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Fuzzy differential inclusions. (English) Zbl 0718.93039

Summary: This paper is devoted to differential inclusions the right-hand sides of which are fuzzy subsets, whose membership functions are cost functions taking their values in $\left[0,\infty \right]$ instead of [0,1]. By doing so, the concept of uncertainty involved in differential inclusions becomes more precise, by allowing the velocities not only to depend in a multivalued way upon the state of the system, but also in a fuzzy way.

The viability theorems are adapted to fuzzy differential inclusions and to sets of state constraints which are either usual or fuzzy. The existence of a largest closed fuzzy viability domain contained in a given closed fuzzy subset is also provided.

##### MSC:
 93C42 Fuzzy control systems 34A60 Differential inclusions
##### Keywords:
differential inclusions; fuzzy viability domain