Dimension and Basis
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The Representation Theorem 2.54 states that every T -indistinguishability operator on a universe X can be generated by a family of fuzzy subsets of X. Nevertheless, there is no uniqueness in the selection of the family. Different families, even having different cardinalities, can generate the same operator. This point lends great interest to the theorem, since if we interpret the elements of the family as degrees of matching between the elements of the universe X and a set of prototypes, we can choose different features in order to establish this matching, thereby giving different semantic interpretations to the same T -indistinguishability operator.
KeywordsIndistinguishability Operator Transitive Closure Fuzzy Subset Fuzzy Relation Reciprocal Matrix
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