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In many applications of fuzzy set theory, the membership of an object is not defined directly. One of its attributes (like height, age, weight, . . . ) is first mapped on a real number (often by means of a physical instrument) and a parametric function then maps this real number on a membership degree in some fuzzy set (like 'tall', 'old', 'heavy', . . . ). A very common parametric function is the trapezoidal one. This paper presents some conditions guaranteeing the existence of such adoi:10.1109/tfuzz.2006.880000 fatcat:slgp5lvkgbgphcpa3hqkxlryka