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Ordering, distance and closness of fuzzy sets. (English) Zbl 1002.03530

Summary: In dense rule bases where the observation usually overlaps with several antecedents in the rule base, various algorithms are used for approximate reasoning and control. If the antecedents are located sparsely, and the observation does not overlap as a rule with any of the antecedents, function approximation techniques combined with the resolution principle lead to applicable conclusions. This kind of approximation is possible only if a new concept of ordering and distance, i.e. a metric in the state space, and a partial ordering among convex and normal fuzzy sets (CNF sets) are introduced. Thus, the fuzzy distance of two CNF sets can be defined and, in terms of this distance, closeness and similarity of CNF sets as well.

MSC:

03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
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References:

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