A construction approach of the distance measure with parameter between intuitionistic fuzzy sets based on the coordinates transformation
Zhang Zhenhua1*，Hu Yong2，Yan Yuqing3
Author information+
{{custom_zuoZheDiZhi}}
About authors:
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
{{custom_authorNodes}}
{{custom_bio.content}}
{{custom_bio.content}}
{{custom_authorNodes}}
Collapse
History+
Published
2017-05-30
Issue Date
2017-05-30
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.
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
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[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.
PDF(1752909 KB)
