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Published in: Group Decision and Negotiation 5/2016

06-01-2016

The Prametric-Based GDM Procedure Under Fuzzy Environment

Author: Fujun Hou

Published in: Group Decision and Negotiation | Issue 5/2016

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Abstract

The prametric is an ‘almost metric’ which does not necessarily satisfy the triangle inequality but able to describe the consensus intransitivity in group decision making (GDM) such as Tom and Jack have preferences in common, also Jack and John have preferences in common, but, Tom and John do not necessarily have preferences in common. A prametric-based consensus formation procedure for GDM was presented in a literature. This paper considers the procedure under fuzzy environment where the individuals’ preferences are provided as fuzzy numbers. The Yager defuzzification method is used for constructing the preference sequence matrix where the (ij)-th entry indicates the alternative i’s position(s) assigned by individual j. An illustrative example for application is also included.

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Literature
go back to reference Armstrong RD, Cook WD, Seiford LM (1982) Priority ranking and consensus formation: the case of ties. Manag Sci 28(6):638–645CrossRef Armstrong RD, Cook WD, Seiford LM (1982) Priority ranking and consensus formation: the case of ties. Manag Sci 28(6):638–645CrossRef
go back to reference Arrow KJ (1951) Social choice and individual values. Wiley, New York Arrow KJ (1951) Social choice and individual values. Wiley, New York
go back to reference Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164CrossRef Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164CrossRef
go back to reference Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst 15(1):1–19CrossRef Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst 15(1):1–19CrossRef
go back to reference Cádenas E, Castillo JC, Cordón O, Herrera F, Peregrín A (1994) Influence of fuzzy implication functions and defuzzification methods in fuzzy control. Busefal 57:69–79 Cádenas E, Castillo JC, Cordón O, Herrera F, Peregrín A (1994) Influence of fuzzy implication functions and defuzzification methods in fuzzy control. Busefal 57:69–79
go back to reference Chandramohan A, Rao MVC, Arumugam MS (2006) Two new and useful defuzzification methods based on root mean square value. Soft Comput 10:1047–1059CrossRef Chandramohan A, Rao MVC, Arumugam MS (2006) Two new and useful defuzzification methods based on root mean square value. Soft Comput 10:1047–1059CrossRef
go back to reference Cook WD, Kress M, Seiford LM (1997) A general framework for distance-based consensus in ordinal ranking models. Eur J Oper Res 96(2):392–397CrossRef Cook WD, Kress M, Seiford LM (1997) A general framework for distance-based consensus in ordinal ranking models. Eur J Oper Res 96(2):392–397CrossRef
go back to reference Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(16):1721–1732CrossRef Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(16):1721–1732CrossRef
go back to reference Cordón O, Herrera F, Márquez FA, Peregrín A (2004) A study on the evolutionary adaptive defuzzification methods in fuzzy modeling. Int J Hybrid Intell Syst 1(1):36–48CrossRef Cordón O, Herrera F, Márquez FA, Peregrín A (2004) A study on the evolutionary adaptive defuzzification methods in fuzzy modeling. Int J Hybrid Intell Syst 1(1):36–48CrossRef
go back to reference Deng H, Yeh CH (2006) Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making. IEEE Trans Syst Man Cybern A 36:968–977CrossRef Deng H, Yeh CH (2006) Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making. IEEE Trans Syst Man Cybern A 36:968–977CrossRef
go back to reference Detyniecki M, Yager RR (2000) Ranking fuzzy numbers using \(\alpha \)-weighted valuations. Int J Uncertain Fuzziness 8(5):573–591CrossRef Detyniecki M, Yager RR (2000) Ranking fuzzy numbers using \(\alpha \)-weighted valuations. Int J Uncertain Fuzziness 8(5):573–591CrossRef
go back to reference Driankov D, Hellendorn H, Reinfrank M (1993) An introduction to fuzzy control. Springer, BerlinCrossRef Driankov D, Hellendorn H, Reinfrank M (1993) An introduction to fuzzy control. Springer, BerlinCrossRef
go back to reference Dubois D, Prade H (1978) Operations on fuzzy numbers. lnt J Syst Sci 9(6):613–626CrossRef Dubois D, Prade H (1978) Operations on fuzzy numbers. lnt J Syst Sci 9(6):613–626CrossRef
go back to reference Dyer JS, Sarin RK (1979) Group preference aggregation rules based on strength of preference. Manag Sci 25(9):822–832CrossRef Dyer JS, Sarin RK (1979) Group preference aggregation rules based on strength of preference. Manag Sci 25(9):822–832CrossRef
go back to reference Facchinetti G, Ricci RG (2004) A characterization of a general class of ranking functions on triangular fuzzy numbers. Fuzzy Sets Syst 146(2):297–312CrossRef Facchinetti G, Ricci RG (2004) A characterization of a general class of ranking functions on triangular fuzzy numbers. Fuzzy Sets Syst 146(2):297–312CrossRef
