Quantifying Fuzziness due to the scale of Measurement in Response Systems

Abstract

When a product or performance is rated or a behavioural response is sought, the alternatives typically do not have well-defined and universally understood demarcations. The resultant fuzziness in response depends, among other factors, on the number of options available to the respondent and this vagueness is quantified in the current work. The measure, expressed as a percentage of the total variability, is arrived at by separating the fuzziness from the randomness present in the data, and it is used to provide a guideline regarding the appropriate number of levels in measurement. While the proposed measure can be computed under stringent assumptions, two approaches of estimating it under weaker assumptions are also discussed in this work. Numerical data analysis on a real as well as a simulated data set suggests that a response scale with five to seven options may be appropriate.