Fuzzy differential inclusions.

*(English)*Zbl 0718.93039Summary: 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 $[0,\infty ]$ 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.