go back to reference Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13(7):613–622CrossRef Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13(7):613–622CrossRef
go back to reference Figueiredo M, Gomide F, Rocha A, Yager R (1993) Comparison of Yager’s level set method for fuzzy logic control with Mamdani’s and Larsen’s methods. IEEE Trans Fuzzy Syst 1(2):156–159CrossRef Figueiredo M, Gomide F, Rocha A, Yager R (1993) Comparison of Yager’s level set method for fuzzy logic control with Mamdani’s and Larsen’s methods. IEEE Trans Fuzzy Syst 1(2):156–159CrossRef
go back to reference Filev DP, Yager RR (1991) A generalized defuzzification method via bad distributions. Int J Intell Syst 6(7):687–697CrossRef Filev DP, Yager RR (1991) A generalized defuzzification method via bad distributions. Int J Intell Syst 6(7):687–697CrossRef
go back to reference Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33(3):469–489CrossRef Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33(3):469–489CrossRef
go back to reference Gavshin Y, Kruusmaa M (2008) Comparative experiments on the emergence of safe behaviours. In: TAROS, pp 65–71 Gavshin Y, Kruusmaa M (2008) Comparative experiments on the emergence of safe behaviours. In: TAROS, pp 65–71
go back to reference Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41(4):587–601CrossRef Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41(4):587–601CrossRef
go back to reference Greenfield S, Chiclana F, Coupland S, John R (2009) The collapsing method of defuzzification for discretised interval type-2 fuzzy sets. Inf Sci 179(13):2055–2069CrossRef Greenfield S, Chiclana F, Coupland S, John R (2009) The collapsing method of defuzzification for discretised interval type-2 fuzzy sets. Inf Sci 179(13):2055–2069CrossRef
go back to reference Greenfield S, Chiclana F (2013) Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. Int J Approx Reason 54:1013–1033CrossRef Greenfield S, Chiclana F (2013) Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. Int J Approx Reason 54:1013–1033CrossRef
go back to reference Hou J (2015) A consensus gap indicator and its application to group decision making. Group Decis Negot 24(3):415–428CrossRef Hou J (2015) A consensus gap indicator and its application to group decision making. Group Decis Negot 24(3):415–428CrossRef
go back to reference Inuma M, Otsuka A, Imai H (2009) Theoretical framework for constructing matching algorithms in biometric authentication systems. In: Proceedings of ICB09, Alghero, Italy. Lecture notes in computer science, 5558, Springer, Berlin, pp 806–815 Inuma M, Otsuka A, Imai H (2009) Theoretical framework for constructing matching algorithms in biometric authentication systems. In: Proceedings of ICB09, Alghero, Italy. Lecture notes in computer science, 5558, Springer, Berlin, pp 806–815
go back to reference Kacprzyk J, Fedrizzi M (1990) Multiperson decision making models using fuzzy sets and possibility theory. Kluwer Academic Pub, DordrechtCrossRef Kacprzyk J, Fedrizzi M (1990) Multiperson decision making models using fuzzy sets and possibility theory. Kluwer Academic Pub, DordrechtCrossRef
go back to reference Keeney RL (2013) Foundations for group decision analysis. Decis Anal 10(2):103–120CrossRef Keeney RL (2013) Foundations for group decision analysis. Decis Anal 10(2):103–120CrossRef
go back to reference Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591 Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591
go back to reference Kichert WJM (1978) Fuzzy theories on decision making. Nijhoff, Leiden Kichert WJM (1978) Fuzzy theories on decision making. Nijhoff, Leiden
go back to reference May KO (1953) A note on the complete independence of the conditions for simple majority decision. Econometrica 21:172–173CrossRef May KO (1953) A note on the complete independence of the conditions for simple majority decision. Econometrica 21:172–173CrossRef
go back to reference Moulin H (1985) Choice functions over a finite set: a summary. Soc Choice Welf 2(2):147–160CrossRef Moulin H (1985) Choice functions over a finite set: a summary. Soc Choice Welf 2(2):147–160CrossRef
go back to reference Patel AV, Mohan BM (2002) Some numerical aspects of center of area defuzzification method. Fuzzy Set Syst 132:401–409CrossRef Patel AV, Mohan BM (2002) Some numerical aspects of center of area defuzzification method. Fuzzy Set Syst 132:401–409CrossRef
go back to reference Rao DH, Saraf SS (1995) Study of defuzzification methods of fuzzy logic controller for speed control of a DC motor. In: Proceedings of the 1996 international conference on power electronics, drives and energy systems for industrial growth, 1996. IEEE, vol 2, pp 782–787 Rao DH, Saraf SS (1995) Study of defuzzification methods of fuzzy logic controller for speed control of a DC motor. In: Proceedings of the 1996 international conference on power electronics, drives and energy systems for industrial growth, 1996. IEEE, vol 2, pp 782–787
