Fuzzy Rating vs. Fuzzy Conversion Scales: An Empirical Comparison through the MSE

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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