nach oben

Granular Computing

Erschienen in:

19.12.2018 | Original Paper

Distance and similarity measures for Pythagorean fuzzy sets

verfasst von: Paul Augustine Ejegwa

Erschienen in: Granular Computing | Ausgabe 2/2020

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The concept of Pythagorean fuzzy sets is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of Pythagorean fuzzy sets is that it is characterized by three parameters, namely, membership degree, non-membership degree, and indeterminate degree, in such a way that the sum of the square of each of the parameters is one. In this paper, we present axiomatic definitions of distance and similarity measures for Pythagorean fuzzy sets, taking into account the three parameters that describe the sets. Some distance and similarity measures in intuitionistic fuzzy sets, viz, Hamming, Euclidean, normalized Hamming, and normalized Euclidean distances, and similarities are extended to Pythagorean fuzzy set setting. However, it is discovered that Hamming and Euclidean distances and similarities fail the metric conditions in Pythagorean fuzzy set setting whenever the elements of the two Pythagorean fuzzy sets, whose distance and similarity are to be measured, are not equal. Finally, numerical examples are provided to illustrate the validity and applicability of the measures. These measures are suggestible to be resourceful in multicriteria decision-making problems (MCDMP) and multiattribute decision-making problems (MADMP), respectively.

Vorheriger Artikel Fuzzy rough soft set and its application to lattice

Nächster Artikel Neighborhood attribute reduction approach to partially labeled data

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren

Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, SofiaMATH

Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20:87–96MATH

Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, HeidelbergMATH

Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, BerlinMATH

Beliakov G, James S (2014) Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs. In: Proc IEEE Int Conf Fuzzy Syst (FUZZ-IEEE), pp 298–305

Chen SM, Chang CH (2015) A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114

Chen SM, Chang YC (2011) Weighted fuzzy rule interpolation based on GA-based weight-learning techniques. IEEE Trans Fuzzy Syst 19(4):729–744MathSciNet

Chen SM, Cheng SH, Chiou CH (2016) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf Fusion 27:215–227

Chen SM, Lee SH, Lee CH (2001) A new method for generating fuzzy rules from numerical data for handling classification problems. Appl Artif Intell 15(7):645–664CrossRef

Chen SM, Munif A, Chen GS, Liu HC, Kuo BC (2012) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst Appl 39(7):6320–6334

Chen SM, Tanuwijaya K (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–1543

Davvaz B, Sadrabadi EH (2016) An application of intuitionistic fuzzy sets in medicine. Int J Biomath 9(3):1650037MathSciNetMATH

De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117(2):209–213MATH

Diamond P, Kloeden P (1994) Metric spaces of fuzzy sets theory and applications. World Scientific, SingaporeMATH

Dick S, Yager RR, Yazdanbakhsh O (2016) On Pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021

Du Y, Hou F, Zafar W, Yu Q, Zhai Y (2017) A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112

Ejegwa PA (2015) Intuitionistic fuzzy sets approach in appointment of positions in an organization via max–min–max rule. Glob J Sci Front Res Math Decis Sci 15(6):1–6

Ejegwa PA, Akubo AJ, Joshua OM (2014) Intuitionistic fuzzy sets in career determination. J Inf Comput Sci 9(4):285–288

Ejegwa PA, Modom ES (2015) Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets. Intern J Fuzzy Math Arch 8(1):1–7

Gao H, Wei GW (2018) Multiple attribute decision making based on interval-valued Pythagorean fuzzy uncertain linguistic aggregation operators. Int J Knowl Based Intell Eng Syst 22:59–81

Garg H (2016a) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920

Garg H (2016b) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540MATH

Garg H (2016c) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision making processes. Int J Intell Syst 31(12):1234–1252

Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm fo multicriteria decision making process. Int J Intell Syst 32(6):597–630

Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision making process. Int J Intell Syst 33(6):1234–1263

Gou XJ, Xu ZS, Ren PJ (2016) The properties of continuous Pythagorean fuzzy information. Int J Intell Syst 31(5):401–424

Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272MathSciNetMATH

Hatzimichailidis AG, Papakostas AG, Kaburlasos VG (2012) A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. Int J Intell Syst 27:396–409

He X, Du Y, Liu W (2016) Pythagorean fuzzy power average operators. Fuzzy Syst Math 30(6):116–124MATH

