Top

Granular Computing

Published in:

22-06-2021 | Original Paper

A novel VIKOR approach based on weighted correlation coefficients and picture fuzzy information for multicriteria decision making

Authors: Rajesh Joshi, Satish Kumar

Published in: Granular Computing | Issue 2/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Uncertain and vague information plays a crucial role in multicriteria decision making (MCDM) problems. Quantification of such information proves to be very helpful in selection of the most suitable alternative. Picture fuzzy set (PFS) studied by Cuong and Kreinovich has been proved to be a very powerful tool in capturing such vague information. In this paper, based on Renyi’s concept, a new picture fuzzy information measure is introduced. Besides its validation, some major properties of the proposed measure are also discussed. Apart from this, a novel decision making method using picture fuzzy information and weighted correlation coefficients based VIKOR (Vlsekriterijumska Optimizacija i Kompromisno Resenje) approach is put forward. The proposed decision making method is well explained through two numerical examples based on supplier selection.

previous article An indirect weak transitivity standard for inconsistent multiplicative reciprocal preference relations

next article Multiattribute decision-making under Fermatean fuzzy bipolar soft framework

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now

Available only for authorised users

Attanasov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

Atanassov KT (1999) Instutionistic fuzzy sets. Springer Verlag, New York

Aqlan F, Lam SS (2015) A fuzzy-based integrated framework for supply chain risk assessment. Int J Prod Econ 161:54–63

Bhandari D, Pal NR (1993) Some new information measures for fuzzy sets. Inf Sci 67(3):204–228MathSciNetMATH

Burillo P, Bustince H (2001) Entropy on intutionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 118:305–316MATH

Boekee DE, Vander Lubbe JCA (1980) The \(R\)-norm information measure. Inf Control 45:136–155MathSciNetMATH

Brans JP, Mareschel V (1984) PROMETHEE: a new family of outranking methods in multicriteria analysis. In: Brans JP (ed) Operational research 84. North-Holland, New York, pp 477–490

Benayoun R, Roy B, Sussman B (1966) ELECTRE Une méthode pour guider le choix en présence de points de vue multiples. Note de travail 49. Direction Scientifique: SEMA-METRA International

Cuong BC, Kreinovich V (2012) Picture fuzzy sets-a new concept for computational intelligence problems. In: Proc. of 3rd World Congress on Information and Communication Technologies (WICT), pp 1–6

Chen S-M, Jong W-T (1997) Fuzzy query translation for relational database systems. IEEE Trans Syst Man Cybern-Part B Cybern 27(4):714–721

Chen S-M, Wang N-Y (2010a) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern-Part B Cybern 40(5):1343–1358

Chen T, Li C (2010b) Determinig objective weights with intutionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180:4207–4222

Chen S-M, Niou S-J (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872

Chen S-M, Randyanto Y (2013) A novel similarity measure between intuitionistic fuzzy sets and its applications. Int J Pattern Recognit Artif Intell. https://doi.org/10.1142/S0218001413500213CrossRef

Chen S-M, Yo Y-K, Chang Y-C, Pan J-S (2009) Weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques. IEEE Trans Fuzzy Syst 17(6):1412–1427

Chen S-M, Randyanto Y, Cheng S-H (2016) Fuzzy queries processing based on intuitionistic fuzzy social relational networks. Inf Sci 327:110–124MathSciNetMATH

Chu ATW, Kalaba RE, Spingarn K (1979) A comparison of two methods for determining the weights of belonging to fuzzy sets. J Optim Theoret Appl 27:531–538MathSciNetMATH

Choo EU, Wedley WC (1985) Optimal criterian weights in repetitive multicriteria decision making. J Oper Res Soc 36:983–992MATH

Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gener Syst 17:191–209MATH

Fan ZP (1996) Complicated multiple attribute decision making: theory and applications. Ph.D. Dissertation, Northeastern university, Shenyang, China (1996)

Grattan-Guiness I (1975) Fuzzy membership mapped onto interval and many-valued quantities. Z Math Log Grundladen Math 22:149–160MathSciNet

Gerstenkorn T, Manko J (1991) Correlation of intuitionistic fuzzy sets. Fuzzy Sets Syst 44:39–43MathSciNetMATH

Havdra JH, Charvat F (1967) Quantification method classification process: concept of structural \(\rho \)-entropy. Kybernetika 3:30–35MathSciNet

Hung WL, Yang MS (2006) Fuzzy entropy on intuitionistic fuzzy sets. Int J Intell Syst 21:443–451MATH

Hwang CL, Hwang CL (1981) Multiple attribute decision-making: methods and applications. Springer- Verlag, New YorkMATH

Hwang CL, Lin MJ (1987) Group decision making under multiple criteria: methods and applications. Springer, BerlinMATH

Jahn KU (1975) Intervall-wertige Mengen. Math Nach 68:115–132MathSciNetMATH

Joshi R (2020a) A novel decision-making method using \(R\)-Norm concept and VIKOR approach under picture fuzzy environment. Experts Syst Appl. https://doi.org/10.1016/j.eswa.2020.113228CrossRef

Joshi R (2020b) A new picture fuzzy information measure based on Tsallis-Havdra-Charavat concept with applications in presaging poll outcome. Comput Appl Math. https://doi.org/10.1007/s40314-020-1106-zCrossRefMATH

Joshi R, Kumar S (2016) \((R, S)\)-norm information measure and a relation between coding and questionnaire theory. Open Syst Inf Dyn. https://doi.org/10.1142/S1230161216500153MathSciNetCrossRefMATH

