Fuzzy Rating Scale-Based Questionnaires and Their Statistical Analysis

Abstract

The fuzzy rating method has been introduced in psychometric studies as a tool, which allows the capture of and accurate reflection of the diversity, subjectivity, and imprecision inherent in human responses to many questionnaires. The lack of statistical techniques for in-depth analysis of these responses has been, for years, the appearance of an important barrier. At present, this barrier is being overcome thanks to new statistical techniques. In this way, the information from fuzzy rating method-based responses can be suitably explored and exploited. This paper aims to formally endorse some of the main statistical benefits of using free-response format fuzzy rating scale-based questionnaires instead of using the closed-response format involving fuzzy linguistic representations.Index Terms-Fuzzy linguistic representation, fuzzy numbers, fuzzy rating method, questionnaires, random fuzzy sets, statistical analysis of fuzzy data.

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.…”

“…In particular, in a fuzzy rating scale along a continuous line between two end-points: (1) a respondent selects or draws a 'representative position/interval' of the respondent rating (i.e., the set of points which she/he considers to be fully compatible with such a rating); (2) and the respondent also indicates 'latitudes of acceptance' on either side by determining the highest and lowest possible positions for the respondent rating (i.e., the set of points she/he considers to be compatible to some extent with such a rating). In this way, the fuzzy rating scale takes advantage of the synergies existing between the visual analogue and the fuzzy linguistic scales (de la Rosa de Saa et al 2015). See de la Rosa de Saa et al (2015) for a detailed discussion on the advantages of this kind of scale and for theoretical, comparative, and applicative aspects.…”

“…In this way, the fuzzy rating scale takes advantage of the synergies existing between the visual analogue and the fuzzy linguistic scales (de la Rosa de Saa et al 2015). See de la Rosa de Saa et al (2015) for a detailed discussion on the advantages of this kind of scale and for theoretical, comparative, and applicative aspects.…”

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

“…Nevertheless, its usefulness presents some drawbacks as it has been pointed out, for instance, in [1,4,11,14,23]. In the literature some authors have suggested to establish a correspondence between each Likert response category and a fuzzy value chosen from a class of flexible fuzzy sets previously stated by experts (see, for instance, [16,17]).…”

“…To overcome these problems, a way for describing each individual opinion/perception/valuation by means of a fuzzy set capturing the subjectiveness or imprecision involved in the answer and without taking into account a pre-fixed enumeration of answers has been proposed in the literature [11,13,12,23].…”