Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Soft Computing
Published in: Soft Computing 11/2014

01-11-2014 | Methodologies and Application

Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making

Authors: Ligang Zhou, Yingdong He, Huayou Chen, Jinpei Liu

Published in: Soft Computing | Issue 11/2014

Log in

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

search-config
loading …

Abstract

We develop a new compatibility for the interval fuzzy preference relations based on the continuous ordered weighted averaging (COWA) operator and use it to determine the weights of experts in group decision making (GDM). We define some concepts of the compatibility degree and the compatibility index for the two interval fuzzy preference relations based on the COWA operator. We study some desirable properties of the compatibility index and investigate the relationship between the each expert’s interval fuzzy preference relation and the synthetic interval fuzzy preference relation. The prominent characteristic of the compatibility index based on the COWA operator is that it can deal with the compatibility of all the arguments by using a controlled parameter considering the attitude of decision maker rather than the compatibility of the simply two points in intervals. To determine the experts’ weights in the GDM with the interval fuzzy preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. In the end, we give a numerical example to develop the new approach to GDM with interval fuzzy preference relations.
previous article A revised discrete particle swarm optimization algorithm for permutation flow-shop scheduling problem
next article A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing

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 "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

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
Appendix
Available only for authorised users
Literature
Calvo T, Mayor G, Mesiar R (2002) Aggregation operators: new trends and applications. Physica-Verlag, New YorkCrossRef
Chen HY, Chen C (2009) Research on compatibility and consistency of combination judgment matrices based on I-IOWG operators. Syst Eng Electron 31:2137–2140MATH
Chen HY, Liu JP, Wang H (2008) A class of continuous ordered weighted harmonic (C-OWHA) averaging operators for interval argument and its applications. Syst Eng Theory Pract 28:86–92
Chen HY, Zhou LG (2011a) An approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator. Expert Syst Appl 38:13432–13440
Chen HY, Zhou LG (2011b) On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowl Based Syst 24:816–823
Chen HY, Zhou LG (2012) A relative entropy approach to group decision making with interval reciprocal relations based on COWA operator. Group Decis Negotiat 21:585–599CrossRef
Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl Based Syst 37:528–540MathSciNetCrossRef
Chen SM, Lee LW, Liu HC, Yang SW (2012) Multiattribute decision making based on interval-valued intuitionistic fuzzy values. Expert Syst Appl 39:10343–10351CrossRef
Dong YC, Xu YF, Yu S (2009) Linguistic multiperson decision making based on the use of multiple preference relations. Fuzzy Sets Syst 160:603–623MathSciNetCrossRefMATH
Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13:613–622CrossRef
Gong ZW, Li LS, Zhou FX, Yao TX (2009) Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Comput Ind Eng 57:1187–1193CrossRef
Herrera F, Herrera-Viedma E, Chiclana F (2001) Multiperson decision-making based on multiplicative preference relations. Eur J Oper Res 129:372–385MathSciNetCrossRefMATH
Herrera-Viedma E, Herrera F, Chiclana F (2004) Some issues on consistency of fuzzy preference relations. Eur J Oper Res 154:98–109MathSciNetCrossRefMATH
Li DF (2011) The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets. Math Comput Model 53:1182–1196CrossRefMATH
Liu PD (2011) A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers[J]. Expert Syst Appl 38:1053–1060CrossRef
Merigó JM (2008) New extensions to the OWA operator and its application in business decision making, PhD thesis, Department of Business Administration, University of Barcelona
Merigó JM (2011) A unified model between the weighted average and the induced OWA operator. Expert Syst Appl 38:11560–11572CrossRef
Merigó JM, Casanovas M (2010) Fuzzy generalized hybrid aggregation operators and its application in decision making. Int J Fuzzy Syst 12:15–24
Merigó JM, Casanovas M (2011a) Induced aggregation operators in the Euclidean distance and its application in financial decision making. Expert Syst Appl 38:7603–7608CrossRef
Merigó JM, Casanovas M (2011b) Induced and uncertain heavy OWA operators. Comput Ind Eng 60:106–116CrossRef
Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179:729–741CrossRefMATH
Merigó JM, Gil-Lafuente AM (2010) New decision making techniques and their application in the selection of financial products. Inf Sci 180:2085–2094CrossRefMATH
Merigó JM, Gil-Lafuente AM (2011a) Fuzzy induced generalized aggregation operators and its application in multi-person decision making. Expert Syst Appl 38:9761–9772CrossRef
Merigó JM, Gil-Lafuente AM (2011b) Decision-making in sport management based on the OWA operator. Expert Syst Appl 38:10408–10413CrossRef
Merigó JM, Gil-Lafuente AM, Zhou LG, Chen HY (2012) Induced and linguistic generalized aggregation operators and their application in linguistic group decision making. Group Decis Negotiat 21:531–549CrossRef
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New YorkMATH
Su ZX, Xia GP, Chen MY, Wang L (2012) Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making. Expert Syst Appl 39:1902–1910CrossRef
Wang TC, Chen YH (2010) Incomplete fuzzy linguistic preference relations under uncertain environments. Inf Fusion 11:201–207CrossRef
Wei GW (2010a) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431CrossRef
Wei GW (2010b) A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information. Expert Syst Appl 37:7895–7900CrossRef
Wei GW, Zhao XF (2012a) Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Syst Appl 39:2026–2034CrossRef
Wei GW, Zhao XF (2012b) Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making. Expert Syst Appl 39:5881– 5886
