Skip to main content
Erschienen in: Group Decision and Negotiation 2/2016

07.07.2015

Consistency in MCGDM Problems with Intuitionistic Fuzzy Preference Relations Based on an Exponential Score Function

verfasst von: Jian Wu

Erschienen in: Group Decision and Negotiation | Ausgabe 2/2016

Einloggen

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

search-config
loading …

Abstract

This paper investigates an approach for multiple criteria decision making problems with intuitionistic fuzzy preference relations (IFPRs). An exponential score function for intuitionistic fuzzy numbers is developed. Its novelty is that it can convert an IFPR into a multiplicative preference relation. Then, the exponential score preference relation is introduced and its associated optimal transfer matrix is proposed. The optimal transfer matrix can guarantee the consistency via the additive transitivity property. Furthermore, an optimal model for aggregating group IFPRs to reach consistency is proposed. Finally, a group decision making approach and a multi-criteria decision making approach with IFPRs are presented.

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!

Literatur
Zurück zum Zitat Atanassov K (1986) Intuitionstic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRef Atanassov K (1986) Intuitionstic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRef
Zurück zum Zitat Atanassov K, Pasi G et al (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36:859–868CrossRef Atanassov K, Pasi G et al (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36:859–868CrossRef
Zurück zum Zitat Boran FE, Genc S, Kurt M, Akayb D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368CrossRef Boran FE, Genc S, Kurt M, Akayb D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368CrossRef
Zurück zum Zitat Chan FTS, Kumar N (2007) Global supplier development considering risk factors using fuzzy extended AHP-based approach. Omega 35:417–731CrossRef Chan FTS, Kumar N (2007) Global supplier development considering risk factors using fuzzy extended AHP-based approach. Omega 35:417–731CrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172CrossRef Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172CrossRef
Zurück zum Zitat Chen TY, Wang HP et al (2011) A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst Appl 38:7647–7658CrossRef Chen TY, Wang HP et al (2011) A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst Appl 38:7647–7658CrossRef
Zurück zum Zitat Chiclana F, Herrera-Viedma E, Herrera F (2007) Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. Eur J Oper Res 182:383–399CrossRef Chiclana F, Herrera-Viedma E, Herrera F (2007) Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. Eur J Oper Res 182:383–399CrossRef
Zurück zum Zitat Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97:33–48CrossRef Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97:33–48CrossRef
Zurück zum Zitat Chiclana F, Herrera F, Herrera-Viedma E (2001) Intergrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277–291CrossRef Chiclana F, Herrera F, Herrera-Viedma E (2001) Intergrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277–291CrossRef
Zurück zum Zitat Chiclana F, Herrera-Viedma E, Herrera F, Alonso S (2004) Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations. Int J Intell Syst 19:233–255CrossRef Chiclana F, Herrera-Viedma E, Herrera F, Alonso S (2004) Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations. Int J Intell Syst 19:233–255CrossRef
Zurück zum Zitat Despic O, Simonovic SP (2000) Aggregation operators for soft decision making in water resources. Fuzzy Sets Syst 115:11–33CrossRef Despic O, Simonovic SP (2000) Aggregation operators for soft decision making in water resources. Fuzzy Sets Syst 115:11–33CrossRef
Zurück zum Zitat Durán O, Aguilo J (2008) Computer-aided machine-tool selection based on a Fuzzy-AHP approach. Expert Syst Appl 34:1787–1794CrossRef Durán O, Aguilo J (2008) Computer-aided machine-tool selection based on a Fuzzy-AHP approach. Expert Syst Appl 34:1787–1794CrossRef
Zurück zum Zitat Gong ZW, Li LS, Cao J, Zhou FX (2010) On additive consistent properties of the intuitionistic fuzzy preference relation. Int J Inf Technol Decis Mak 9(6):1009–1025CrossRef Gong ZW, Li LS, Cao J, Zhou FX (2010) On additive consistent properties of the intuitionistic fuzzy preference relation. Int J Inf Technol Decis Mak 9(6):1009–1025CrossRef
