Piecewise parametric polynomial fuzzy sets
International Journal of Approximate Reasoning
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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, etc.) is first mapped to a real number (often by means of a physical instrument) and a parametric function then maps this real number to a membership degree in some fuzzy set (like "tall," "old," "heavy," etc.). A very common parametric function is the trapezoidal one. This paper presents some conditions guaranteeing the existence of such a trapezoidal membership function representing the knowledge of an expert. Further experimental research is needed for testing whether these conditions are satisfied by human agents