Ambiguity and Social Judgment: Fuzzy Set Model and Data Analysis

Fuzzy Rating Scale-Based Questionnaires and Their Statistical Analysis

“…The key guidelines in the fuzzy rating method by Hesketh et al [27] (see also Hesketh et al [30]- [32], Hesketh and Hesketh [29], Takemura [33]- [35], and González-Rodríguez et al [43]) are the following: S.1) Respondents select a representative rating on the given bounded interval (this interval will be referred to hereinafter as the referential). This representative rating will be either a single point or a subinterval of the referential.…”

“…We are yet to see easily adapted packages that allow for researchers to use the fuzzy concept and then to apply appropriate statistical and other analyses to these in order to both test hypotheses and ensure that meaning is captured. "; in fact, only a few statistical descriptive studies have been carried out for fuzzy rating scale data, like the ones by Hesketh et al [27], [31], [32] and those by Takemura [33]- [35]. At this point, we should remark that, because a natural language is not identifiable with a continuous scale, fuzzy numbers/intervals could not be unequivocally labeled with words but their meaning is quite clear.…”

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

“…• the fuzzy linguistic scales, which are frequently considered for different goals as an a posteriori tool to encode data from a discrete (often a Likert) scale by means of fuzzy numbers (see, for instance, Zadeh [67], Tong and Bonissone [59], Pedrycz [42], Herrera et al [27,26], Lalla et al [32], and also Li [33], Akdag et al [1], Estrella et al [18], Massanet et al [39], Tejeda-Lorente et al [57,58], Villacorta et al [62], Wang et al [63], García-Galán et al [19], Liu et al [34] and Tavana [56], about some very recent developments and applications in connection with perceived quality, satisfaction, etc. ); • the fuzzy rating scale, which 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; this scale has been introduced by Hesketh et al [30] (see also, among others, Hesketh and Hesketh [29], Matsui and Takeya [40], Takemura [53][54][55], Yamashita [65], Hesketh et al [28] and De la Rosa de Sáa et al [14] for some developments and applications). The Likert, visual analogue and fuzzy linguistic scales have been commonly involved in research with questionnaires.…”

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.…”