Abstract
Lotfi Zadeh initiated three fundamental concepts: (1) the concept of a linguistic variable, (2) the concept of a fuzzy set (with a membership function (MF) for linguistic terms that gradually changes between 0 and 1), and (3) the concept a matrix of linguistic rules that connect linguistic variables. These concepts are outside of the main stream of concepts used in both the probability theory and the control theory. These concepts are critical for the area that Zadeh later denoted as Computing with Words (CWW) [17]. The elegance and intuitiveness of these three concepts deeply impressed me when I learned about them a long time ago.
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
Cheeseman, P.: Probabilistic vs. Fuzzy Reasoning. In: Kanal, L.N., Lemmer, J.F. (eds.) Uncertainty in Artificial Intelligence, pp. 85–102. Elsevier (North-Holland), Amsterdam (1986)
Hall, L.O., Szabo, S., Kandel, A.: On the Derivation of Memberships for Fuzzy Sets in Expert Systems. Information Sciences 40, 39–52 (1986)
Hisdal, E.: Logical Structures for Representation of Knowledge and Uncertainty. Springer (Physica), New York (1998)
Kovalerchuk, B., Talianski, V.: Comparison of Empirical and Computed Values of Fuzzy Conjunction. Fuzzy Sets and Systems 46, 49–53 (1992)
Kovalerchuk, B., Klir, G.J.: Linguistic Context Spaces and Modal Logic for Approximate Reasoning and Fuzzy Probability Comparison. In: Proceedings of the Third International Symposium on Uncertainty Modeling and Analysis and NAFIPS 1995, pp. A23–A28. IEEE Press (1995)
Kovalerchuk, B.: Context Spaces as Necessary Frames for Correct Approximate Reasoning. International Journal of General Systems 25(1), 61–80 (1996)
Kovalerchuk, B.: Second Interpolation for Fuzzy Control. In: Fifth IEEE International Conference on Fuzzy Systems, New Orleans, pp. 150–155 (1996)
Kovalerchuk, B., Vityaev, E.: Data Mining in Finance: Advances in Relational and Hybrid Methods (ch. 7 on fuzzy systems). Kluwer, Boston (2000)
Kovalerchuk, B.: Interpretable Fuzzy Systems: Analysis of T-norm interpretability. In: Proceedings of the WCCI World Congress on Computational Intelligence, Barcelona, pp. 20–35 (July 2010)
Kovalerchuk, B.: BISC-group posts (2010-2012), http://mybisc.blogspot.com/
Resconi, G., Kovalerchuk, B.: Agents’ Model of uncertainty. Knowledge and Information Systems 18(2), 213–229 (2009)
Thole, U., Zimmermann, H.-J., Zysno, P.: On the Suitability of Minimum and Product Operations for the Intersection of Fuzzy Sets. Fuzzy Sets and Systems 2, 173–186 (1979)
Von Altrock, C.: Fuzzy Logic and Neuro Fuzzy Applications in Business and Finance. Prentice Hall, New Jersey (1997)
Wright, G., Ayton, P. (eds.): Subjective Probability. Wiley, Chichester (1994)
Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Information Sciences 8, 199–249 (1977)
Zadeh, L.A.: Dicussion: Probability Theory and Fuzzy Logic are Complementary Rather than Competitive. Technometrics 37(3), 271–276 (1996)
Zadeh, L.A.: From Computing with Numbers to Computing with Words – From Manipulation of Measurements to Manipulation of Perceptions. IEEE Transactions on Circuits Systems 45, 105–119 (1999)
Zadeh, L.A.: Toward a Perception-based Theory of Probabilistic Reasoning with Imprecise Probabilities. Journal of Statistical Planning and Inference 105, 233–264 (2002)
Zadeh, L.A.: A Note on Z-numbers. Information Sciences 181, 2923–2932 (2011)
Zadeh, L.A.: BISC-group posts, 8.17.2011,03/29/2012, 04.16.2012, 04.19.2012, http://mybisc.blogspot.com/
Zimmermann, H.-J.: Fuzzy Sets, Decision Making, and Expert Systems. Kluwer-Nijhoff, Boston (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kovalerchuk, B. (2013). Quest for Rigorous Combining Probabilistic and Fuzzy Logic Approaches for Computing with Words. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35641-4_47
Download citation
DOI: https://doi.org/10.1007/978-3-642-35641-4_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35640-7
Online ISBN: 978-3-642-35641-4
eBook Packages: EngineeringEngineering (R0)