Skip to main content
SpringerLink
Log in

The Prametric-Based GDM Procedure Under Fuzzy Environment

  • Published:
Group Decision and Negotiation Aims and scope Submit manuscript

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 (i, j)-th entry indicates the alternative i’s position(s) assigned by individual j. An illustrative example for application is also included.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Armstrong RD, Cook WD, Seiford LM (1982) Priority ranking and consensus formation: the case of ties. Manag Sci 28(6):638–645

    Article  Google Scholar 

  • Arrow KJ (1951) Social choice and individual values. Wiley, New York

    Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164

    Article  Google Scholar 

  • Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst 15(1):1–19

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Chandramohan A, Rao MVC, Arumugam MS (2006) Two new and useful defuzzification methods based on root mean square value. Soft Comput 10:1047–1059

    Article  Google Scholar 

  • Cook WD, Kress M, Seiford LM (1997) A general framework for distance-based consensus in ordinal ranking models. Eur J Oper Res 96(2):392–397

    Article  Google Scholar 

  • Cook WD, Seiford LM (1978) Priority ranking and consensus formation. Manag Sci 24(16):1721–1732

    Article  Google Scholar 

  • 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):36–48

    Article  Google Scholar 

  • Deng H, Yeh CH (2006) Simulation-based evaluation of defuzzification-based approaches to fuzzy multiattribute decision making. IEEE Trans Syst Man Cybern A 36:968–977

    Article  Google Scholar 

  • Detyniecki M, Yager RR (2000) Ranking fuzzy numbers using \(\alpha \)-weighted valuations. Int J Uncertain Fuzziness 8(5):573–591

    Article  Google Scholar 

  • Driankov D, Hellendorn H, Reinfrank M (1993) An introduction to fuzzy control. Springer, Berlin

    Book  Google Scholar 

  • Dubois D, Prade H (1978) Operations on fuzzy numbers. lnt J Syst Sci 9(6):613–626

    Article  Google Scholar 

  • Dyer JS, Sarin RK (1979) Group preference aggregation rules based on strength of preference. Manag Sci 25(9):822–832

    Article  Google Scholar 

  • Facchinetti G, Ricci RG (2004) A characterization of a general class of ranking functions on triangular fuzzy numbers. Fuzzy Sets Syst 146(2):297–312

    Article  Google Scholar 

  • Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13(7):613–622

    Article  Google Scholar 

  • 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):156–159

    Article  Google Scholar 

  • Filev DP, Yager RR (1991) A generalized defuzzification method via bad distributions. Int J Intell Syst 6(7):687–697

    Article  Google Scholar 

  • Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33(3):469–489

    Article  Google Scholar 

  • Gavshin Y, Kruusmaa M (2008) Comparative experiments on the emergence of safe behaviours. In: TAROS, pp 65–71

  • Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41(4):587–601

    Article  Google Scholar 

  • 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):2055–2069

    Article  Google Scholar 

  • Greenfield S, Chiclana F (2013) Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. Int J Approx Reason 54:1013–1033

    Article  Google Scholar 

  • Hou J (2015) A consensus gap indicator and its application to group decision making. Group Decis Negot 24(3):415–428

    Article  Google Scholar 

  • 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

  • Kacprzyk J, Fedrizzi M (1990) Multiperson decision making models using fuzzy sets and possibility theory. Kluwer Academic Pub, Dordrecht

    Book  Google Scholar 

  • Keeney RL (2013) Foundations for group decision analysis. Decis Anal 10(2):103–120

    Article  Google Scholar 

  • Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591

    Google Scholar 

  • Kichert WJM (1978) Fuzzy theories on decision making. Nijhoff, Leiden

    Google Scholar 

  • May KO (1953) A note on the complete independence of the conditions for simple majority decision. Econometrica 21:172–173

    Article  Google Scholar 

  • Moulin H (1985) Choice functions over a finite set: a summary. Soc Choice Welf 2(2):147–160

    Article  Google Scholar 

  • Patel AV, Mohan BM (2002) Some numerical aspects of center of area defuzzification method. Fuzzy Set Syst 132:401–409

    Article  Google Scholar 

  • 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

  • Roychowdhury S, Pedrycz W (2001) A survey of defuzzification strategies. Int J Intell Syst 16(6):679–695

    Article  Google Scholar 

  • Runkler TA (1997) Selection of appropriate defuzzification methods using application specific properties. IEEE Trans Fuzzy Syst 5(1):72–79

    Article  Google Scholar 

  • Runkler TA (2013) Kernel based defuzzification. In: Moewes C, Nürnberger A (eds) Computational intelligence in intelligent data analysis. Springer, Berlin, pp 61–72

    Chapter  Google Scholar 

  • 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

    Google Scholar 

  • Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217

    Article  Google Scholar 

  • Skala MA (2008) Aspects of metric spaces in computation. Ph.D. thesis, University of Waterloo, Ontario, Canada, p 2

  • Slater P (1961) Inconsistencies in a schedule of paired comparisons. Biometrica 48:303–312

    Article  Google Scholar 

  • Typke R, Walczak-Typke A (2010) Indexing techniques for non-metric music dissimilarity measures. Advances in music information retrieval. Springer, Berlin

    Google Scholar 

  • 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

    Google Scholar 

  • Van Leekwijck W, Kerre E (1999) Defuzzification: criteria and classification. Fuzzy Set Syst 108(2):159–178

    Article  Google Scholar 

  • Wang YM (2009) Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets. Comput Ind Eng 57:228–236

    Article  Google Scholar 

  • Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Set Syst 118(3):375–385

    Article  Google Scholar 

  • Wang X, Kerre EE (2001) Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Set Syst 118(3):387–405

    Article  Google Scholar 

  • Wierman MJ (1997) Central values of fuzzy numbers—defuzzification. Inf Sci 100(1):207–215

    Article  Google Scholar 

  • Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24(2):143–161

    Article  Google Scholar 

  • Yager RR, Filev D (1993) On the issue of defuzzification and selection based on a fuzzy set. Fuzzy Set Syst 55(3):255–271

    Article  Google Scholar 

  • Yager RR, Filev D (1999) On ranking fuzzy numbers using valuations. Int J Intell Syst 14(12):1249–1268

    Article  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. IFSA World congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013 Joint. IEEE, pp 57–61

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

Download references

Acknowledgments

The author would like to thank the Editor-in-Chief, the Associate Editor and the anonymous Referees for their helpful comments and suggestions. The work was supported by the National Natural Science Foundation of China (No. 71571019).

Author information

Authors and Affiliations

  1. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Fujun Hou

Authors
  1. Fujun Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fujun Hou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hou, F. The Prametric-Based GDM Procedure Under Fuzzy Environment. Group Decis Negot 25, 1071–1084 (2016). https://doi.org/10.1007/s10726-015-9468-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10726-015-9468-0

Keywords

Search

Navigation