Membership functions II: Trends in fuzziness and implications

Results from a set o f questionnaires designed to compare methods of obtaining membership functions were analyzed to identify general trends in fuzziness. It was found that fuzziness in comprehension is ahvays reflected in the answer; concepts such as difficulty, imprecision, and shape of membership functions are clearly interrelated; and the transition between crisp extremes through fuzziness has characteristic manifestations. Emphasis is placed on the practical implications of these ideas, applications include developing standard and type H fuzzy sets, improving the completeness and consistency of available data, and supporting the development o f knowledge-based systems using fuzzy sets.