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The expansible and recursively spreadable measures of specificity are introduced to improve the performance of computing measures of specificity of fuzzy sets when the universe of candidates is increased. The contractible measures of specificity and recursively reductible measures of specificity again improves the performance to compute the measure of specificity of a fuzzy set when the universe of candidates is decreased from the previous one. These kind of measures of specificity allows to compute very efficiently measures of specificity of fuzzy sets when a universe of discourse is variable.