go back to reference Roychowdhury S, Pedrycz W (2001) A survey of defuzzification strategies. Int J Intell Syst 16(6):679–695CrossRef Roychowdhury S, Pedrycz W (2001) A survey of defuzzification strategies. Int J Intell Syst 16(6):679–695CrossRef
go back to reference Runkler TA (1997) Selection of appropriate defuzzification methods using application specific properties. IEEE Trans Fuzzy Syst 5(1):72–79CrossRef Runkler TA (1997) Selection of appropriate defuzzification methods using application specific properties. IEEE Trans Fuzzy Syst 5(1):72–79CrossRef
go back to reference Runkler TA (2013) Kernel based defuzzification. In: Moewes C, Nürnberger A (eds) Computational intelligence in intelligent data analysis. Springer, Berlin, pp 61–72CrossRef Runkler TA (2013) Kernel based defuzzification. In: Moewes C, Nürnberger A (eds) Computational intelligence in intelligent data analysis. Springer, Berlin, pp 61–72CrossRef
go back to reference Saneifard R (2015) Another method for defuzzification based on signal/noise ratios and its applications in comparing DMUs. Commun Adv Comput Sci Appl 1:32–36 Saneifard R (2015) Another method for defuzzification based on signal/noise ratios and its applications in comparing DMUs. Commun Adv Comput Sci Appl 1:32–36
go back to reference Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217CrossRef Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217CrossRef
go back to reference Skala MA (2008) Aspects of metric spaces in computation. Ph.D. thesis, University of Waterloo, Ontario, Canada, p 2 Skala MA (2008) Aspects of metric spaces in computation. Ph.D. thesis, University of Waterloo, Ontario, Canada, p 2
go back to reference Slater P (1961) Inconsistencies in a schedule of paired comparisons. Biometrica 48:303–312CrossRef Slater P (1961) Inconsistencies in a schedule of paired comparisons. Biometrica 48:303–312CrossRef
go back to reference Typke R, Walczak-Typke A (2010) Indexing techniques for non-metric music dissimilarity measures. Advances in music information retrieval. Springer, Berlin Typke R, Walczak-Typke A (2010) Indexing techniques for non-metric music dissimilarity measures. Advances in music information retrieval. Springer, Berlin
go back to reference Van Broekhoven E, De Baets B (2004) A comparison of three methods for computing the center of gravity defuzzification. IEEE Int Conf Fuzzy Syst 3(1):1537–1542 Van Broekhoven E, De Baets B (2004) A comparison of three methods for computing the center of gravity defuzzification. IEEE Int Conf Fuzzy Syst 3(1):1537–1542
go back to reference Van Leekwijck W, Kerre E (1999) Defuzzification: criteria and classification. Fuzzy Set Syst 108(2):159–178CrossRef Van Leekwijck W, Kerre E (1999) Defuzzification: criteria and classification. Fuzzy Set Syst 108(2):159–178CrossRef
go back to reference Wang YM (2009) Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Comput Ind Eng 57:228–236CrossRef Wang YM (2009) Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Comput Ind Eng 57:228–236CrossRef
go back to reference Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Set Syst 118(3):375–385CrossRef Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Set Syst 118(3):375–385CrossRef
go back to reference Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Set Syst 118(3):387–405CrossRef Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Set Syst 118(3):387–405CrossRef
go back to reference Wierman MJ (1997) Central values of fuzzy numbers—defuzzification. Inf Sci 100(1):207–215CrossRef Wierman MJ (1997) Central values of fuzzy numbers—defuzzification. Inf Sci 100(1):207–215CrossRef
go back to reference Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24(2):143–161CrossRef Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24(2):143–161CrossRef
go back to reference Yager RR, Filev D (1993) On the issue of defuzzification and selection based on a fuzzy set. Fuzzy Set Syst 55(3):255–271CrossRef Yager RR, Filev D (1993) On the issue of defuzzification and selection based on a fuzzy set. Fuzzy Set Syst 55(3):255–271CrossRef
go back to reference Yager RR, Filev D (1999) On ranking fuzzy numbers using valuations. Int J Intell Syst 14(12):1249–1268CrossRef Yager RR, Filev D (1999) On ranking fuzzy numbers using valuations. Int J Intell Syst 14(12):1249–1268CrossRef
go back to reference Yager RR (2013) Pythagorean fuzzy subsets. IFSA World congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013 Joint. IEEE, pp 57–61 Yager RR (2013) Pythagorean fuzzy subsets. IFSA World congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013 Joint. IEEE, pp 57–61
Metadata
Title
The Prametric-Based GDM Procedure Under Fuzzy Environment
Author
Fujun Hou
Publication date
06-01-2016
Publisher
Springer Netherlands
Published in
Group Decision and Negotiation / Issue 5/2016
Print ISSN: 0926-2644
Electronic ISSN: 1572-9907
DOI
https://doi.org/10.1007/s10726-015-9468-0

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