Zurück zum Zitat Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394–4402CrossRef Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394–4402CrossRef
Zurück zum Zitat 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 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
Zurück zum Zitat Huang CC, Chub PY, Chiang YH (2008) A fuzzy AHP application in government-sponsored R&D project selection. Omega 36:1038–1052CrossRef Huang CC, Chub PY, Chiang YH (2008) A fuzzy AHP application in government-sponsored R&D project selection. Omega 36:1038–1052CrossRef
Zurück zum Zitat Kuo RJ, Chi SC, Kao SS (1999) A decision support system for locating convenience store through fuzzy AHP. Comput Ind Eng 37:323–326CrossRef Kuo RJ, Chi SC, Kao SS (1999) A decision support system for locating convenience store through fuzzy AHP. Comput Ind Eng 37:323–326CrossRef
Zurück zum Zitat Kwong CK, Bai H (2003) Determining the importance weights for the customer requirements in QFD using a fuzzy AHP with an extent analysis approach. IIE Trans 35:619–626CrossRef Kwong CK, Bai H (2003) Determining the importance weights for the customer requirements in QFD using a fuzzy AHP with an extent analysis approach. IIE Trans 35:619–626CrossRef
Zurück zum Zitat Lee AHI, Chang HJ, Lin CY (2009) An evaluation model of buyer-supplier relationships in high-tech industry—the case of an electronic components manufacturer in Taiwan. Comput Ind Eng 57:1417–1430CrossRef Lee AHI, Chang HJ, Lin CY (2009) An evaluation model of buyer-supplier relationships in high-tech industry—the case of an electronic components manufacturer in Taiwan. Comput Ind Eng 57:1417–1430CrossRef
Zurück zum Zitat Li DF (2004) Some measures of dissimilarity in intuitionistic fuzzy structures. J Comput Syst Sci 68:115–122CrossRef Li DF (2004) Some measures of dissimilarity in intuitionistic fuzzy structures. J Comput Syst Sci 68:115–122CrossRef
Zurück zum Zitat Li DF (2011) The GOWA operator based approach to multiattribute decision naking using intuitionistic fuzzy sets. Math Comput Model 53:1182–1196CrossRef Li DF (2011) The GOWA operator based approach to multiattribute decision naking using intuitionistic fuzzy sets. Math Comput Model 53:1182–1196CrossRef
Zurück zum Zitat Liu HW, Wang GJ (2007) Multi-criteria decision-making methods based on intuitionnistic fuzzy sets. Eur J Oper Res 179:220–233CrossRef Liu HW, Wang GJ (2007) Multi-criteria decision-making methods based on intuitionnistic fuzzy sets. Eur J Oper Res 179:220–233CrossRef
Zurück zum Zitat Liu PD (2011) A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Syst Appl 38:1053–1060CrossRef Liu PD (2011) A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Syst Appl 38:1053–1060CrossRef
Zurück zum Zitat Ma YD, Hu MD (1997) Improved analysis of hierarchy process and its application to multi objective decision. Syst Eng Theory Pract 6:40–44 Ma YD, Hu MD (1997) Improved analysis of hierarchy process and its application to multi objective decision. Syst Eng Theory Pract 6:40–44
Zurück zum Zitat Saaty TL (1980) The analytic hierarchy process. McGrawHill, New York Saaty TL (1980) The analytic hierarchy process. McGrawHill, New York
Zurück zum Zitat Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1037–1053 Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1037–1053
Zurück zum Zitat Tan CQ (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37:149–157CrossRef Tan CQ (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37:149–157CrossRef
Zurück zum Zitat Wang JQ, Li K, Zhang H (2012) Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function. Knowl Based Syst 27:119–215CrossRef Wang JQ, Li K, Zhang H (2012) Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function. Knowl Based Syst 27:119–215CrossRef
Zurück zum Zitat Wang JQ, Han ZQ, Zhang HY (2014) Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group decis Negotiat 23(4):715–733CrossRef Wang JQ, Han ZQ, Zhang HY (2014) Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group decis Negotiat 23(4):715–733CrossRef
