8-9 October 2020 • Burgas, Bulgaria

Submission: 15 May 2020 • Notification: 31 May 2020 • Final Version: 15 June 2020

Issue:A new fractal dimension definition based on intuitionistic fuzzy logic

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Title of paper: A new fractal dimension definition based on intuitionistic fuzzy logic
Author(s):
Oscar Castillo
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
ocastilloAt sign.pngtectijuana.mx
Patricia Melin
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
pmelinAt sign.pngtectijuana.mx
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 2, pages 53–59
DOI: https://doi.org/10.7546/nifs.2019.25.2.53-59
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Abstract: In this paper we describe a method for the estimation of the fractal dimension of a geometrical object using Intuitionistic fuzzy logic techniques. The mathematical concept of

fractal dimension serves to measure the geometrical complexity of an object. The algorithms for estimating the fractal dimension compute a numerical value using as input the time series data for a particular problem. The result is a crisp value (number) that defines the complexity of the geometrical object or the time series. The estimation of the fractal dimension exhibits some inherent uncertainty due to the fact that we only use a sample of points of the object, as well as due to the incomplete accuracy of the numerical algorithms for fractal dimension. For this reason, a new definition of the fractal dimension is being proposed, incorporating the concept of intuitionistic fuzzy sets, which we consider to better capture the uncertainty of the concept.

Keywords: Fractal dimension, Geometrical complexity, Fuzzy sets, Intuitionistic fuzzy sets.
AMS Classification: 03E72, 28A80, 91Gxx.
References:
  1. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham, Switzerland.
  2. Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press.
  3. Castillo, O., & Melin, P. (1994). Developing a new method for the identification of microorganisms for the food industry using the fractal dimension, Journal of Fractals, 2 (3), 457–460.
  4. Castillo, O., & Melin, P. (1998). A new fuzzy-fractal-genetic method for automated mathematical modelling and simulation of robotic dynamic systems, Proc. of FUZZ’98, IEEE Press, Alaska, USA, Vol. 2, 1182–1187.
  5. Castillo, O., & Melin, P. (1999). A new Fuzzy Inference System for Reasoning with Multiple Differential Equations for Modelling Complex Dynamical Systems, Proc. of CIMCA'99, IOS Press, Vienna, 224–229.
  6. Castillo, O., & Melin, P. (2000). A new method for fuzzy estimation of the fractal dimension and its applications to time series analysis and pattern recognition, Proc. of NAFIPS’2000, Atlanta, GA, USA. 451–455.
  7. Castillo, O., & Melin P. (2004). A new approach for plant monitoring using type-2 fuzzy logic and fractal theory, Int. J. General Systems, 33(2–3), 305–319.
  8. González, C. I., Melin, P., Castro, J. R., Castillo, O., & Mendoza, O. (2016). Optimization of interval type-2 fuzzy systems for image edge detection, Appl. Soft Computing, 47, 631–643.
  9. González, C. I., Melin, P., Castro, J. R., Mendoza, O., & Castillo, O. (2016). An improved sobel edge detection method based on generalized type-2 fuzzy logic, Soft Computing, 20 (2), 773–784.
  10. Mandelbrot, B. (1987). The Fractal Geometry of Nature, W.H. Freeman and Company.
  11. Melin, P., & Castillo, O. (1998). An adaptive model-based neuro-fuzzy-fractal controller for biochemical reactors in the food industry, Proceedings of IJCNN’98, IEEE Computer Society Press, Alaska, USA, Vol. 1, 106–111.
  12. Melin, P., & Castillo O. (2003). Adaptive intelligent control of aircraft systems with a hybrid approach combining neural networks, fuzzy logic and fractal theory, Appl. Soft Comput., 3(4), 353–362.
  13. Melin, P., Amezcua, J., Valdez, F., & Castillo, O. (2014). A new neural network model based on the LVQ algorithm for multi-class classification of arrhythmias, Inf. Sci. 279, 483–497.
  14. Melin,P., & Castillo O. (2007). An intelligent hybrid approach for industrial quality control combining neural networks, fuzzy logic and fractal theory, Inf. Sci., 177 (7), 1543–1557.
  15. Olivas, F., Valdez, F., Castillo, O., González, C. I., Martinez, G. E., & Melin, P. (2017): Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems. Appl. Soft Comput., 53, 74–87.
  16. Ontiveros, E., Melin, P., Castillo O. (2018). High order α-planes integration: A new approach to computational cost reduction of general type-2 fuzzy systems. Eng. Appl. of AI, 74, 186–197.
  17. Sánchez, D., & Melin, P. (2014). Optimization of modular granular neural networks using hierarchical genetic algorithms for human recognition using the ear biometric measure, Eng. Appl. of AI, 27, 41–56.
  18. Yager, R., & Filev, D. (1994). Generation of fuzzy rules by mountain clustering, Intelligent and Fuzzy Systems, 2 (3), 209–219.
  19. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 8, 43–80.
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