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Approximate distances, pointless geometry and incomplete information. (English) Zbl 1103.68837
Summary: An abstract notion of approximate metric space is proposed by means of an interval-valued distance between regions. Regions are interpreted as pieces of information in a space. The resulting theory supports some promising applications to some topics of fuzzy set theory, rough set theory and clustering.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
54A40 Fuzzy topology
68T10 Pattern recognition, speech recognition
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