✦ LIBER ✦

Topological interpretation of fuzzy sets and intervals

✍ Scribed by Rudolf F. Albrecht

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 324 KB
Volume: 135
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(02)00247-6

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✦ Synopsis

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 ÿlter bases, their homomorphisms and the rounding of ÿlter 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.

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