The direct and inverse problem of the matching of fuzzy sets depending on fuzziness

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Abstract
Addresses the problem of matching two fuzzy sets. Proposes a matching method that considers the extent to which both fuzzy sets have the same meaning. For a given degree of similarity between two sets, the same meaning decreases as the fuzziness increases and, in particular, for equal fuzzy sets the degree of matching is a function of the fuzziness only. A complete matching of two sets is obtained only when they are equal and crisp. Finally, the inverse problem is studied, of characterizing one of the sets used in the match when knowing the other set and the result of the matching.

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