Abstract
The paper presents modified formalism to perform fuzzy operations on correlated assessments. The application of the standard formalism used in Zadeh’s fuzzy logic requires an arbitrary setting of triangular norms and sometimes provides ridiculous results which are inconsistent with the gathered experimental data. The author discovered that the membership function’s value may be treated as the mean of statements individually evaluated into YES or NO by a panel of human judges with identifiable identity. It leads to a fundamental change because a pair of triangular norms selected for fuzzy logic is proven and not arbitrarily set. The paper proposes generalization of the fuzzy description into a form of a binary vector. It moves evaluation of statements with fuzzy logic variables into the space of vectors of Boolean components. The new interpretation gives fuzzy variables and values an identity, which is necessary for operations with correlations. Additionally, due to a binary vector data structure, it potentially allows to perform computations utilizing collective intelligence methods such as genetic algorithms.
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
ISO2631: Mechanical vibration and shock – Evaluation of human exposure to whole-body vibration – Part 1: General requirements. ISO, Geneve (1997)
BS6841: Guide to measurement and evaluation of human exposure to whole-body mechanical vibration and repeated shoc. BSI, London (1987)
Griffin, M.J.: Discomfort from feeling vehicle vibration. Vehicle Syst. Dyn. 45, 679–698 (2007)
BS6472-1: Guide to evaluation of human exposure to vibration in buildings. Vibration sources other than blasting. BSI, London (2008)
CEN_ENV12299: Railway applications - Ride comfort for passengers - Measurement and evaluation. CEN-CENELEC, Brussels (2009)
Grzegożek, W., Szczygieł, J., Król, S.: An Attempt of an Employment of a Continuous Wavelet Transform for Evaluation of Temporary Comfort Distrubances. Journal of KONES Powertrain and Transport 16, 165–172 (2009)
Pietraszek, J., Grzegożek, W., Szczygieł, J.: Forecasting of Subjective Comfort in Tram Using Ordinal Logistic Regression and Manifold Learning. Journal of KONES Powertrain and Transport 19, 403–410 (2012)
Pietraszek, J.: Fuzzy Regression Compared to Classical Experimental Design in the Case of Flywheel Assembly. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS (LNAI), vol. 7267, pp. 310–317. Springer, Heidelberg (2012)
Ling, C.H.: Representation of associative functions. Publ. Math., Debrecen 6, 167–173 (1973)
Paalman de Miranda, A.B.: Topological semigroups. Math. Centre Tracts 11 Math. Centrum, Amsterdam (1964)
Schweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10, 313–334 (1960)
Bellman, R.E., Zadeh, L.A.: Local and fuzzy logics. In: Dunn, J.M., Epstein, D. (eds.) Modern Uses of Multiple Valued Logic, pp. 103–165. D. Reidel, Dordrecht (1977)
Zadeh, L.A.: Fuzzy Sets. Inform Control 8, 338–353 (1965)
Klement, E.P., Mesiar, R., Pap, E.: Fuzzy Set Theory: ‘AND’ is more than just the Minimum. In: Hryniewicz, O. (ed.) Issues in Soft Computing. Decisions and Operations Research, pp. 39–52. EXIT Press, Warszawa (2005)
Aczel, J.: Lectures on functional equations and their applications. Academic Press, New York (1966)
Fuchs, L.: Partially ordered algebraic systems. Pergamon Press, Oxford (1963)
Cignoli, R.: Injective De-Morgan and Kleene Algebras. P. Am. Math. Soc. 47, 269–278 (1975)
Negoita, C.V., Ralescu, D.A.: Applications of fuzzy sets to systems analysis. Birkhäuser Verlag, Stuttgart (1975)
Atanassov, K.T.: Intuitionistic Fuzzy-Sets. Fuzzy Set Syst. 20, 87–96 (1986)
Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy events and their probabilities. Notes on Intuitionistic Fuzzy Sets 4, 68–72 (1999)
Pedrycz, W.: Shadowed sets: bridging fuzzy and rough sets. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization. A New Trend in Decision-Making, pp. 179–199. Springer, Singapore (1999)
Dubois, D., Prade, H.: Operations on Fuzzy Numbers. Int. J. Syst. Sci. 9, 613–626 (1978)
Grzegorzewski, P., Mrówka, E.: Trapezoidal approximations of fuzzy numbers. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 237–244. Springer, Heidelberg (2003)
Grzegorzewski, P.: Fuzzy number approximation via shadowed sets. Inform. Sciences 225, 35–46 (2012)
de Finetti, B.: Foresight: its logical laws, its subjective sources. In: Kyburg, H.E., Smokler, H.E. (eds.) Studies in Subjective Probability. John Wiley & Sons, New York (1964)
Tyrala, R.: Linear Systems with Fuzzy Solution. In: Grzegorzewski, P. (ed.) Issues in Soft Computing. Theory and Applications, pp. 277–288. EXIT Press, Warszawa (2005)
Buckley, J.J.: Fuzzy Probability and Statistics. Springer, Berlin (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pietraszek, J. (2013). The Modified Sequential-Binary Approach for Fuzzy Operations on Correlated Assessments. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-38658-9_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38657-2
Online ISBN: 978-3-642-38658-9
eBook Packages: Computer ScienceComputer Science (R0)