Smooth Fuzzy Topological Spaces

Most of our traditional tools modeling, reasoning and computing are crisp, deterministic and precise in character. By crisp we mean dichotomous, that is, yes-or-no type rather than more-or-less type. Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known and that there are no doubts about their values or their occurrence. For factual model or modeling languages two major complications arise: (1) Real situations are very often not crisp and deterministic and they cannot be described precisely. (2) The complete description of areal system often would require by far more detailed data than a human being could ever recognize, process and understand simultaneously.