In this chapter we study the existence of a sum of fuzzy observables in a fuzzy
quantum space which generalizes the Kolmogorov probability space using the ideas of
fuzzy set theory. We also study some properties of the sum of fuzzy observables. To study
the above mentioned, we also include the basic notions from the probability theory on
fuzzy quantum space in this chapter, i.e. the notion of fuzzy quantum space, a fuzzy
observable, an indicator of a fuzzy set, a null fuzzy observable, a Boolean algebra on
fuzzy quantum space, fuzzy state etc.