Joshi R, Kumar S (2018a) An intuitionistic fuzzy \((\delta ,\gamma )\)-norm entropy with its application in supplier selection problem. Comput Appl Math. https://doi.org/10.1007/s40314-018-0656-9MathSciNetCrossRefMATH

Joshi R, Kumar S (2018b) A new parametric intuitionistic fuzzy entropy and its applications in multiple attribute decision making. Int J Appl Comput Math 4:52–74MathSciNetMATH

Joshi R, Kumar S (2018c) A new weighted \((\alpha , \beta )\)-norm information measure with applications in coding theory. Phys A Stat Mech Appl 510:538–551MathSciNet

Joshi R, Kumar S (2018d) A novel fuzzy decision making method using entropy weights based correlation coefficients under intuitionistic fuzzy environment. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-018-0538-8CrossRef

Joshi R, Kumar S (2019) An intuitionistic fuzzy information measure of order \((\rho , \beta )\) with a new approach in supplier selection problems using an extended VIKOR method. J Appl Math Comput. https://doi.org/10.1007/s12190-018-1202-zMathSciNetCrossRef

Lin H-C, Wang L-H, Chen S-M (2006) Query expansion for document retrieval based on fuzzy rules and user relevance feedback techniques. Experts Syst Appl 31(2):397–405

Liu P, Chen S-M, Wang Y (2019) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Int Sci 512:830–854MathSciNetMATH

Luca AD, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy set theory. Inf Control 20:301–312MATH

Nie RX, Wang JQ, Li L (2017) A shareholder voting method for proxy advisory firm selection based on 2-tuple linguistic picture preference relation. Appl Soft Comput 60:520–539

Pillay A, Wang J (2015) A risk ranking approach incorporating fuzzy set theory and grey theory. Reliab Eng Syst Saf 1(10):23–25

Opricovic S (1998) Multi-criteria optimization of civil engineering systems. Ph.D. Thesis, University of Belgrade, Belgrade, Serbia

Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178:514–529MATH

Renyi A (1961) On measures of entropy and information. In: Proc. 4th Barkley symp. on Math. Stat. and Probability. University of California Press 1:547–561

Saaty TL (1980) The analytical hierarchy process. McGraw-Hill, New YorkMATH

Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetMATH

Son LH (2016) Generalized picture distance measure and its application to picture fuzzy clustering. Appl Soft Comput 46:284–295

Son LH (2017) Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optim Decis Making 16:1–20MathSciNetMATH

Tsallis C (1988) Possible generalization of Boltzman-Gibbs statistics. J Stat Phys 52:480–487

Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28(2):197–206

Wang J, Wang P (2012) Intutionistic lingustic fuzzy multi-creitria decision-making method based on intutionistic fuzzy entropy. Control Decis 27:1694–1698MathSciNet

Wang L, Zhang HY, Wang JQ, Li L (2018) Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project. Appl Soft Comput J. https://doi.org/10.1016/j.asoc.2017.12.014CrossRef

Wei GW (2018) Some more similarity measures for picture fuzzy sets and their applications. Iran J Fuzzy Syst 15(1):77–89MathSciNetMATH

Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gener Syst 35:417–433MathSciNetMATH

Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48:246–262MATH

Yu PL (1980) A class of solutions for group decision making problem. Manag Sci 19:936–946

Yager RR (1979) On the measure of fuzziness and negation part I: membership in the unit interval. Int J Gener Syst 5(4):221–229MATH

Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18:183–190MATH

Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Making 3:93–107MathSciNetMATH

Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204MATH

Zadeh LA (1965) Fuzzy sets. Inf Comput 8(3):338–353MATH

Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249MathSciNetMATH

Zeng W, Yu F, Yu X, Chen H, Wu S (2009) Entropy on intuitionistic fuzzy set based on similarity measure. Int J Innov Comput Inf Control 5(12):4737–4744

Zeng S, Chen S-M, Kuo L-W (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inf Sci 488:76–92

Zhu B, Xu Z (2018) Probability-Hesitant fuzzy sets and the representation of preference relations. Technol Econ Dev Econ 24(3):1029–1040

Zhang XY, Wang JQ, Hu JH (2017) On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. Int J Fuzzy Syst 20(6):1–12MathSciNet

Zhao N, Xu ZS (2016) Entropy measures for interval valued intuitionistic fuzzy information from a comparative perspective and their application to decision making. Informatica 27:203–228MATH

Zou X-Y, Chen S-M, Fan K-Y (2020) Multiple attribute decision making using improved intuitionistic fuzzy weighted geometric operators of intuitionistic fuzzy values. Int J Artif Intell Pattern Recognit. https://doi.org/10.1016/j.ins.2020.05.011CrossRefMATH

Title: A novel VIKOR approach based on weighted correlation coefficients and picture fuzzy information for multicriteria decision making
Authors: Rajesh Joshi
Satish Kumar
Publication date: 22-06-2021
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 2/2022
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-021-00267-1

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 2/2022

Multiple attribute decision-making based on cubical fuzzy aggregation operators

Some modified Pythagorean fuzzy correlation measures with application in determining some selected decision-making problems

Correction to: Generalized similarity measures under linguistic q-rung orthopair fuzzy environment with application to multiple attribute decision-making

Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers

The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosphic numbers

Applications of a picture fuzzy correlation coefficient in pattern analysis and decision-making

Premium Partner