Abstract
Mamdani Systems are very well known in the area of Fuzzy Control, where they have been, they are, and they will continue to be successfully used. Efforts to linguistically interpret Mamdani Systems as a method for inference in fuzzy logic have faced the difficulty of interpreting the output of such systems before defuzzification, which consists of an aggregation of normally truncated fuzzy sets. The present chapter offers a metasemantic approach to alleviate this problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7, 1–13 (1975)
Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. In: Mamdani, E.H., Gaines, B.R. (eds.) Fuzzy Reasoning and its Applications. Academic Press (1981)
Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning. Information Sciences 8, 199–249, 301–357, 9, 43–80 (1975)
Zadeh, L.A.: A fuzzy-set-theoretic interpretation of hedges. Memorandum M-335, Electronics Research Laboratory, University of California, Berkeley (1972)
Novak, V.: A horizon shifting model of linguistic hedges for approximate reasoning. In: Proc. 5th IEEE International Conference on Fuzzy Systems, vol. 1, pp. 423–427. IEEE-CS-Press (1996)
Macvicar-Whelen, P.J.: Fuzzy sets, the concept of height, and the hedge ‘very’. IEEE Trans. on Systems, Man, and Cybernetics, SMC 8, 507–511 (1978)
Trillas, E., Moraga, C., Sobrino, A.: On ‘family resemblances’ with fuzzy sets. In: Proc. International Conference IFSA/Eusflat 2009, vol. 8, pp. 306–311 (2009); ISBN 978–989–95079–6–8
Moraga, C., Trillas, E.: A CWW path from fuzzy logic to natural language. In: Proc. International Conference IFSA/Eusflat 2009, pp. 687–692 (2009); ISBN 978–989–95079–6–8
Moraga, C.: A Metasemantics to refine fuzzy if-then-rules. In: Proc. 34th IEEE Internaional Symposium on Multiple-Valued Logic, pp. 148–153. IEEE-CS-Press (2004)
Eshragh, F., Mamdani, E.H.: A general approach to linguistic approximation. In: Mamdani, E.H., Gaine, B.R. (eds.) Fuzzy Reasoning and its Applications. Academic Press (1981)
Hersh, H.M., Caramazza, A.: Fuzzy set approach to modifiers and vagueness in natural language. Journal of Experimental Psychology: General 105, 254–276 (1976)
Hawking, S. (ed.): God created the integers: The Mathematical Breakthroughs that changed History.Running Pr. Book Pub. (2005); ISBN: 9780762419227
Pappis, C.P., Mamdani, E.H.: A fuzzy logic controller for a traffic junction. Research Report, Dept. Electrical Engineering, Queen Mary College, London (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Moraga, C. (2012). An Essay on the Interpretability of Mamdani Systems. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds) Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing, vol 271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24666-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-24666-1_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24665-4
Online ISBN: 978-3-642-24666-1
eBook Packages: EngineeringEngineering (R0)