Fuzzy differential inclusion
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Fuzzy differential inclusion is the extension of differential inclusion to fuzzy sets introduced by Lotfi A. Zadeh.[1][2]
with
![{\displaystyle x'(t)\in [f(t,x(t))]^{\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a01062827cbe73779ab92ee5ef1dff4cfbc7340)
![{\displaystyle x(0)\in [x_{0}]^{\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae55b8b969824cb3b921a247a0224f1cd91c1da6)
Suppose is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upper semi-continuous, convex, compactly supported fuzzy subsets of .
![{\displaystyle x''(t)\in [kx]^{\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6e2872d4ef491f0c5f1a123b179c0d383f53cbb5)
![{\displaystyle k\in [K]^{\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7aac88efa972bfb4a3ecbfa72e60d62b2284fd1)