Wu J, Cao QW (2013) Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl Math Model 37:318–327MathSciNetCrossRef
Wu J, Cao QW, Zhang JL (2010) Some properties of the induced continuous ordered weighted geometric operators in group decision making. Comput Ind Eng 59:100–106CrossRef
Wu J, Cao QW, Zhang JL (2011) An ILOWG operator based group decision making method and its application to evaluate the supplier criteria. Math Comput Model 54:19–34MathSciNetCrossRefMATH
Wu J, Li JC, Li H, Duan WQ (2009) The induced continuous ordered weighted geometric operators and their application in group decision making. Comput Ind Eng 58:1545–1552CrossRef
Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl Based Syst 31:78–88CrossRef
Xu RN, Zhai XY (1992) Extensions of the analytic hierarchy process in fuzzy environment. Fuzzy Sets Syst 52:251–257MathSciNetCrossRef
Xu ZS (2004a) On compatibility of interval fuzzy preference relations. Fuzzy Optim Decis Making 3:217–225CrossRefMATH
Xu ZS (2004b) EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int J Uncertain Fuzziness Knowl Based Syst 12:91–810MATH
Xu ZS (2004c) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing
Xu ZS (2004d) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30CrossRefMATH
Xu ZS (2006a) An approach based on the uncertain LOWG and the induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decis Support Syst 41:488–499CrossRef
Xu ZS (2006b) A C-OWA operator based approach to decision making with interval fuzzy preference relation. Int J Intell Syst 21:1289–1298CrossRefMATH
Xu ZS (2007b) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379CrossRefMATH
Xu ZS (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180:181–190CrossRefMATH
Xu ZS (2011) Consistency of interval fuzzy preference relations in group decision making. Appl Soft Comput 11:3898–3909CrossRef
Xu ZS, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl Based Syst 16:529–555CrossRefMATH
Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17:469–483
Xu YJ, Wang HM (2012) The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making. Appl Soft Comput 12:1168–1179CrossRef
Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24:197–209CrossRef
Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern B 18:183–190MathSciNetCrossRefMATH
Yager RR (2004a) OWA aggregation over a continuous interval argument with applications to decision making. IEEE Trans Syst Man Cybern Part B 34:1952–1963CrossRef
Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern B 29:141–150CrossRef
Yager RR, Kacprzyk J (1997) The ordered weighted averaging operators: theory and applications. Kluwer Academic Publishers, NorwellCrossRef
Yager RR, Kacprzyk J, Beliakov G (2011) Recent developments in the ordered weighted averaging operators: theory and practice. Springer, BerlinCrossRef
Yager RR, Xu ZS (2006) The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets Syst 157:1393–1402MathSciNetCrossRefMATH
Yang W, Chen ZP (2012) The quasi-arithmetic intuitionistic fuzzy OWA operators. Knowl Based Syst 27:219–233CrossRef
Yu DJ, Wu YY, Lu T (2012) Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making. Knowl Based Syst 30:57–66CrossRef
Yue ZL (2011) Deriving decision maker’s weights based on distance measure for interval-valued intuitionistic fuzzy group decision making. Expert Syst Appl 38:11665–11670CrossRef
Zeng SZ, Su WH (2011) Intuitionistic fuzzy ordered weighted distance operator. Knowl Based Syst 24:1224–1232CrossRef
Zhang QS, Jiang SY, Jia BG, Luo SH (2011) Some information measures for interval-valued intuitionistic fuzzy sets. Inf Sci 180:5130–5145
Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25:1–30
Zhou LG, Chen HY (2010) Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. Int J Intell Syst 25:683–707CrossRefMATH
Zhou LG, Chen HY (2011) Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst 168:18–34CrossRefMATH
Zhou LG, Chen HY (2012) A generalization of the power aggregation operators for linguistic environment and its application in group decision making. Knowl Based Syst 26:216–224CrossRef
Zhou LG, Chen HY, Liu JP (2012a) Generalized power aggregation operators and their applications in group decision making. Comput Ind Eng 62:989–999CrossRef
Zhou LG, Chen HY, Merigó JM, Gil-Lafuente AM (2012b) Uncertain generalized aggregation operators. Expert Syst Appl 39:1105–1117CrossRef
Zhou LG, Chen HY, Liu JP (2013) Generalized multiple averaging operators and their applications to group decision making. Group Decis Negotiat 22:331–358CrossRef
Zhou SM, Chiclana F, John RI, Garibaldi JM (2008) Type-1 OWA operators for aggregation uncertain information with uncertain weights induced by type-2 linguistic quantifiers. Fuzzy Sets Syst 159:3281–3296MathSciNetCrossRefMATH
Zhou SM, Chiclana F, John RI, Garibaldi JM (2011) Alpha-level aggregation: a practical approach to type-1 OWA operation for aggregating uncertain information with applications to breast cancer treatments. IEEE Trans Knowl Data Eng 23:1455–1468CrossRef
Zhu B (2013) Studies on consistency measure of hesitant fuzzy preference relations. Proc Comput Sci 17:457–464CrossRef
Metadata
Title
Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making
Authors
Ligang Zhou
Yingdong He
Huayou Chen
Jinpei Liu
Publication date
01-11-2014
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 11/2014
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-013-1201-9

Other articles of this Issue 11/2014

Soft Computing 11/2014 Go to the issue

Methodologies and Application

Global migration strategy with moving colony for hierarchical distributed evolutionary algorithms

Methodologies and Application

FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization

Methodologies and Application

A computational intelligence method for solving a class of portfolio optimization problems

Methodologies and Application

Uncertain minimum cost flow problem

Foundations

Boolean lifting property for residuated lattices

Methodologies and Application

A complex multi-attribute large-group decision making method based on the interval-valued intuitionistic fuzzy principal component analysis model

Premium Partner

    Image Credits