Abstract
Overlap functions are a particular instance of aggregation functions, consisting by non-decreasing continuous commutative bivariate functions defined over the unit square, satisfying appropriate boundary conditions. Overlap functions play an important role in classification problems, image processing and in some problems of decision making based on fuzzy preference relations. The concepts of indifference and incomparability defined in terms of overlap functions may allow the application in several different contexts. The aim of this papers is to introduce the notion of additive generators of overlap functions, allowing the definition of overlap functions (as two-place functions) by means of one-place functions, which is important since it can reduce the computational complexity in applications. Also, some properties of an overlap function presenting a generator can be related to properties of its generator, pointing to a more systematic methodology for their selection for the various applications.KeywordsAdditive GeneratorAggregation FunctionNeutral ElementAssociative FunctionFuzzy Preference RelationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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