Skip to main content
Erschienen in: Soft Computing 6/2019

03.11.2017 | Methodologies and Application

A new approach to construct similarity measure for intuitionistic fuzzy sets

verfasst von: Yafei Song, Xiaodan Wang, Wen Quan, Wenlong Huang

Erschienen in: Soft Computing | Ausgabe 6/2019

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The intuitionistic fuzzy set (IFS), as a generation of Zadeh’s fuzzy set, can express and process uncertainty much better. Similarity measures between IFSs are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for IFSs have been proposed in previous studies, some of them cannot satisfy the axioms of similarity, or provide counterintuitive cases. In this paper, we first review several widely used similarity measures and then propose a new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined based on the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measure satisfies the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. Experiments on medical diagnosis and cluster analysis are carried out to illustrate the applicability of the proposed similarity measure in practice.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Balasubramaniam P, Ananthi VP (2014) Image fusion using intuitionistic fuzzy sets. Inf Fusion 20(1):21–30CrossRef Balasubramaniam P, Ananthi VP (2014) Image fusion using intuitionistic fuzzy sets. Inf Fusion 20(1):21–30CrossRef
Zurück zum Zitat Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57MathSciNetCrossRefMATH Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57MathSciNetCrossRefMATH
Zurück zum Zitat Chen TY (2007) A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 158:2523–2525MathSciNetCrossRefMATH Chen TY (2007) A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 158:2523–2525MathSciNetCrossRefMATH
Zurück zum Zitat De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117:209–213CrossRefMATH De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117:209–213CrossRefMATH
Zurück zum Zitat Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328MathSciNetCrossRefMATH Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328MathSciNetCrossRefMATH
Zurück zum Zitat Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25:1603–1611CrossRef Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25:1603–1611CrossRef
Zurück zum Zitat Hwang CM, Yang MS, Hung WL, Lee MG (2012) A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition. Inf Sci 189:93–109MathSciNetCrossRefMATH Hwang CM, Yang MS, Hung WL, Lee MG (2012) A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition. Inf Sci 189:93–109MathSciNetCrossRefMATH
Zurück zum Zitat Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225CrossRefMATH Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225CrossRefMATH
Zurück zum Zitat Li J, Deng G (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 188:314–321MathSciNetCrossRefMATH Li J, Deng G (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 188:314–321MathSciNetCrossRefMATH
Zurück zum Zitat Li F, Xu Z (2001) Similarity measures between vague sets. J Softw 12:922–927 Li F, Xu Z (2001) Similarity measures between vague sets. J Softw 12:922–927
Zurück zum Zitat Li Y, Chi Z, Yan D (2002) Similarity measures between vague sets and vague entropy. J Comput Sci 29:129–132 Li Y, Chi Z, Yan D (2002) Similarity measures between vague sets and vague entropy. J Comput Sci 29:129–132
Zurück zum Zitat Li Y, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28:278–285CrossRef Li Y, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28:278–285CrossRef
Zurück zum Zitat Liang ZZ, Shi PF (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693CrossRefMATH Liang ZZ, Shi PF (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693CrossRefMATH
Zurück zum Zitat Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104CrossRef Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104CrossRef
Zurück zum Zitat Ngan SC (2016) An activation detection based similarity measure for intuitionistic fuzzy sets. Expert Syst Appl 60(1):62–80CrossRef Ngan SC (2016) An activation detection based similarity measure for intuitionistic fuzzy sets. Expert Syst Appl 60(1):62–80CrossRef
Zurück zum Zitat Own CM (2009) Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis. Appl Intell 31(3):283–291CrossRef Own CM (2009) Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis. Appl Intell 31(3):283–291CrossRef
Zurück zum Zitat Papakostas GA (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recognit Lett 34:1609–1622CrossRef Papakostas GA (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recognit Lett 34:1609–1622CrossRef
Zurück zum Zitat Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Springer, New YorkCrossRefMATH Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Springer, New YorkCrossRefMATH
Zurück zum Zitat Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1055–1057MATH Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1055–1057MATH
Zurück zum Zitat Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: ICAISC, pp 388–393 Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: ICAISC, pp 388–393
Zurück zum Zitat Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-application to pattern recognition. Pattern Recognit Lett 28:197–206CrossRef Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-application to pattern recognition. Pattern Recognit Lett 28:197–206CrossRef
Zurück zum Zitat Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069CrossRef Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069CrossRef
Zurück zum Zitat Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286MathSciNetCrossRefMATH Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286MathSciNetCrossRefMATH
Zurück zum Zitat Xia M, Xu Z (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19:430–452CrossRef Xia M, Xu Z (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19:430–452CrossRef
Zurück zum Zitat Xu Z (2007) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121MathSciNetCrossRefMATH Xu Z (2007) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121MathSciNetCrossRefMATH
Zurück zum Zitat Xu Z, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness 16:529–555MathSciNetCrossRefMATH Xu Z, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness 16:529–555MathSciNetCrossRefMATH
Zurück zum Zitat Xu Z, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139MathSciNetCrossRefMATH Xu Z, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139MathSciNetCrossRefMATH
Zurück zum Zitat Zeng W, Guo P (2008) Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inf Sci 178:1334–1342MathSciNetCrossRefMATH Zeng W, Guo P (2008) Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inf Sci 178:1334–1342MathSciNetCrossRefMATH
Zurück zum Zitat Zhang H, Yu L (2013) New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf Sci 245:181–196MathSciNetCrossRefMATH Zhang H, Yu L (2013) New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf Sci 245:181–196MathSciNetCrossRefMATH
Metadaten
Titel
A new approach to construct similarity measure for intuitionistic fuzzy sets
verfasst von
Yafei Song
Xiaodan Wang
Wen Quan
Wenlong Huang
Publikationsdatum
03.11.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 6/2019
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2912-0

Weitere Artikel der Ausgabe 6/2019

Soft Computing 6/2019 Zur Ausgabe