Abstract
This chapter extends the fuzzy models to the probabilistic domain using the probabilistic fuzzy rules with multiple outputs. The focus has been to effectively model the uncertainty in the real world situations using the extended fuzzy models. The extended fuzzy models capture both the aspects of uncertainty, vagueness and random occurence. We also look deeper into the concepts of fuzzy logic, possibility and probability that sets the background for laying out the mathematical framework for the extended fuzzy models. The net conditional probabilistic possibility is computed that forms the key ingredient in the extension of the fuzzy models. The proposed concepts are well illustrated through two case-studies of intelligent probabilistic fuzzy systems. The study paves the way for development of computationally intelligent systems that are able to represent the real world situations more realistically.
This is a preview of subscription content, log in via an institution to check access.
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
Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems 1, 3–28 (1978)
Dubois, D., Prade, H.: When upper probabilities are possibility measures. Fuzzy Sets and Systems 49, 65–74 (1992)
Dubois, D., Prade, H., Sandri, S.: On possibility/probability transformations. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic, pp. 103–112 (1993)
Roisenberg, M., Schoeninger, C., Silva, R.R.: A hybrid fuzzy-probabilistic system for risk analysis in petroleum exploration prospects. Expert Systems with Applications 36, 6282–6294, 103–112 (2009)
De Cooman, G., Aeyels, D.: Supremum-preserving upper probabilities. Inform. Sci. 118, 173–212 (1999)
Walley, P., de Cooman, G.: A behavioural model for linguistic uncertainty. Inform. Sci. 134, 1–37 (1999a)
Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 167–181. North-Holland (1982)
Dubois, D.: Possibility theory and statistical reasoning. Computational Statistics & Data Analysis 51(1), 47–69 (2006)
Meghdadi, A.H., Akbarzadeh-T, M.-R.: Probabilistic fuzzy logic and probabilistic fuzzy systems. In: The 10th IEEE International Conference on Fuzzy Systems, vol. 3, pp. 1127–1130 (2001)
Van den Berg, J., Van den Bergh, W.M., Kaymak, U.: Probabilistic and statistical fuzzy set foundations of competitive exception learning. In: The 10th IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1035–1038 (2001)
Van den Bergh, W.M., Kaymak, U., Van den Berg, J.: On the data-driven design of Takagi-Sugeno probabilistic furzy systems. In: Proceedings of the EUNlTE Conference, Portugal (2002)
Azeem, M.F., Hanmandlu, M., Ahmad, N.: Generalization of adaptive neuro-fuzzy inference systems. IEEE Transactions on Neural Networks 11(6), 1332–1346 (2000)
Kosko, B.: Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion (1993)
Klir, G.J.: Fuzzy Sets: An Overview of Fundamentals, Applications and Personal Views. Beijing Normal University Press, Beijing (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Agarwal, M., Biswas, K.K., Hanmandlu, M. (2013). Handling Fuzzy Models in the Probabilistic Domain. In: Madani, K., Dourado, A., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2011. Studies in Computational Intelligence, vol 465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35638-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-35638-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35637-7
Online ISBN: 978-3-642-35638-4
eBook Packages: EngineeringEngineering (R0)