冠男，姜妍丽，付景超．直觉模糊集的单调贴近度及其与熵、包含度的关系．数学的实践与认识，2014，44(22)：286－292.(Deng G N，Jiang Y L，Fu J C．The monotonic approximation degree of intuitionistic fuzzy sets and its relation to entropy and inclusion.Mathematics in Practice and Theory，2014，44(22)：286－292.) [23] Pechwitz M，Maddouri S S，Märgner V，et al.IFN/ENIT database of handwritten Arabic words.In：Francophone International Conference on Writing and Document(CIFSD2002)．Hammamet，Tunisia：CIFED，2002：129－136. [24] Pechwitz M，Abed H E，Märgner V．Handwritten arabic word recognition using the IFN/ENITdatabase.Guide to OCR for Arabic Scripts.London：Springer，2012，169－213.

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