Topological interpretation of fuzzy sets and intervals
Fuzzy set theory and interval mathematics were independently invented and developed in the mid 1960s as tools for a quantitative analysis of approximations to mathematically exact values, which may not be observable, representable or computable. We show that both approaches are covered by a general topological theory developed almost two decades earlier. We start with the concepts of naive fuzzy set and interval theory and discuss the underlying common features. Then we represent the theory of topological filter bases, their homomorphisms and the rounding of filter bases. Fuzzy set theory and interval mathematics can be described in terms of this theory. In addition, some of the concepts of classical fuzzy and interval theory are extended. (C) 2002 Elsevier Science B.V. All rights reserved.
topology fuzzy sets theory of approximations interval analysis