Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
A generalization of the representation theorem
Fuzzy Sets and Systems
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Interval methods in knowledge representation
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Representability of binary relations through fuzzy numbers
Fuzzy Sets and Systems
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
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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.