Averaging procedures in defuzzification processes
Defuzzification is the ultimate step in approximate reasoning, consisting in the replacement of a fuzzy set with a suitable crisp value. This process is decomposed in two steps: first, replacing a fuzzy set by a crisp set, then replacing the obtained crisp set by a single value. We investigate the natural conditions the first replacement-called averaging procedure-should satisfy. Some interesting examples are given. The compatibility of averaging procedures with algebraic and order structures is studied. The algebraic structure of the set of averaging procedures is investigated. (C) 2002 Elsevier Science B.V. All rights reserved.
averaging defuzzification fuzzy set hedge