Abstract
There exist different types of gradual rules, involving graduality on the truth value, the possibility, the certainty associated with propositions, or dealing with the degree of similarity or the proximity of observations with reference propositions, or a graduality on the values taken by variables. In this paper, we describe the properties of gradual rules according to variations of values of the variables. Then, we extend the results to a graduality expressed through linguistic modifiers. Finally, we show that a gradual knowledge representation through modifiers can be linked with analogical reasoning.
Preview
Unable to display preview. Download preview PDF.
References
Bouchon B., Stability of linguistic modifiers compatible with a fuzzy logic, in Uncertainty in Intelligent Systems, Lecture Notes in Computer Science, vol. 313, Springer Verlag, 1988
Bouchon-Meunier B., Comment remplacer des calculs par des règles simples dans le cadre d'une logique floue, Cognitiva 90,1990
Bouchon B. and S. Desprès, Acquisition numérique/symbolique de connaissances graduelles, Actes des 3èmes journées du PRC-GDR Intelligence Artificielle, Paris, Hermès, 1990
Bouchon-Meunier B., Fuzzy logic and knowledge representation using linguistic modifiers, in Fuzzy logic for the management of uncertainty (L.A. Zadeh, J. Kacprzyk, eds.), John Wiley & Sons, 1992, pp. 399–414
Bouchon-Meunier B. and Jia Yao, Linguistic modifiers and gradual membership to a category, International Journal of Intelligent Systems 7, pp 25–36, 1992
Bouchon-Meunier B. and L. Valverde, Analogical Reasoning and Fuzzy Resemblance, in Uncertainty in Intelligent Systems (B. Bouchon-Meunier, L. Valverde, R.R. Yager, eds.), Elsevier Science Pub, pp 247–255, 1993
Buisson B. and Prade H., Un système d'inférence pratiquant l'interpolation au moyen de règles à prédicats graduels — Une application au calcul de rations caloriques, Actes de la convention Intelligence Artificielle 88-89, Publ. Hermès, Paris, 1989
Dubois D. and H. Prade, Fuzzy numbers: an Overview, in J.C. Bezdek (dir.) Analysis of Fuzzy Information, vol. 1, Mathematics and Logic, CRC Press, Boca Raton, pp 3–39
Dubois D. and H. Prade, A typology of fuzzy “If...then...rules”, in Proc. 3rd Inter. Fuzzy Systems Association Congress, Seattle, Wash., 1989, pp 782–785
Dubois D. and H. Prade, Gradual inference rules in approximate reasoning, Information Sciences, 1990
Dubois D. and H. Prade, Fuzzy rules in knowledge-based systems-Modelling gradeness, uncertainty and preference-, in An introduction to fuzzy logic applications in intelligent systems, (R.R. Yager, L.A. Zadeh, eds.) Kluwer Academic Publishers, 1992
Dubois D., H. Prade and L. Ughetto, On Fuzzy Interpolation, in Systèmes de Règles Floues: cohérence, redondance et interpolation, Rapport IRIT/96-17-R, mai 1996
Koczy L.T., Hirota K., Approximate Reasoning by Linear Rule Interpolation and General Approximation, International Journal of Approximate Reasoning, 9:197–225, 1993
Mizumoto M., Multifold Fuzzy Reasoning as Interpolative Reasoning, in Fuzzy Sets, Neural Networks and Soft Computing, (R.R. Yager and L.A. Zadeh, eds.) Van Nostrand Reinhold, New-York, 1994
Sanchez E., Solution of fuzzy equations with extended operations, Fuzzy Sets Syst., 12, p237, 1984
Turksen I.B. and Zhao Zhong, An Approximate Analogical Reasoning Approach Based on Similarity Measures, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 18, no 6, nov./dec. 1988
Ughetto L., Dubois D. and H. Prade, La cohérence des systèmes de règles graduelles, Rencontres francophones sur la logique floue, Cepadues Editions, 1995
Zadeh L.A., A Fuzzy-Set Theoretic Interpretation of Linguistic Hedges, J. Cybernetics 2, 2, pp. 4–34, 1972
Zadeh L.A., The role of fuzzy logic in the management of uncertainty in Expert Systems, Fuzzy Sets and Systems 11, pp. 199–227, 1983.
Zadeh L.A., Interpolative Reasoning Based on Fuzzy Logic and its Application to Control and System Analysis, invited lecture, abstract in the Proc. of the Int. Conf. on Fuzzy Logic & Neural Networks, Iizuka, Japan, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Delechamp, J., Bouchon-Meunier, B. (1997). Graduality by means of analogical reasoning. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds) Qualitative and Quantitative Practical Reasoning. FAPR ECSQARU 1997 1997. Lecture Notes in Computer Science, vol 1244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035624
Download citation
DOI: https://doi.org/10.1007/BFb0035624
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63095-1
Online ISBN: 978-3-540-69129-7
eBook Packages: Springer Book Archive