Fuzzy differential inclusion
Fuzzy differential inclusion is tha culmination of Fuzzy concept and Differential inclusion introduced by Lotfi A. Zadeh which became popular.[1][2] [math]\displaystyle{ x' (t) \epsilon [ f(t , x(t)]^\alpha }[/math] ,[math]\displaystyle{ x(0) \epsilon [x_0]^\alpha }[/math]
f(t,x(t)] is a fuzzy valued continuous function on euclidian space which is collection of all normal, upper semi-continuous, Convex set
,Compact space, supported fuzzy subsets of [math]\displaystyle{ R^n }[/math] .
Second order differential
The second order differential is
[math]\displaystyle{ x''(t) \epsilon [kx]^ \alpha }[/math] where [math]\displaystyle{ k \epsilon [K]^ \alpha }[/math]
K is trapezoidal fuzzy number (-1,-1/2,0,1/2)
[math]\displaystyle{ x_0 }[/math] is a trianglular fuzzy number (-1,0,1) .
Applications
Fuzzy differential inclusion (FDI) has applications in
- Cybernetics[3]
- Artificial intelligence, Neural network,[4][5]
- Medical imaging
- Robotics
- Atmospheric dispersion modeling
- Weather forecasting
- Cyclone
- Population biology[6]
- Stochastic process, Probability theory[citation needed]
References
- ↑ Lakshmikantham, V.; Mohapatra, Ram N. (11 September 2019). Theory of Fuzzy Differential Equations and Inclusions. ISBN 978-0-367-39532-2. https://www.routledge.com/Theory-of-Fuzzy-Differential-Equations-and-Inclusions/Lakshmikantham-Mohapatra/p/book/9780367395322.
- ↑ Min, Chao; Liu, Zhi-bin; Zhang, Lie-hui; Huang, Nan-jing (2015). "On a System of Fuzzy Differential Inclusions". Filomat 29 (6): 1231–1244. doi:10.2298/FIL1506231M. ISSN 0354-5180. https://www.jstor.org/stable/24898205.
- ↑ "Fuzzy differential inclusion in atmospheric and medical cybernetics". https://www.isibang.ac.in/~kaushik/kaushik_files/tumor.pdf.
- ↑ Tafazoli, Sina; Menhaj, Mohammad Bagher (March 2009). "Fuzzy differential inclusion in neural modeling". 2009 IEEE Symposium on Computational Intelligence in Control and Automation. pp. 70–77. doi:10.1109/CICA.2009.4982785. ISBN 978-1-4244-2752-9. https://ieeexplore.ieee.org/document/4982785.
- ↑ Min, Chao; Zhong, Yihua; Yang, Yan; Liu, Zhibin (May 2012). "On the implicit fuzzy differential inclusions". 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery. pp. 117–119. doi:10.1109/FSKD.2012.6234283. ISBN 978-1-4673-0024-7. https://ieeexplore.ieee.org/document/6234283.
- ↑ Antonelli, Peter L.; Křivan, Vlastimil (1992). "Fuzzy differential inclusions as substitutes for stochastic differential equations in population biology". Open Systems & Information Dynamics 1 (2): 217–232. doi:10.1007/BF02228945.
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