On the Precision of Adjectives Which Denote Fuzzy Sets
Manfred Kochen, Albert N. Badre · Journal of Cybernetics · 1974
The characteristic function of a fuzzy set denoted by a phrase “much larger than 5,” or “heavy,” is investigated experimentally. The S-shaped curve for the characteristic function is derived from some plausible assumptions involving a differential equation, and its parameters are estimated statistically. It was found that the precision of the fuzzy set–measured by the maximum slope of the characteristic function–denoted by “much greater than 5” is less than that denoted by “very much greater than 5.” When the subject is allowed to be fuzzy in his response about grade of membership, there is greater consistency in the response. Anchoring was also found to make an adjective denoting fuzzy set more precise.