Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications

Abstract

The fuzzy rating scale was introduced as a tool to measure intrinsically ill-defined/ imprecisely-valued attributes in a free way. Thus, users do not have to choose a value from a class of prefixed ones (like it happens when a fuzzy semantic representation of a linguistic term set is considered), but just to draw the fuzzy number that better represents their valuation or measurement. The freedom inherent to the fuzzy rating scale process allows users to collect data with a high level of richness, accuracy, expressiveness, diversity and subjectivity, what is especially valuable for statistical purposes. This paper presents an inferential approach to analyze data obtained by using the fuzzy rating scale. More concretely, the paper is to be focussed on testing different hypothesis about means, on the basis of a sound methodology which has been stated during the last years. All the procedures that have been developed to this aim will be presented in an algorithmic way adapted to the usual generic fuzzy rating scale-based data, and they will be illustrated by means of a real-life example.

An Empirical Analysis of the Coherence Between Fuzzy Rating Scale- and Likert Scale-Based Responses to Questionnaires

“…In fact, it seems that people take advantage of the flexibility, freedom and expressiveness of the fuzzy rating scale to draw their valuations and they make it rather independently of their Likert assessment even in case they have to do it simultaneously. This corroborates what has been statistically concluded by Lubiano et al [6,7]: Likert scales 'aggregate' in some sense valuations which could be 'precisiated' through fuzzy numbers, so relevant information can be lost when using Likert scales.…”

“…In previous papers, responses to items in synthetic and real-life questionnaires based both on Likert and fuzzy rating scales have been empirically compared by means of different statistical tools (see, for instance, De la Rosa de Sáa et al [1], Gil et al [3] and Lubiano et al [7]).…”

Case Study-Based Sensitivity Analysis of Scale Estimates w.r.t. the Shape of Fuzzy Data

“…The discussions in this paper will be based on the following case study. To get more expressive responses and informative conclusions, some items selected from the original questionnaire form (see Table 1) have been adapted to allow a double-type response: the original Likert and a fuzzy rating scalebased one with reference interval [0, 10] (see Figure 2 for one of the items, and http://bellman.ciencias.uniovi.es/smire/Archivos/FormandDatasetFRS-TP.pdf for the full paper-and-pencil form, and Hesketh et al [5] and Lubiano et al [6,8]).…”

Flexible bootstrap based on the canonical representation of fuzzy numbers

“…In particular, the bootstrapped version of statistical tests for fuzzy data were considered, e.g., by Colubi et al [3], Gil et al [8], González-Rodríguez et al [9,10], Grzegorzewski and Ramos-Guajardo [12], Montenegro et al [17] and Ramos-Guajardo and Lubiano [20]. Some other examples on the bootstrap application in fuzzy modeling of the real-life problems, like fuzzy rating in questionnaires [16], quality control in cheese manufacturing [19] or fuzzy nonparametric Shewhart's control chart construction [23] are worth mentioning too.…”