Abstract
This paper proposes an automated approach for constructing the intuitionistic fuzzy histograms (IF-histograms) of a gray-scale digital image, based on the notion of intuitionistic fuzzy numbers (IF-numbers). A method for constructing parametric IF-numbers from their fuzzy counterparts using intuitionistic fuzzy generators (IFGs) is also presented, using an entropic optimization criterion. Finally, experimental results demonstrate the ability of the proposed approach to obtain efficiently the IF-histograms of gray-scale images.
Keywords
- Membership Function
- Fuzzy Number
- Gray Level
- Fuzzy Statistic
- Intuitionistic Fuzzy Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your 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
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Atanassov, K.T.: More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33, 37–45 (1989)
Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. In: Studies in Fuzziness and Soft Computing, Physica–Verlag, Heidelberg (1999)
Bustince, H., Kacprzyk, J., Mohedano, V.: Intuitionistic Fuzzy Generators–Application to Intuitionistic Fuzzy Complementation. Fuzzy Sets Syst. 114(3), 485–504 (2000)
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice-Hall, Englewood Cliffs (1988)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Application. Prentice-Hall, Englewood Cliffs (1995)
Jawahar, C.V., Ray, A.K.: Fuzzy statistics of digital images. IEEE Signal Process. Lett. 3, 225–227 (1996)
Jawahar, C.V., Ray, A.K.: Incorporation of gray-level imprecision in representation and processing of digital images. Pattern Recognit. Lett. 17, 541–546 (1996)
Vlachos, I.K., Sergiadis, G.D.: Intuitionistic Fuzzy Image Processing. In: Soft Computing in Image Processing: Recent Advances. Studies in Fuzziness and Soft Computing, vol. 210, pp. 385–416. Springer, Heidelberg (2006)
Zadeh, L.A.: The conept of a linguistic variable and its application to approximate reasoning–I. Inform. Sci. 8, 199–249 (1975)
Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78, 305–316 (1996)
Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118, 467–477 (2001)
Szmidt, E., Kacprzyk, J.: Entropy and similarity of intuitionistic fuzzy sets. In: Proc. Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, France, pp. 2375–2382 (2006)
Pal, S.K., King, R.A.: Image enhancement using fuzzy set. Electron. Lett. 16, 376–378 (1980)
Pal, S.K., King, R.A.: Image enhancement using smoothing with fuzzy sets. IEEE Trans. Syst. Man Cybern. 11, 495–501 (1981)
Pal, S.K., King, R.A.: A note on the quantitative measure of image enhancement through fuzziness. IEEE Trans. Pattern Anal. Mach. Intell. 4, 204–208 (1982)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Vlachos, I.K., Sergiadis, G.D. (2007). Intuitionistic Fuzzy Histograms of an Image. 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_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-72950-1_9
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)