Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Artificial Intelligence Review
Erschienen in: Artificial Intelligence Review 3/2019

30.11.2017

Pythagorean fuzzy set: state of the art and future directions

verfasst von: Xindong Peng, Ganeshsree Selvachandran

Erschienen in: Artificial Intelligence Review | Ausgabe 3/2019

Einloggen

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

search-config
loading …

Abstract

Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade \(\mu \) and non-membership \(\nu \) satisfying the condition \(\mu ^2+\nu ^2\le 1\). It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.
Vorheriger Artikel A survey of parameter reduction of soft sets and corresponding algorithms
Nächster Artikel TP-TA: a comparative analytical framework for trust prediction models in online social networks based on trust aspects

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 "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

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
Literatur
Alcantud JCR (2016) Some formal relationships among soft sets, fuzzy sets, and their extensions. Int J Approx Reason 68:45–53MathSciNetMATHCrossRef
Atanssov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96CrossRef
Beg I, Rashid T (2016) An intuitionistic 2-tuple linguistic information model and aggregation operators. Int J Intell Syst 31(6):569–592CrossRef
Beliakov G, James S (2014) Averaging aggregation functions for preferences expressed as pythagorean membership grades and fuzzy orthopairs. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 298–305
Dick S, Yager R, Yazdanbakhsh O (2016) On pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021CrossRef
Du YQ, 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):1085–1112CrossRef
Fodor J, Marichal J, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236–240CrossRef
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):886–920CrossRef
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):529–540MATHCrossRef
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 (2017b) Generalized pythagorean fuzzy geometric aggregation operators using einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630
Ghorabaee MK, Amiri M, Sadaghiani J, Goodarzi G (2014) Multiple criteria group decision-making for supplier selection based on copras method with interval type-2 fuzzy sets. Int J Adv Manuf Technol 75:1115–1130CrossRef
Ghorabaee MK, Zavadskas EK, Olfat L, Turskis Z (2015) Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 26:435–451CrossRef
Ghorabaee MK, Zavadskas EK, Amiri M, Turskis Z (2016) Extended edas method for fuzzy multi-criteria decision-making: an application to supplier selection. Int J Comput Commun Control 11:358–371CrossRef
Gou XJ, Xu ZS, Ren PJ (2016) The properties of continuous pythagorean fuzzy information. Int J Intell Syst 31(5):401–424CrossRef
Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272MathSciNetMATHCrossRef
He X, Du Y, Liu W (2016) Pythagorean fuzzy power average operators. Fuzzy Syst Math 30(6):116–124MATH
Herrera F, Herrera-Viedma E, Verdegay J (1996) A model of consensus in group decision making under linguistic assessments. Fuzzy Set Syst 79(1):73–87MathSciNetMATHCrossRef
Li D, Zhang B, Leung Y (2004) On knowledge reduction in inconsistent decision information systems. Int J Uncertain Fuzziness Knowl-Based Syst 12(5):651–672MathSciNetMATHCrossRef
Li M, Yu Y, Xu Y (2015) Knowledge checking service selection method in pythagorean fuzzy environment. In: International conference on logistics engineering. Management and Computer Science, pp 1438–1443
Liang DC, Xu Z (2017) The new extension of topsis method for multiple criteria decision making with hesitant pythagorean fuzzy sets. Appl Soft Comput 60:167–179CrossRef
Liang DC, Xu ZS, Darko AP (2017) Projection model for fusing the information of pythagorean fuzzy multicriteria group decision making based on geometric bonferroni mean. Int J Intell Syst 32:966–987CrossRef
Liang J, Wang F, Dang C, Qian Y (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53(6):912–926MathSciNetCrossRef
