Averaging procedures in defuzzification processes

Authors:
Eugene Roventa;Tiberiu Spircu
Affiliations:
Department of Computer Science, Glendon College, York University, Toronto, Ont., Canada M4N 3M6;Department of Medical Informatics, "Carol Davila" University of Medicine and Pharmacy, Bucharest, Romania
Venue:
Fuzzy Sets and Systems - Theme: Basic concepts
Year:
2003

Citing 5
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Abstract

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.