Abstract
The scale of fuzzy numbers have been used in the literature to measurement of many ratings/perceptions/valuations, expectations, and so on. Among the most common uses one can point out: the so-called ‘fuzzy rating’, which is based on a free fuzzy numbered response scheme, and the ‘fuzzy conversion’, which corresponds to the conversion of linguistic (often Likert-type) labels into fuzzy numbers. This paper aims to present an empirical comparison of the two scales. This comparison has been carried out by considering the following steps: fuzzy responses have been first freely simulated; these responses have been ‘Likertized’ in accordance with a five-point measurement and a plausible criterion; each of the five Likert class has been transformed into a fuzzy number (two fuzzification procedures will be examined); the mean squared error (MSE) has been employed to perform the comparison. On the basis of the simulations we will conclude that for most of the simulated samples the Aumann-type mean is more representative for the fuzzy rating than for the fuzzy conversion scale.
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de la Rosa de Sáa, S., Gil, M.Á., García, M.T.L., Lubiano, M.A. (2013). Fuzzy Rating vs. Fuzzy Conversion Scales: An Empirical Comparison through the MSE. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_15
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DOI: https://doi.org/10.1007/978-3-642-33042-1_15
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