Abstract
It is shown that the family of all valued sets on a finite universe with values in a finite linear order is a medium. Stochastic properties of these media are investigated.
Ovchinnikov’s work is supported by NSF grant No SES-9986269 to J.-Cl. Falmagne at UC Irvine.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Barbut and B. Monjardet, Ordre et Classification (Collection Hachete Université, 1970 ).
G. Birkhoff, Lattice Theory (AMS Colloquium Publications, 3rd ed., vol. XXV, AMS, Providence, R.I., 1967 ).
J.-P. Doignon and J.-Cl. Falmagne, “Well-graded families of relations”, Discrete Math. 173 (1997) 35–44.
J.-Cl. Falmagne, “A stochastic theory for the emergence and the evolution of preference structure”, Math. Social Sci. 31 (1996) 63–84.
J.-Cl. Falmagne, “Stochastic Token Theory”, J. Math. Psych. 41(2) (1997) 129–143.
J.-Cl. Falmagne and J.-P. Doignon, “Stochastic evolution of rationality”, Theory and Decision 43 (1997) 107–138.
J.-C1. Falmagne and S. Ovchinnikov, “Media theory”, Discrete Appl. Math. (to appear)
J.-C. Falmagne, M. Regenwetter and B. Grofman, “A stochastic model for the evolution of preferences”, in Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce, ed. A.A.J. Marley ( Lawrence Erlbaum Associates, NJ, 1997 ) pp. 111–129.
S. Ovchinnikov and A. Dukhovny, “Advances in media theory”, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8 (1) (2000) 45–71.
V. B. Kuz’min and S. V. Ovchinnikov, “Geometry of preference spaces I”, Automat. Remote Control 36 (1975) 2059–2063.
S. V. Ovchinnikov, “Convexity in subsets of lattices”, Stochastica IV (1980) 129–140.
M. Regenwetter, J.-Cl. Falmagne, and B. Grofman, “A stochastic model of preference change and its applications to 1992 Presidential Election Panel Data”, Psychological Review, 106 (1999) 362–384.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dukhovny, A., Ovchinnikov, S. (2002). Families of Valued Sets as Media. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol 89. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1797-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1797-3_16
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-662-00329-9
Online ISBN: 978-3-7908-1797-3
eBook Packages: Springer Book Archive