Zurück zum Zitat Wei GW (2009) Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting. Int J Uncertain Fuzziness Knowl Based Syst 17:179–196CrossRef Wei GW (2009) Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting. Int J Uncertain Fuzziness Knowl Based Syst 17:179–196CrossRef
Zurück zum Zitat Wei GW (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431CrossRef Wei GW (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431CrossRef
Zurück zum Zitat Wei GW, Tang XJ (2011) An intuitionistic fuzzy group decision-making approach based on entropy and similarity measures. Int J Inf Technol Decis Mak 10:1111–1130CrossRef Wei GW, Tang XJ (2011) An intuitionistic fuzzy group decision-making approach based on entropy and similarity measures. Int J Inf Technol Decis Mak 10:1111–1130CrossRef
Zurück zum Zitat Wu J, Cao QW (2011) Some issues on properties of the extended IOWA operators in fuzzy group decision making. Expert Syst Appl 38:7059–7066CrossRef Wu J, Cao QW (2011) Some issues on properties of the extended IOWA operators in fuzzy group decision making. Expert Syst Appl 38:7059–7066CrossRef
Zurück zum Zitat Wu J, Chiclana F (2012) Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations. Expert Syst Appl 39:13049–13416 Wu J, Chiclana F (2012) Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations. Expert Syst Appl 39:13049–13416
Zurück zum Zitat 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 56:1545–1552CrossRef 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 56:1545–1552CrossRef
Zurück zum Zitat Xu ZS (2013) Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decis Negotiat 22:463–482CrossRef Xu ZS (2013) Compatibility analysis of intuitionistic fuzzy preference relations in group decision making. Group Decis Negotiat 22:463–482CrossRef
Zurück zum Zitat Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187CrossRef Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187CrossRef
Zurück zum Zitat Xu ZS (2007b) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379CrossRef Xu ZS (2007b) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379CrossRef
Zurück zum Zitat Xu ZS (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180(1):181–190CrossRef Xu ZS (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180(1):181–190CrossRef
Zurück zum Zitat Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl Based Syst 24(6):749–760CrossRef Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl Based Syst 24(6):749–760CrossRef
Zurück zum Zitat Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139CrossRef Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139CrossRef
Zurück zum Zitat Yang YJ, Chiclana F (2012) Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Syst Appl 39:8665–8670CrossRef Yang YJ, Chiclana F (2012) Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Syst Appl 39:8665–8670CrossRef
Zurück zum Zitat Ye F (2010a) An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Syst Appl 37:7050–7055CrossRef Ye F (2010a) An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection. Expert Syst Appl 37:7050–7055CrossRef
Zurück zum Zitat Ye J (2010b) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204CrossRef Ye J (2010b) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204CrossRef
Zurück zum Zitat Yue ZL (2012) Approach to group decision making based on determining the weights of experts by using projection method. Appl Math Model 36:2900–2910CrossRef Yue ZL (2012) Approach to group decision making based on determining the weights of experts by using projection method. Appl Math Model 36:2900–2910CrossRef
Zurück zum Zitat Zhang X, Liu PD (2010) Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making. Technol Econ Dev Econ 16:280–290CrossRef Zhang X, Liu PD (2010) Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making. Technol Econ Dev Econ 16:280–290CrossRef
Metadaten
Titel
Consistency in MCGDM Problems with Intuitionistic Fuzzy Preference Relations Based on an Exponential Score Function
verfasst von
Jian Wu
Publikationsdatum
07.07.2015
Verlag
Springer Netherlands
Erschienen in
Group Decision and Negotiation / Ausgabe 2/2016
Print ISSN: 0926-2644
Elektronische ISSN: 1572-9907
DOI
https://doi.org/10.1007/s10726-015-9447-5

Weitere Artikel der Ausgabe 2/2016

Group Decision and Negotiation 2/2016 Zur Ausgabe