Kacprzyk J (1997) Multistage fuzzy control. Wiley, ChichesterMATH

Khan M S. A, Abdullah S, Ali A, Amin F (2018a) An extension of VIKOR method for multiattribute decision making under Pythagorean hesitant fuzzy setting. Granul Comput. https://doi.org/10.1007/s41066-018-0102-9

Khan MSA, Abdullah S, Ali A, Amin F (2018b) Pythagorean fuzzy prioritized aggregation operators and their application to multiattribute group decision making. Granul Comput. https://doi.org/10.1007/s41066-018-0093-6

Li DQ, Zeng WY (2018) Distance measure of Pythagorean fuzzy sets. Int J Intell Syst 33:348–361

Liang D, Xu Z (2017) The new extension of topsis method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179

Liu P, Chen SM (2017) Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514–2530

Mohagheghi V, Mousavi SM, Vahdani B (2017) Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets. Appl Soft Comput 61:527–535

Mohd WRW, Abdullah L (2018) Similarity measures of Pythagorean fuzzy sets based on combination of cosine similarity measure and Euclidean distance measure. AIP Conf Proc 1974:030017–1–030017-7. https://doi.org/10.1063/1.5041661 CrossRef

Peng X, Selvachandran G (2017) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev. https://doi.org/10.1007/s10462-017-9596-9

Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160

Perez-Dominguez L, Rodriguez-Picon LA, Alvarado-Iniesta A, Cruz DL, Xu Z (2018) Moora under Pythagorean fuzzy sets for multiple criteria decision making. Complex. https://doi.org/10.1155/2018/2602376 MATH

Rahman K, Abdullah S (2018) Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision making. Granul Comput. https://doi.org/10.1007/s41066-018-0082-9

Rahman K, Abdullah S, Ali A (2018a) Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbers. Granul Comput. https://doi.org/10.1007/s41066-018-0091-8

Rahman K, Abdullah S, Shakeel M, Khan M. S. A, Ullah M (2017) Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Math. https://doi.org/10.1080/23311835.2017.1338638

Rahman K, Ali A, Abdullah S, Amin F (2018b) Approaches to multi-attribute group decision making based on induced interval-valued Pythagorean fuzzy einstein aggregation operator. New Math Nat Comput 14(3):343–361MathSciNetMATH

Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Springer, SwitzerlandMATH

Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Set Syst 114(3):505–518MathSciNetMATH

Szmidt E, Kacprzyk J (2001) Intuitionistic fuzzy sets in some medical applications. Note IFS 7(4):58–64MATH

Szmidt E, Kacprzyk J (2004) Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets. Note IFS 10(4):61–69MATH

Wang HY, Chen SM (2008) Evaluating students’ answerscripts using fuzzy numbers associated with degrees of confidence. IEEE Trans Fuzzy Syst 16(2):403–415

Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recogn Lett 26:2063–2069

Yager RR (2013a) Pythagorean fuzzy subsets. In: Proc Joint IFSAWorld Congress NAFIPS annual meeting, pp 57–61

Yager R R (2013b) Pythagorean membership grades in multicriteria decision making. Technical report MII-3301. Machine Intelligence Institute, Iona College, New Rochelle

Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

Yager RR (2016) Properties and applications of Pythagoean fuzzy sets. Springer, Berlin

Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436–452

Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353MATH

Zeng W, Li D, Yin Q (2018) Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making. Int J Intell Syst. https://doi.org/10.1002/int.22027

Zhang XL, Xu ZS (2014) Extension of topsis to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078MathSciNet

Titel: Distance and similarity measures for Pythagorean fuzzy sets
verfasst von: Paul Augustine Ejegwa
Publikationsdatum: 19.12.2018
Verlag: Springer International Publishing
Erschienen in: Granular Computing / Ausgabe 2/2020
Print ISSN: 2364-4966
Elektronische ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-018-00149-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2020

Interval methods for robust gain scheduling controllers

Improved composite relation for pythagorean fuzzy sets and its application to medical diagnosis

Novel distance measures for cubic intuitionistic fuzzy sets and their applications to pattern recognitions and medical diagnosis

Neighborhood attribute reduction approach to partially labeled data

Novel hybrid decision-making methods based on mF rough information

Fuzzy rough soft set and its application to lattice