Abstract
Mamdani’s inference has an incredible success, especially in areas such as decision making and control. Yet, it is well known that it uses a min-based implication that does not verify classical boolean logic requirements.
This contribution aims at, in the one hand, exploring Mamdani’s choice from a practical point of view, and in the other hand, explaining the success of Mamdani’s inference from a logical perspective, by introducing a simple variant of the Generalized Modus Ponens (GMP) that uses standard fuzzy implications.
In addition, this new formulation opens the way for new methods of inference that have the same benefits as Mamdani’s.
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References
Narayanan, R.: Fuzzy Logic Control of Washing Machines. Electronic For You Magazine (December 2003)
Bonissone, P.P.: Fuzzy logic controllers: an industrial reality. In: Zurada, J.M., Marks II, R.J., Robinson, C.J. (eds.) Computational Intelligence: Imitating Life, pp. 316–327. IEEE Press, Piscataway (1994)
Hirota, K. (ed.): Industrial Applications of Fuzzy Technology. Springer, Tokyo (1993)
Yager, R., Filev, D.: Essentials of Fuzzy Modeling and Control. John Wiley and Sons, NewYork (1994)
Alsina, C., Guadarrama, S., Renedo, E., Trillas, E.: Studying Fuzzy Modus Ponens. In: Proceedings of the Annual meeting of the North American Fuzzy Information Processing Society (NAFIPS), Montreal, Canada, pp. 426–429 (2006)
Bouchon-Meunier, B.: La logique floue et ses applications. Addison-Wesley (1995)
Trillas, E., Valverde, L.: On modus ponens in fuzzy logic. In: Proceedings of the 15th International Symposium on Multivalued Logics (ISMVL), Kingston, Canada, pp. 294–301 (1985)
Dubois, D., Prade, H.: Combination of fuzzy information in the framework of possibility theory. In: Abidi, M.A., Gonzalez, R.C. (eds.) Data Fusion in Robotics and Machine Intelligence, pp. 481–505. Academic Press, Inc., Boston (1992)
Trillas, E.: On logic and fuzzy logic. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1(2), 107–137 (1993)
Mamdani, E.H., Assilian, S.: IAn experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7, 1–13 (1975)
Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. Proceedings of the Institution of Electrical Engineers (IEE) 121(12), 1585–1588 (1974)
Moser, B., Navara, M.: Fuzzy controllers with conditionally firing rules. IEEE Transactions of fuzzy systems 10(3), 340–348 (2002)
Sugeno, M., Griffin, M.F., Bastian, A.: Fuzzy hierarchical control of an unmanned helicopter. In: Proceedings of the 17th IFSA World Congress, Korea (1993)
Terano, T., Asai, K., Sugeno, M.: Applied fuzzy systems. Academic Press, Inc., Boston (1994)
Trillas, E., Mas, M., Monserrat, M., Torrens, J.: On the representation of fuzzy rules. International Journal Approximate Reasoning 597, 583–597 (2008)
Wilmott, R.: Two fuzzier implication in the theory of fuzzy power sets. Fuzzy Sets and Systems 4, 31–36 (1980)
Lukasiewicz, J.: Interpretacja liczbowa teorii zdan. Ruch Filozoczny 7, 93–93 (1923)
Mizumoto, M.: Fuzzy control under various fuzzy reasoning methods. In: Proceedings of the first IFSA World Congress, Mallorca, Spain (1985)
Dienes, Z.: On an implication function in many-valued systems of logic. Journal Symbolic Logic 14, 95–97 (1949)
Bouchon-Meunier, B., Dubois, D., Godo, L., Prade, H.: Fuzzy sets and possibility theory in approximate and plausible reasoning. In: Bezdek, J., Dubois, D., Prade, H. (eds.) Fuzzy sets in approximate reasoning and information systems, part of the Handbook of Fuzzy Sets and Possibility Theory, pp. 15–190. Kluwer Academic Publishers (1999)
Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Information Sciences 9, 43–80 (1976)
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Detyniecki, M., Moubêche, B., Bouchon-Meunier, B. (2012). On the Paradoxical Success of Mamdani’s Minimum-Based Inference. 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_19
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DOI: https://doi.org/10.1007/978-3-642-24666-1_19
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