Typicality and fuzzy sets

Abraham Kandel, Ming Ma, Menahem Friedman · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996

Given an arbitrary fuzzy set, there are various linguistic expressions which represent different approaches to the concept of typicality and may often be transformed to suitable numerals -- typical values. These quantities can then be replaced (not uniquely) by integral forms. A more natural approach for obtaining typical values is to apply an inverse procedure: Based on the linguistic expression and the fuzzy set, a biased measure is designed such that associated integrals over the fuzzy set with respect to this measure, yields the typical value and the balance point of the set.

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