Fuzzy Methods for the Analysis of Psychometric Data

Psychometrics should ideally measure multidimensional concepts like skills, knowledge, abilities, attitudes, personality traits and educational achievement, which cannot be captured by a single variable. In this paper, we suggest a method based on fuzzy set theory for the construction of a fuzzy synthetic index of the latent psychometric phenomenon, using the set of variables obtained with instruments such as questionnaires or tests. Criteria for assigning values to the membership function as well as criteria for defining the weights of the variables are discussed. For discrete variables, we use a fuzzy quantification method based on the sampling cumulative function. An application regarding the measurement of reading disability in students attending elementary and middle school in Italy is presented.