Abstract
We discuss the means to efficiently propagate imprecise (but crisp) inputs in fuzzy control-like rule based systems in which fuzzy rules are chained in several levels. We consider a genuine implication-based model, in contrast to most of classical fuzzy control systems, using Rescher-Gaines implication to model the gradual relation between premises and conclusion of rules. The result of each inference is a crisp interval and we propose an efficient and sound method that provides with the tightest output intervals at one reasoning level, propagate them as input in the next level, and only pick a precise value at the very last level.
This is a revised and expanded version of the paper ‘“Dealing with imprecise inputs in Fuzzy rule-based systems” appearing in the Proc. of IPMU’2000, Madrid (Spain), pp. 1055-1062.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bouchon-Meunier B., Dubois D., Godo L., Prade H. Fuzzy Sets and Possibility Theory in Approximate and Plausible Reasoning. In Bezdek et al. (eds.).Fuzzy Sets in Approximate Reasoning and Information Systems, 15–190, Kluwer,1999.
Driankov, D., Hellendoorn, H., Reinfrank, M. An Introduction to Fuzzy Control. Springer-Verlag, 1996.
Dubois D., Esteva F., Garcia P., Godo L., Prade H. A Logical approach to interpolation based on similarity relations. Int. J. of Approximate Reasoning 17 (1), 1–36, 1997.
Dubois D., Prade H. What are fuzzy rules and how to use them. Fuzzy Sets and Systems 84, 169–185, 1996.
Dubois D., Prade H., Ughetto L. Coherence of Fuzzy Knowledge Bases. In Proc. Fuzz-IEEE’96, New Orleans (USA), 1858–1864, 1996.
Gottwald S., Petri U. An algorithmic approach towards consistency checking for systems of fuzzy control rules. In Proc. of EUFIT’95, Aachen (Germany) 28–31, 1995.
Galichet S., Foulloy L. Fuzzy Control with non-Precise Inputs. In Bouchon-Meunier et al. (eds.). Fuzzy Logic and Soft Computing, 146–153, World Scientific Press, 1995.
Kóczy L.T., Hirota K. Approximate inference in hierarchical structured rule bases. In Proc. of IFSA’93, Seoul (Korea), 1262–1265, 1993.
Pedrycz W., Gomide F. An introduction to Fuzzy sets: Analysis and Design. MIT Press,1998.
Yager R.R., Larsen H.L. On discovering potential inconsistencies in validating uncertain knowledge bases by reflecting on the input. IEEE Trans. on Systems, Man and Cibernetics 21, 790–801, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Godo, L., Sandri, S. (2002). Dealing with Imprecise Inputs in a Fuzzy Rule-Based System using an Implication-based Rule Model. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol 89. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1797-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1797-3_4
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-662-00329-9
Online ISBN: 978-3-7908-1797-3
eBook Packages: Springer Book Archive