Abstract
By means of a careful analysis of early papers by Zadeh on fuzzy rules, we suggest an explanation of why Mamdani came up with his way of modelling fuzzy control rules. And then we recall the semantics of fuzzy rules so as to position Mamdani,s rules in possibility theory. We also explain the links between (probabilistic) conditionals, as well as association rules, and Mamdani’s rules. Finally, we comment on Mamdani’s constant taste for applied Artificial Intelligence (AI), while the whole field of fuzzy rule-based systems he created, and viewed as part of AI, eventually moved away from it.
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
Assilian, S.: Artificial intelligence in the control of real dynamic systems. Ph. D. Thesis, London University (1974)
Babuska, R., Mamdani, E.H.: Fuzzy control. Scholarpedia 3(2), 2103 (2008), http://www.scholarpedia.org/article/Fuzzy_control
Baczyński, M., Jayaram, B.: QL-implications: Some properties and intersections. Fuzzy Sets and Syst. 161, 158–188 (2010)
Baldwin, J.F., Guild, N.C.F.: Modelling controllers using fuzzy relations. Kybernetes 9, 223–229 (1980)
Buchanan, B.G., Shortliffe, E.H.: Rule-Based Expert Systems – The MYCIN Experiments of the Stanford Heuristic Programming Project. Addison- Wesley, Reading (1984)
Buchanan, B.G., Sutherland, G., Feigenbaum, E.A.: Heuristic DENDRAL: A program for generating explanatory hypotheses in organic chemistry. In: Machine Intelligence, vol. 4, pp. 209–254. Elsevier (1969)
Di Nola, A., Pedrycz, W., Sessa, S.: An aspect of discrepancy in the implementation of modus ponens in the presence of fuzzy quantities. Int. J. Approx. Reason. 3, 259–265 (1989)
Dubois, D., Hüllermeier, E., Prade, H.: A systematic approach to the assessment of fuzzy association rules. Data Mining and Knowledge Discovery 13, 167–192 (2006)
Dubois, D., Prade, H.: The generalized modus ponens under sup-min composition – A theoretical study. In: Gupta, M.M., Kandel, A., Bandler, W., Kiszka, J.B. (eds.) Approximate Reasoning in Expert Systems, pp. 217–232. North- Holland, Amsterdam (1985)
Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty (with the collaboration of Farreny, H., Martin-Clouaire, R., Testemale, C.) Plenum Press, New York
Dubois, D., Prade, H.: Gradual inference rules in approximate reasoning. Information Sciences 61, 103–122 (1992)
Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets and Syst. 84, 169–186 (1996)
Dubois, D., Prade, H., Ughetto, L.: Checking the coherence and redundancy of fuzzy knowledge bases. IEEE Trans. on Fuzzy Syst. 5, 398–417 (1997)
Dubois, D., Prade, H., Ughetto, L.: A new perspective on reasoning with fuzzy rules. Inter. J. of Intelligent Systems 18, 541–567 (2003)
Duda, R., Gaschnig, J., Hart, P.: Model design in the Prospector consultant system for mineral exploration. In: Michie, D. (ed.) Expert Systems in the Microelectronic Age, pp. 153–167. Edinburgh University Press (1981)
Elkan, C.: The paradoxical success of fuzzy logic. IEEE Expert, 3–8, with discussions by many scientists (9–46) and a reply by the author (47–49) (August 1994)
Heckerman, D., Mamdani, E.H., Wellman, M.P.: Real-world applications of Bayesian networks – Introduction. Commun. of ACM 38(3), 24–26 (1995)
Heckerman, D., Mamdani, E.H., Wellman, M.P.: Editorial: Real-world applications of uncertain reasoning. Int. J. Hum.- Comput. Stud. 42, 573–574 (1995)
Lindsay, R.K., Buchanan, B.G., Feigenbaum, E.A.: DENDRAL: a case study of the first expert system for scientific hypothesis formation. Artificial Intelligence 61, 209–261 (1993)
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. Int. J. Man-Machine Studies 8, 669–678 (1976)
Mamdani, E.H., Efstathiou, J.: An analysis of formal logics as inference mechanisms in expert systems. Inter. J. of Man-Machine Studies 21, 213–227 (1984)
Mamdani, E.H., Efstathiou, J.: Higher-order logics for handling uncertainty in expert systems. Inter. J. of Man-Machine Studies 22, 283–293 (1985)
Mamdani, E.H.: A misconception of theory and application. IEEE Expert ( August 27-28, 1994)
Mendel, J.: Fuzzy logic systems for engineering: A tutorial. Proc. of IEEE, Special Issue on Fuzzy Logic Eng. Appl. 83(3), 345–377 (1995)
Pitt, J., Venkataram, P., Mamdani, A.: QoS Management in mANETs Using Norm-Governed Agent Societies. In: Dikenelli, O., Gleizes, M.-P., Ricci, A. (eds.) ESAW 2005. LNCS (LNAI), vol. 3963, pp. 221–240. Springer, Heidelberg (2006)
Smets, P., Mamdani, E.H., Dubois, D., Prade, H. (eds.): Non-Standard Logics for Automated Reasoning. Academic Press, London (1988)
Sugeno, M.: An introductory survey of fuzzy control. Information Sciences 36, 59–83 (1985)
Takagi, T., Sugeno, M.: Fuzzy identication of systems and its applications to modeling and control. IEEE Trans. on Syst., Man, and Cybern. 15, 116–132 (1985)
Trillas, E., Valverde, L.: On some functionally expressable implications for fuzzy set theory. In: Klement, E.P. (ed.) Proc. 3rd Internat. Seminar on Fuzzy Set Theory, Linz, Austria, pp. 173–190 (1981)
Trillas, E., Valverde, L.: On mode and implication in approximate reasoning. In: Gupta, M.M., Kandel, A., Bandler, W., Kiszka, J.B. (eds.) Approximate Reasoning in Expert Systems, pp. 157–166. North-Holland (1985)
Van Broekhoven, E., De Baets, B.: Only smooth rule bases can generate monotone Mamdani-Assilian models under center-of-gravity defuzzification. IEEE Trans. on Fuzzy Systems 17, 1157–1174 (2009)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics 3(1), 28–44 (1973)
Zadeh, L.A.: On the analysis of large scale systems. In: Göttinger, H. (ed.) Systems Approaches and Environment Problems, Vandenhoeck and Ruprecht, Gottingen, pp. 23–37 (1974)
Zadeh, L.A.: Calculus of fuzzy restrictions. In: Zadeh, L.A., Fu, K.S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Processes, pp. 1–39. Academic Press, New York
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Syst. 1, 3–28 (1978)
Zadeh, L.A.: A theory of approximate reasoning. In: Mitchie, D., Hayes, J.E., Mikulich, L.I. (eds.) Machine Intelligence, vol. 9, pp. 149–194. Elsevier (1979)
Zadeh, L.A.: The calculus of fuzzy if-then rules. AI Expert 7(3), 23–27 (1992)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dubois, D., Prade, H. (2012). Abe Mamdani: A Pioneer of Soft Artificial Intelligence. 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_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-24666-1_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24665-4
Online ISBN: 978-3-642-24666-1
eBook Packages: EngineeringEngineering (R0)