Liang W, Zhang X, Liu M (2015) The maximizing deviation method based on interval-valued pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc 2015:1–15MathSciNetMATH
Liao HC, Xu Z (2014) Intuitionistic fuzzy hybrid weighted aggregation operators. Int J Intell Syst 29(11):971–993CrossRef
Liao HC, Xu Z (2015) Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput 19(9):2551–2564MATHCrossRef
Liao HC, Xu ZS, Zeng XJ (2015) Hesitant fuzzy linguistic vikor method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355CrossRef
Liao HC, Gou XJ, Xu ZS (2017) A survey of decision making theory and methodologies of hesitant fuzzy linguistic term set. Syst Eng Theor Pract 37(1):35–48
Liou JJ, Tamosaitiene J, Zavadskas E, Tzeng G (2016) New hybrid copras-g madm model for improving and selecting suppliers in green supply chain management. Int J Prod Res 54:114–134CrossRef
Liu C, Tang G, Liu P (2017) An approach to multi-criteria group decision making with unknown weight information based on pythagorean fuzzy uncertain linguistic aggregation operators. Math Probl Eng 2017:1–18
Liu W, Chang J, He X (2016) Generalized pythagorean fuzzy aggregation operators and applications in decision making. Control Decis 31(12):2280–2286MATH
Liu ZM, Liu PD, Liu WL, Pang JY (2017c) Pythagorean uncertain linguistic partitioned bonferroni mean operators and their application in multi-attribute decision making. J Intell Fuzzy Syst 32(3):2779–2790MathSciNetMATHCrossRef
Luca AD, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–312MATHCrossRef
Ma ZM, Xu ZS (2016) Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219CrossRef
Merigó JM (2011) A unified model between the weighted average and the induced owa operator. Expert Syst Appl 38(9):11,560–11,572CrossRef
Pamucar D, Cirovic G (2015) The selection of transport and handling resources in logistics centers using multi-attributive border approximation area comparison (mabac). Expert Syst Appl 42(6):3016–3028CrossRef
Peng DH, Gao C, Gao Z (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37:5837–5850MathSciNetMATHCrossRef
Peng XD, Dai J (2017) Approaches to pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32(11):1187–1214CrossRef
Peng XD, Liu C (2017) Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set. J Intell Fuzzy Syst 32(1):955–968MATHCrossRef
Peng XD, Yang Y (2016a) Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487CrossRef
Peng XD, Yang Y (2016b) Multiple attribute group decision making methods based on pythagorean fuzzy linguistic set. Comput Eng Appl 52(23):50–54
Peng XD, Yang Y (2016c) Pythagorean fuzzy choquet integral based mabac method for multiple attribute group decision making. Int J Intell Syst 31(10):989–1020MathSciNetCrossRef
Peng XD, Yang Y, Song J, Jiang Y (2015a) Pythagorean fuzzy soft set and its application. Comput Eng 41(7):224–229
Peng XD, Yang Y, Zhu YL (2015b) Similarity measure and its application based on multi-parametric intuitionistic fuzzy sets. Comput Eng Appl 51(13):122–125
Peng XD, Dai J, Yuan H (2017a) Interval-valued fuzzy soft decision making methods based on MABAC, similarity measure and EDAS. Fund Inform 152:1–24MathSciNetMATHCrossRef
Peng XD, Yuan H, Yang Y (2017b) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32(10):991–1029CrossRef
Phong PH, Son L (2017) Linguistic vector similarity measures and applications to linguistic information classification. Int J Intell Syst 32(1):67–81CrossRef
Qian Y, Liang J, Dang C (2010a) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern A 40(2):420–431CrossRef
Rahman K, Abdullah S, Ahmed R, Ullah M (2017a) Pythagorean fuzzy einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J Intell Fuzzy Syst 33(1):635–647MATHCrossRef
Rahman K, Khan MS, Ullah M, Fahmi A (2017b) Multiple attribute group decision making for plant location selection with pythagorean fuzzy weighted geometric aggregation operator. The Nucleus 54(1):66–74
Reformat MZ, Yager RR (2014) Suggesting recommendations using pythagorean fuzzy sets illustrated using netflix movie data. In: Proceedings of the information processing and management of uncertainty in knowledge-based systems, pp 546–556
Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy todim approach to multi-criteria decision making. Appl Soft Comput 42:246–259CrossRef
Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Tech Inf 33:8–9
Wang P (1983) Fuzzy sets and its applications. Shanghai Science and Technology Press, ShanghaiMATH
Wei CP, Liao H (2016) A multigranularity linguistic group decision-making method based on hesitant 2-tuple sets. Int J Intell Syst 31(6):612–634MathSciNetCrossRef
Wei GW, Wang H, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26(2):337–349CrossRef
Xu ZS (2016) Additive intuitionistic fuzzy aggregation operators based on fuzzy measure. Int J Uncertain Fuzz Based Syst 24(1):1–12MathSciNetMATHCrossRef
Xu ZS, Da Q (2004) Linguistic approaches to multiple attribute decision making in uncertain linguistic setting. J Southeast Univ 20(4):482–485MATH
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433MathSciNetMATHCrossRef
Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybernet B 41(2):568–578CrossRef
Xue YX, You JX, Lai X, Liu H (2016) An interval-valued intuitionistic fuzzy mabac approach for material selection with incomplete weight information. Appl Soft Comput 38:703–713CrossRef
Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, pp 57–61
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRef
Yager RR (2016) Properties and applications of pythagorean fuzzy sets. Springer, BerlinMATHCrossRef
Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452CrossRef
Yang Y, Ding H, Chen ZS, Li YL (2016) A note on extension of topsis to multiple criteria decision making with pythagorean fuzzy sets. Int J Intell Syst 31(1):68–72CrossRef
Yu SM, Wang J, Wang JQ (2017) An interval type-2 fuzzy likelihood-based mabac approach and its application in selecting hotels on a tourism website. Int J Fuzzy Syst 19(1):47–61MathSciNetCrossRef
Zavadskas EK, Kaklauskas A, Sarka V (1994) The new method of multicriteria complex proportional assessment of projects. Technol Econ Dev Eco 1:131–139
Zeng SZ (2017) Pythagorean fuzzy multiattribute group decision making with probabilistic information and owa approach. Int J Intell Syst 33(11):1136–1150CrossRef
Zeng SZ, Chen J, Li X (2016) A hybrid method for pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis 15(2):403–422CrossRef
Zhang C, Li D (2016) Pythagorean fuzzy rough sets and its applications in multi-attribute decision making. J Chin Compu Syst 37(7):1531–1535
Zhang C, Li D, Ren R (2016) Pythagorean fuzzy multigranulation rough set over two universes and its applications in merger and acquisition. Int J Intell Syst 31(9):921–943CrossRef
Zhang XL (2016a) Multicriteria pythagorean fuzzy decision analysis: a hierarchical qualiflex approach with the closeness index-based ranking methods. Inf Sci 330:104–124CrossRef
Zhang XL (2016b) A novel approach based on similarity measure for pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31(6):593–611CrossRef
Zhang XL, Xu ZS (2014) Extension of topsis to multiple criteria decision making with pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078MathSciNetCrossRef
Metadaten
Titel
Pythagorean fuzzy set: state of the art and future directions
verfasst von
Xindong Peng
Ganeshsree Selvachandran
Publikationsdatum
30.11.2017
Verlag
Springer Netherlands
Erschienen in
Artificial Intelligence Review / Ausgabe 3/2019
Print ISSN: 0269-2821
Elektronische ISSN: 1573-7462
DOI
https://doi.org/10.1007/s10462-017-9596-9

Weitere Artikel der Ausgabe 3/2019

Artificial Intelligence Review 3/2019 Zur Ausgabe

ReviewPaper

A systematic review of data-driven approaches in player modeling of educational games

OriginalPaper

A survey on sentiment analysis of scientific citations

OriginalPaper

Comparison of algorithms to divide noisy phone sequences into syllables for automatic unconstrained English speaking proficiency scoring

OriginalPaper

How important is syntactic parsing accuracy? An empirical evaluation on rule-based sentiment analysis

OriginalPaper

A methodology for applying k-nearest neighbor to time series forecasting

OriginalPaper

An immune memory inspired case-based reasoning system to control interrupted flow at a signalized intersection