The aggregation of membership values by means of theiterate application of an s-norm is of cardinal relevance for thedevelopment of any general theory of approximate reasoning whichrelies on a {\em sup-t} model for relation composition. Here wepresent a definition of s-norm aggregation for possibly infinitecollections, which can be demonstrated to consistently generalizeprevious approaches. It provides a common framework in which classical{\em sup-t} and finite {\em s-t} compositions can be analyzed as wellas other significant cases. General properties of the s-normaggregation concept, its specialization for the class of continuouss-norms and its relationship with fuzzy measure theory are discussed
S-Norm aggregation of infinite collections / R., Rovatti; Fantuzzi, Cesare. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 84:(1996), pp. 255-269.
S-Norm aggregation of infinite collections
FANTUZZI, Cesare
1996
Abstract
The aggregation of membership values by means of theiterate application of an s-norm is of cardinal relevance for thedevelopment of any general theory of approximate reasoning whichrelies on a {\em sup-t} model for relation composition. Here wepresent a definition of s-norm aggregation for possibly infinitecollections, which can be demonstrated to consistently generalizeprevious approaches. It provides a common framework in which classical{\em sup-t} and finite {\em s-t} compositions can be analyzed as wellas other significant cases. General properties of the s-normaggregation concept, its specialization for the class of continuouss-norms and its relationship with fuzzy measure theory are discussed
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