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Fuzzy Mandelbrot sets
- Source :
- Fuzzy Sets and Systems. 435:78-88
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- In this paper, we present a new approach to the Mandelbrot set via fuzzy set theory. We introduce and characterize the fuzzy Mandelbrot set by describing its membership function that determines the degrees of belonging of the points to this set under the iteration even if the orbit of the point is not limited. Then we investigate the basic topological properties of the fuzzy Mandelbrot set and its strong α-cut such as closedness, openness, boundness, connectedness and simply connectedness.
- Subjects :
- 0209 industrial biotechnology
Logic
Social connectedness
Fuzzy set
02 engineering and technology
Mandelbrot set
Fuzzy logic
Set (abstract data type)
Algebra
Computer Science::Graphics
020901 industrial engineering & automation
Artificial Intelligence
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Point (geometry)
Orbit (control theory)
Membership function
Mathematics
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 435
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi...........8335663c71795e80ad2497c3b26dcb7b