Generalisations of the concept of a non-stationary fuzzy set - a starting point to a formal discussion

In this paper we propose the concept of an instantiative fuzzy set which, in our opinion, constitutes a meaningful addition to the notion of a non-stationary fuzzy set. We begin with a formal definition of an instantiative fuzzy set, and follow specifying basic classes of instantiative fuzzy set operators: the union, the intersection and the complement. Furthermore, we provide formal definitions of selected notions relevant to instantiative fuzzy sets. At the end, we present a subclasses of instantiative fuzzy sets that might be useful for dealing with randomness and vagueness simultaneously. The work presented in this paper is at a very preliminary stage; it is meant as a starting point to a formal discussion on the capture of different facets of uncertainty.