Abstract
Estimation of membership function is one of the most important problems in the application of fuzzy sets. This paper presents one of approaches to this problem. A method for estimation of membership function is proposed, based on fuzzy measures: fuzzy entropy and fuzzy index. Examples of generating membership function in the field of image processing are shown.The method presented in this paper can be used in other fields of computer sciences, where statistical data are available.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Al-sharhan, S., Karray, F., Basir, O.: Fuzzy Entropy: a Brief Survey. In: IEEE Proceedings of the 10th International Conference on Fuzzy Systems, Melbourne, Vic., Australia, vol. 3, pp. 1135–1138 (2001)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Bharathi, B., Sarma, V.V.S.: Estimation of Fuzzy Membership from Histograms. Information Sciences 35, 43–59 (1985)
Bloch, I., Aurdal, L., Bijno, D., Müller, J.: Estimation of Class Membership Functions for Grey Level Based Image Fusion. In: Proc. of the Int. Conf. of Image Processing, pp. 268–271 (1997)
Cheng, H.D., Cheng, J.R.: Automatically Determine the Membership Function Based on the Maximum Entropy Principle. Information Sciences 96, 163–182 (1997)
Cheng, H.D., Cheng, Y.H.: Thresholding Based on Fuzzy Partition of 2D Histogram. In: IEEE International Conference on Pattern Recogition, Australia, vol. 2, pp. 1616–1618 (1998)
Civanlar, M.R., Trussel, H.J.: Construction Membership Functions using Statistical Data. Fuzzy Sets and Systems 18, 1–13 (1986)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press Inc., London (1980)
Kacprzyk, J.: Fuzzy Sets in Systems Analysis (in Polish). Państwowe Wydawnictwa Naukowe (1986)
Kaufmann, A.: Introduction to the theory of fuzzy subsets. Academic Press, London (1975)
Kennedy, J., Eberhart, J.: Particle Swarm Optimization. In: IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1949 (1995)
Kennedy, J., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs (1988)
Medasani, S., Kim, J., Krishnapuram, R.: An Overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning 19, 391–417 (1998)
Pal, N.R., Bezdek, J.C.: Measuring Fuzzy Uncertainty. IEEE Transactions of Fuzzy Systems 2(2), 107–118 (1994)
Pedrycz, W., Czołgała, E.: Elements and Methods of fuzzy sets theory (in Polish). Państwowe Wydawnictwa Naukowe (1985)
Zadeh, L.A.: A fuzzy-algorithmic approach to the definition of complex or imprecise concepts. International Journal Man-Machines Studies 8, 249–291 (1976)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Nieradka, G., Butkiewicz, B. (2007). A Method for Automatic Membership Function Estimation Based on Fuzzy Measures. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-72950-1_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
eBook Packages: Computer ScienceComputer Science (R0)