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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 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.
CitationRecasens, J.; Lawry, J. Normalizing possibility distributions using t-norms. "International journal of uncertainty fuzziness and knowledge-based systems", Juny 2003, vol. 11, núm. 3, p. 343-360.
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