Abstract
Financial valuation methods use additive aggregation operators. But a patrimony should be regarded as an organized set, and additivity makes it impossible for these aggregation operators to formalize such phenomena as synergy or mutual inhibition between the patrimony’s components. This paper considers the application of fuzzy measures and fuzzy integrals (such as Sugeno, Grabisch, Choquet) to financial valuation. More specifically, we show how integration with respect to a non additive measure can be used to handle positive or negative synergy in value construction.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abdel-Magid M.F. (1979), “Toward a better understanding of the role of measurement in accounting”, The Accounting Review, April, 54(2), 346–357.
Bry X., Casta J.F. (1995), “Measurement, imprecision and uncertainty in financial accounting”, Fuzzy Economic Review, November, 43–70.
Casta J.F. (1994) “Le nombre et son ombre. Mesure, imprécision et incertitude en comptabilité”, in Annales du Management, XIIèmes Journées Nationales des IAE, Montpellier, 78–100.
Casta J.F., Bry X. (1998), “Synergy, financial assessment and fuzzy integrals”, in Proceedings of IVth Meeting of the International Society for Fuzzy Management and Economy ( SIGEF ), Santiago de Cuba, II, 17–42.
Casta J.F., Lesage C. (2001), “Accounting and Controlling in Uncertainty: concepts, techniques and methodology”, in J. Gil-Aluja (ed.) Handbook of Management under Uncertainty, Kluwer Academic Publishers, Dordrecht.
Choquet G. (1953), “Théorie des capacités”, Annales de l’Institut Fourier, 5, 131–295.
Denneberg D. (1994), Non-additive measures and integral, Kluwer Academic Publishers, Dordrecht.
Ellerman D.P. (1986), “Double—entry multidimensional accounting”, Omega, International Journal of Management Science, 14 (1), 13–22.
Grabisch M. (1995), “Fuzzy integral in multicriteria decision making”, Fuzzy Sets and Systems, 69, 279–298.
Grabisch M., Nguyen H.T., Wakker E.A (1995), Fundamentals of uncertainty calculi with applications to fuzzy inference, Kluwer Academic Publishers, Dordrecht.
Grabisch M., Nicolas J.M. (1994), “Classification by Fuzzy Integral: Performance and Tests”, Fuzzy sets and systems, 65, 255–271.
Ijiri Y. (1967), The foundations of accounting measurement: a mathematical, economic and behavioral inquiry, Prentice Hall, Englewood Cliffs.
Ijiri Y. (1975), “The theory of accounting measurement, Studies” in Accounting Research, 10, American Accounting Association.
Korvin A. (1995), “Uncertainty methods in accounting: a methodological overview”, in Seigel P.H., de Korvin A., Omer K. (eds), Applications of fuzzy sets and the theory of evidence to accounting, JAI Press, Stamford, Conn., 3–18.
March J.G. (1987), “Ambiguity and accounting: the elusive link between information and decision making”, Accounting, Organizations and Society, 12 (2), 153–168.
Mattessich R. (1964), Accounting and analytical methods, Richard D. Irwin, Inc.
Morgenstern O. (1950), On the accuracy of economic observations, Princeton University Press. Schmeidler D. (1989), “Subjective probability and expected utility without additivity”, Econometrica, 57 (3), 571–587.
Sterling R.R. (1970), Theory of the measurement of enterprise income,The University Press of Kansas.
Stevens S.S. (1951), “Mathematical measurement and psychophysics”, in Stevens S.S (ed.) Handbook of Experimental Psychology, John Wiley and Sons, New-York, 1–49.
Stevens S.S. (1959), “Measurement, psychophysics and utility”, in Churman C.W., Ratoosh P. (eds.), Measurement: Definitions and Theories, John Wiley and Sons, New-York, 18–63.
Sugeno M. (1977) “Fuzzy measures and fuzzy integrals: a survey”, in Gupta, Saridis, Gaines (eds.), Fuzzy Automata and Decision Processes, 89–102.
Tippett M. (1978), “The axioms of accounting measurement”, Accounting and Business Research, Autumn, 266–278.
Vickrey D.W. (1970), “Is accounting a measurement discipline ?”, The Accounting Review, October, 45, 731–742.
Wakker P. (1990), “A behavioral foundation for fuzzy measures”, Fuzzy Sets and Systems, 37, 327–350.
Willett R.J. (1987), “An axiomatic theory of accounting measurement”, Accounting and Business Research, Spring, 66, 155–171.
Zebda A. (1991), “The problem of ambiguity and vagueness in accounting and auditing”, Behavioral Research in Accounting, 3, 117–145.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bry, X., Casta, JF. (2003). Synergy modelling and financial valuation: the contribution of Fuzzy Integrals. In: Lesage, C., Cottrell, M. (eds) Connectionist Approaches in Economics and Management Sciences. Advances in Computational Management Science, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3722-6_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3722-6_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5379-7
Online ISBN: 978-1-4757-3722-6
eBook Packages: Springer Book Archive