Abstract
This paper proposes a new method for directly discovering the uncertainty from a sample of discrete data, which is then used in the formation of an Interval Type-2 Fuzzy Inference System. A Coefficient of Variation is used to measure the uncertainty on a finite sample of discrete data. Based on the maximum possible coverage area of the Footprint of Uncertainty of Gaussian membership functions, with uncertainty on the standard deviation, which then are modified according to the found index values, obtaining all antecedents in the process. Afterwards, the Cuckoo Search algorithm is used to optimize the Interval Sugeno consequents of the Fuzzy Inference System. Some sample datasets are used to measure the output interval coverage.
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
References
Yu, X., Mehrotra, S.: Capturing uncertainty in spatial queries over imprecise data. In: Database and Expert Systems Applications, pp. 192–201. Springer, Berlin (2003)
Klir, G.J.: Uncertainty and Information: Foundations of Generalized Information Theory. Wiley, New York (2005)
Weise, K., Woger, W.: A Bayesian theory of measurement uncertainty. Meas. Sci. Technol. 3 (1992)
Jurado, K., Ludvigson, S.C., Ng, S.: Measuring uncertainty. Am. Econ. Rev. (AEA) 105(3), 1177–1216 (2013)
Chen, G., Ying, M., Liu, Y.: Dealing with uncertainty and fuzziness in intelligent systems. Int. J. Intell. Syst. 24, 223–225 (2009)
Klir, G.J., Wierman, M.J.: Uncertainty-Based Information. Springer, Heidelberg (1999)
Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 808–821 (2006)
Castillo, O., Melin, P.: Recent Advances in Interval Type-2 Fuzzy Systems. Springer, Berlin (2012)
Mo, H., Wang, F.-Y., Zhou, M., Li, R., Xiao, Z.: Footprint of uncertainty for type-2 fuzzy sets. Inf. Sci. (Ny) 272, 96–110 (2014)
Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10, 191–203 (1984)
Yang, X.-S.: Cuckoo search via lévy flights. In: World Congress on Nature and Biologically Inspired Computing (NaBIC) 2009, pp. 210–214. IEEE (2009)
Ying, H.: Interval type-2 Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators. In: NAFIPS 2009—2009 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 1–5. IEEE (2009)
Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)
Melin, P., Castillo, O.: Fuzzy modeling fundamentals. Wiley Encycl. Comput. Sci. Eng. (2007)
Mendel, J.: General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans. Fuzzy Syst. 22, 1 (2013)
The MathWorks, Inc.: Natick. MATLAB Release, Massachusetts, U.S. 2013b, (2013)
Acknowledgments
We thank the MyDCI program of the Division of Graduate Studies and Research, UABC, and Tijuana Institute of Technology the financial support provided by our sponsor CONACYT contract grant number: 314,258.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sanchez, M.A., Castillo, O., Castro, J.R. (2015). Method for Measurement of Uncertainty Applied to the Formation of Interval Type-2 Fuzzy Sets. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Studies in Computational Intelligence, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-17747-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-17747-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17746-5
Online ISBN: 978-3-319-17747-2
eBook Packages: EngineeringEngineering (R0)