Abstract
Often in a group of decision makers there is a considerable variability in the scores that decision makers assign to the alternatives. In this paper we represent this variability with fuzzy numbers. Moreover we present an algorithm for the achievement of consensus based on suitable fuzzy numbers, on preorder and order relations in sets of fuzzy numbers, and on a procedure to decrease the spreads.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Arrow KJ (1951) Social choice and individual value. Yale University Press, New Haven
Banon G (1981) Distinction between several subsets of fuzzy measures. Int J Fuzzy Sets Syst 5:291–305
Boudon R (1979) La logique du social, Hachette, Paris
Carlsson C, Ehrenberg D, Eklund P, Fedrizzi M, Gustafsson P, Lindholm P, Merkurieva G, Riissanen T, Ventre AGS (1992) Consensus in distributed soft environments. Eur J Oper Res 61:165–185
Coletti G, Scozzafava R (2002) Probabilistic logic in a coherent setting. Kluwer Academic Publishers, Dordrecht
de Finetti B (1974) Theory of probability. J. Wiley, New York
Delli Rocili L, Maturo A, (2013) Teaching mathematics to children: social aspects, psychological problems and decision making models. In: Soitu, Gavriluta, Maturo (eds) Interdisciplinary approaches in social sciences, Editura Universitatii A.I. Cuza, Iasi, Romania
Dubois D, Prade H (1980) Fuzzy set and systems. Academic Press, New York
Dubois D, Prade H (1988) Fuzzy numbers: an overview. In: Bedzek JC (ed) Analysis of fuzzy information, vol 2 CRC-Press, Boca Raton, pp 3–39
Ehrenberg D, Eklund P, Fedrizzi M, Ventre AGS (1989) Consensus in distributed soft environments. Rep Comput Sci Math Åbo 88:1–24
Eklund P, Rusinowska A, De Swart H (2007) Consensus reaching in committees. Eur J Oper Res 178:185–193
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic. Prentice Hall, Jersey
Lindley DV (1985) Making decisions. Wiley, London
Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York
March JG (1994) A primer on decision making: how decisions happen. The Free Press, New York
Mares M (1997) Weak arithmetic on fuzzy numbers. Fuzzy Sets Syst 91(2):143–154
Mares M (2001) Fuzzy cooperative games. Springer, New York
Maturo A (2009) Alternative fuzzy operations and applications to social sciences. Int J Intell Syst 24:1243–1264
Maturo A (2009) Coherent conditional previsions and geometric hypergroupoids. Fuzzy Sets, Rough Sets, Multivalued Oper Appl 1(1):51–62
Maturo A (2009) On some structures of fuzzy numbers. Iran J Fuzzy Syst 6(4):49–59
Maturo A, Ventre AGS (2008) Models for consensus in multiperson decision making. In: NAFIPS 2008 conference proceedings. Regular Papers 50014. IEEE Press, New York
Maturo A, Ventre AGS (2009) An application of the analytic hierarchy process to enhancing consensus in multiagent decision making. In: Proceeding of the international symposium on the analytic hierarchy process for multicriteria decision making, July 29–August 1, 2009, paper 48. University of Pittsburg, Pittsburgh, pp 1–12
Maturo A, Ventre AGS (2009) Aggregation and consensus in multi objective and multi person decision making. Int J Uncertain Fuzziness Knowl-Based Syst 17(4):491–499
Maturo A, Ventre A (2009) Multipersonal decision making, consensus and associated hyperstructures. In: Proceeding of AHA 2008. University of Defence, Brno, pp 241–250
Maturo A, Squillante M, Ventre AGS (2006) Consistency for assessments of uncertainty evaluations in non-additive settings. In: Amenta P, D’Ambra L, Squillante M, Ventre AGS (eds) Metodi, modelli e tecnologie dell’informazione a supporto delle decisioni. Franco Angeli, Milano, pp 75–88
Maturo A, Squillante M, Ventre AGS (2006) Consistency for nonadditive measures: analytical and algebraic methods. In: Reusch B (ed) Computational intelligence, theory and applications. Springer, Berlin, pp 29–40
Maturo A, Squillante M, Ventre AGS (2010) Coherence for fuzzy measures and applications to decision making. In: Greco S et al. (eds) Preferences and decisions, STUDFUZZ 257 Springer, Heidelberg, pp 291–304
Maturo A, Squillante M, Ventre AGS (2010) Decision making. Fuzzy Meas Hyperstruct Adv Appl Stat Sci 2(2):233–253
Maturo A, Maturo F (2013) Research in social sciences: fuzzy regression and causal complexity. Springer, Heidelberg, pp 237–249
Maturo A, Maturo F (2014) Finite geometric spaces, steiner systems and cooperative games. Analele Universitatii “Ovidius” Constanta. Seria Matematica 22(1): 189–205
Maturo A, Maturo F (2017) Fuzzy events, fuzzy probability and applications in economic and social sciences. Springer International Publishing, Cham, pp 223–233
Maturo A, Sciarra E, Tofan I (2008) A formalization of some aspects of the social organization by means of the fuzzy set theory. Ratio Sociologica 1(2008):5–20
Maturo F (2016) Dealing with randomness and vagueness in business and management sciences: the fuzzy probabilistic approach as a tool for the study of statistical relationships between imprecise variables. Ratio Mathematica 30:45–58
Maturo F (2016) La regressione fuzzy. Fuzziness: Teorie e Applicazioni. Aracne Editrice, Roma, Italy, pp 99–110
Maturo F, Fortuna F (2016) Bell-shaped fuzzy numbers associated with the normal curve. Springer, Cham, pp 131–144
Maturo F, Hošková-Mayerová S (2017) Fuzzy regression models and alternative operations for economic and social sciences. Springer, Cham, pp 235–247
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
Saaty TL (2008) Relative measurement and its generalization in decision making, why pairwise comparisons are central in mathematics for the measurement of intangible factors, the analytic hierarchy/network process. Rev R Acad Cien Serie A Mat 102(2):251–318
Shapley LS (1953) A value for n-person games. Ann Math Stud (Princeton Univ) 28: 307–317
Shapley LS (1962) Simple games. An outline of the theory. Behav Sci 7:59–66
Simon HA (1982) Models of bounded rationality, Mit Press, Cambridge (Mass.)
Sugeno M (1974) Theory of fuzzy integral and its applications, PhD Thesis, Tokyo
Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton
Weber S (1984) Decomposable measures and integrals for Archimedean t-conorms. J Math Anal Appl 101(1):114–138
Yager R (1986) A characterization of the extension principle. Fuzzy Sets Syst 18:205—217
Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci, Part I 8:199–249, Part 2: 301–357
Zadeh L (1975) The concept of a linguistic variable and its applications to approximate reasoning, Part III. Inf Sci 9:43–80
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Maturo, A., Ventre, A.G.S. (2018). Fuzzy Numbers and Consensus. In: Collan, M., Kacprzyk, J. (eds) Soft Computing Applications for Group Decision-making and Consensus Modeling. Studies in Fuzziness and Soft Computing, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-60207-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-60207-3_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60206-6
Online ISBN: 978-3-319-60207-3
eBook Packages: EngineeringEngineering (R0)