Normalizing possibility distributions using t-norms

Authors:
J. Recasens;J. Lawry
Affiliations:
Secció Matemàtiques i Informàtica - ETSAV, Univ. Politècnica de Catalunya, Pere Serra 1-15, Sant Cugat del Vallès, Barcelona, Spain;Department of Engineering Mathematics, University of Bristol, Queens Building, University Walk, Bristol, BS8 1TR, UK
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2003

Citing 6
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Abstract

A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms.For a given fuzzy subset μ, the corresponding normalized fuzzy subset μ can be viewed as the distribution of μ conditioned on the (degree of) existence of its elements with maximal membership. From this view point we investigate the less specific normal fuzzy subset of X among the most similar fuzzy subsets to μ and the normal fuzzy subset generating the same fuzzy T-preorder as μ.