Chaotic fuzzy iterated function systems

Article type: Research Article

Authors: Selvy, R.^{a; *} | Vinod Kumar, P.B.^b

Affiliations: [a] Rajagiri School of Engineering and Technology, A P J Abdul Kalam Technical University, Kerala, India | [b] Centre for Topology and Applications, Department of Mathematics. Rajagiri School of Engineering and Technology, A P J Abdul Kalam Technical University, Kerala, India

Correspondence: [*] Corresponding author. Selvy R, Rajagiri School of Engineering and Technology, A P J Abdul Kalam Technical University, Kerala, India. E-mail: [email protected].

Abstract: It is observed that IFSs are defined based on the concept that the iterates take only an integer number of times. This work studies the dynamics of functions, where a function can iterate r times for every r ∈ R. Utilizing concepts from fuzzy sets, r-times iterates of a function are defined for r ∈ R. The study demonstrates that the chaotic property can be generalized to this new iterative concept. The chaotic behavior of a function is then extended using this iterative concept.

Keywords: Iterated function systems, fuzzy functions, chaotic functions

DOI: 10.3233/JIFS-236563

Journal: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 4, pp. 9261-9270, 2024