Information uncertainty in management systems is a subject of research of many scientific disciplines. Research concerning a quantitative modelling of uncertainty verging on mathematics, information technology, and logic is extremely important. The purpose of the article is to present possibilities and limitations of the most popular approaches in uncertainty modelling in social sciences with particular emphasis on management problems. Achieving such a goal always requires accepting certain basic epistemological assumptions. Therefore, an assumption was accepted about a subjective character of information. Information is treated as a feature of a cognition process. It is not an objective element of the reality. Furthermore, there was also assumed that uncertainty is a result of interference in mapping information and processes connected with cognition of the reality by human. Starting from these assumptions, the article demonstrates the way uncertainty is modelled and perceived in terms of probability, in fuzzy logic, in rough set theory, and in grey systems theory, which has been gaining popularity in recent years. In order to compare the mentioned approaches to a maximum extent, an attempt was made to show their essence referring to a classical set theory. To this aim, mathematical formalism was used for a precise description of particular types of uncertainty. It is of great significance as in management sciences and generally in social sciences some terms, for example, fuzziness, probability or greyness are overinterpreted and used in descriptive way to pretend scientific statements.
Aczel, A.D. (1993). Complete business statistics. Irwin Professional Publishing.
Altrock, C. (1996). Fuzzy logic and neurofuzzy applications in business and finance. Prentice-Hall, Inc.
Buckley, J.J., Eslami E., Feuring T., (2013). Fuzzy mathematics in economics and engineering. “Physica” Vol. 91.
Ballentine, L.E. (2001). Interpretations of probability and quantum theory. Foundations of probability and physics, World Scientific Singapore.
Cox, R.T. (1964). Probability, frequency and reasonable expectation. “American Journal of Physics” 14(1), p. 1–13.
—— (1961). Algebra of Probable Inference. JHU Press.
de Finetti, B. (1972). Probability, induction, and statistics. New York: Wiley.
Delcea, C. (2014). Not black not even white definitively grey economic systems. “The Journal of Grey System” 26(1), p. 11–26.
—— (2015). Grey systems theory in economics – a historical applications review. Grey Systems: Theory and Application, 5(2), p. 263–276.
De Soto, J.H. (1998). The ongoing methodenstreit of the Austrian school. Centre d'analyse économique.
Dow, S., Hillard, J. (1995). Keynes, knowledge and uncertainty. Edward Elgar Publishing.
Good, I.J. (1983). Good thinking: The foundations of probability and its applications. University of Minnesota Press.
Hoppe, H.H. (2007). The limits of numerical probability: Frank H. Knight and Ludwig von Mises and the frequency interpretation. “Quarterly Journal of Austrian Economics” 10(1), p. 1–20.
Jaynes, E.T. (2003). Probability theory: The logic of science. Cambridge University Press.
Jeffreys, H. (1973). Scientific inference. Cambridge University Press.
Kolmogorov, A.N. (1950). Foundations of probability theory. Chelsea, New York.
Kosiński, W., Prokopowicz, P. (2016). Algebra of fuzzy numbers. “Mathematica Applicanda” 32(46/05), p. 37–63.
Kosiński, W., Prokopowicz, P., Ślęzak, D. (2003). Ordered fuzzy numbers. “Bulletin of the Polish Academy of Sciences, Series Science Mathematica” 51(3).
Lee, C.C. (1990). Fuzzy logic in control systems: fuzzy logic controller. IEEE Transactions on systems, man, and cybernetics, 20(2), p. 404–418.
Mierzwiak, R., Xie, N., Nowak, M. (2018). New axiomatic approach to the concept of grey information. Grey Systems: Theory and Application, 8(2), p. 201–2012.
Mises, R. (1957). Probability, statistics, and truth. Courier Corporation.
Pawlak, Z. (2002). Rough sets and intelligent data analysis. “Information sciences” 147(1–4), p. 1–12.
—— (2004). Rough sets. New method of data analysis. “Warsaw University Magazine”, Vol. 5 (in Polish).
—— (1982). Rough sets. “International Journal of Parallel Programming” 11(5), p. 341–356.
Pietrewicz, L. Uncertainty, postmodernism and economic growth. “Humanities and Social Sciences”, Vol. 22 24 (2) (in Polish), p. 233–246.
Popper, K.R. (1957). The propensity interpretation of the calculus of probability, and the quantum theory [In:] Körner S. (ed.), Observation and Interpretation, Butterworths, p. 65–70.
Lin, Y., Liu, S. (2004). A historical introduction to grey systems theory, IEEE Internation-al Conference: Systems, Man and Cybernetics, p. 2403–2408.
Liu, S., Yang, Y., Forrest, J. (2016). Grey Data Analysis: Methods, Models and Applications. Springer, 2016, p. 14–18.
Ragin, C.C. (2000). Fuzzy-set social science. University of Chicago Press.
Savage, L.J. (1951). The theory of statistical decision. “Journal of the American Statistical Association” 46(253), p. 55–67.
Tadeusiewicz, R. (2017). Polish Island in archipelago of Artificial Intelligence – rough sets. [access: 17.10.2017]. access on the internet: http://ryszardtadeusiewicz.natemat.pl/150285,polska-wyspa-w-archipelagu-sztucznej-inteligencji-zbiory-przyblizone
Zadeh, L.A. (1965). Fuzzy sets. „Information and control” 8(3), p. 338–353.
—— (1975). The concept of a linguistic variable and its application to approximate reasoning. “Information sciences” 8(3), p. 199–249.
—— (1983). The role of fuzzy logic in the management of uncertainty in expert systems. “Fuzzy sets and systems” 11(1–3), p. 199–227.