In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.

The main purpose of this paper is to introduce the concept of $F$-type fuzzy topological spaces. Further variational principle and Caristi’s fixed point theorem have been extended in the $F$-type fuzzy topological spaces.

In this paper, the observability of fuzzy logic second order control system is studied from the aspect of fuzzy differential equations. The fuzzy observability in the weak sense is created using the concept of “likelihood” to indicate on which level and along which solution the state is most likely observable. One of the initial state range has been derived with the given input and output. The result generalizes the previous results.

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