Fuzzy numbers and equality relations

A general approach to the concept of a fuzzy number associated to a generalized equality on the real line is given. As a result, the use of triangular and trapezoidal fuzzy numbers, among other types, is justified and a representation theorem that allows the construction of indistinguishability operators on the real line based on t-norms is presented. The families of fuzzy numbers invariant under translations are characterized.<
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