(Quantum) spacetime as a statistical geometry of fuzzy lumps and the connection with random metric spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may also view it as a dynamical randomization of the causal-set framework developed by, for example, Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.