Descriptive analysis of responses to items in questionnaires. Why not using a fuzzy rating scale?

Abstract

In evaluating aspects like quality perception, satisfaction or attitude which are intrinsically imprecise, the fuzzy rating scale has been introduced as a psychometric tool that allows evaluators to give flexible and quite accurate, albeit non numerical, ratings. The fuzzy rating scale integrates the skills associated with the visual analogue scale, because of the total freedom in assessing ratings, with the ability of fuzzy linguistic variables to capture the natural imprecision in evaluating such aspects. Thanks to a recent methodology, the descriptive analysis of the responses to a fuzzy rating scale-based questionnaire can be now carried out. This paper aims to illustrate such an analysis through a real-life example, as well as to show that statistical conclusions can often be rather different from the conclusions one could get from either Likert scale-based responses or their fuzzy linguistic encoding. This difference encourages the use of the fuzzy rating scale when statistical conclusions are important, similarly to the use of exact real-valued data instead of grouping them.

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

“…--Fuzzy rating scale This scale has been introduced by Hesketh et al (1988). See also, among others, Hesketh and Hesketh (1994), Matsui and Takeya (1994), Takemura (1999Takemura ( , 2007Takemura ( , 2012, Yamashita (2006), Hesketh et al (2011) and de la Rosa de Saa et al (2015), Lubiano et al (2016a, b) for some developments and applications. This kind of scale is considered as an a priori tool to directly assess fuzzy values and integrating the continuous nature and free assessment of the visual analogue scales with the ability to cope with imprecision of the fuzzy linguistic ones.…”

“…For a deep and interesting discussion on the different approaches, see de la Rosa de Saa et al (2015) and Lubiano et al (2016a, b).…”

Fuzzy data analysis and classification

“…Körner (2000), Montenegro et al (2001), Gil et al (2006), González-Rodríguez et al (2012), Ramos-Guajardo et al (2010), Ramos-Guajardo and Lubiano (2012) and Lubiano et al (2016b) Fuzzy estimates of location of random fuzzy numbers; robustness Lubiano and Gil (1999) and Sinova et al (2016) Statistical comparison of fuzzy scale with other imprecise-valued scales De la Rosa de Sáa et al (2016), Gil et al (2015) and Lubiano et al (2016aLubiano et al ( , 2017 Fuzzy inequality Gil et al (1998) Discriminant analysis Colubi et al (2011) Cluster analysis Hathaway et al (1996), Pedrycz et al (1998), Auephanwiriyakul and Keller (2002), D'Urso (2007) and Coppi et al (2012) Regression analysis Celminš (1987), Diamond (1988), Näther and Albrecht (1990) …”

Enhancing The Reliability Of Measurements And Evaluations Based On Service Quality Models

“…It is a discrete scale by choosing the most appropriate 'values' within a class according to the rater's judgement, opinion, valuation (Gil and González-Rodríguez, 2012) and lead to ordinal data from a set of pre-fixed categories. When Likert-type data are analysed for statistical purposes, the techniques to analyse them are quite limited (Lubiano et al, 2016). Different studies have been carried out to discuss the reliability of the analysis of these responses pointing out that increasing the number of responses results in an increase of information and reliability (Lozano et al, 2008).…”

“…Another disadvantage originates from the fact that when values are encoded by their relative position in accordance with a certain ranking, differences between codes cannot be interpreted as differences in their magnitude. It means that only statistical conclusions addressed to ordinal data can be reliable and relevant information can be lost (Lubiano et al, 2016). To some extent the ideal solution would be increasing the number of choices, but it cannot be achieved by using a natural language (Sowa, 2013).…”