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

• Published in: European journal of operational research Vol. 251; no. 3; pp. 918 - 929
• Main Authors: Lubiano, María Asunción, Montenegro, Manuel, Sinova, Beatriz, de la Rosa de Sáa, Sara, Gil, María Ángeles
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.06.2016; Elsevier Sequoia S.A
• Subjects: Algorithms; Computational intelligence and information management; Fuzzy; Fuzzy logic; Fuzzy rating scale; Fuzzy sets; Hypotheses; Hypothesis testing; Linguistics; Measuring instruments; Operational research; Random fuzzy numbers; Ratings; Representations; Research methodology; Semantics; Sound; Statistical analysis; Stochastics and statistics; Studies; Fuzzy rating scale; Random fuzzy numbers; Fuzzy sets; Computational intelligence and information management; Stochastics and statistics
• ISSN: 0377-2217; 1872-6860; 1872-6860
• DOI: 10.1016/j.ejor.2015.11.016

•We review and update one/multi-sample testing hypothesis about means of fuzzy data.•We detail the algorithms for testing and particularize them to trapezoidal fuzzy data.•We discuss some differences with testing with either Likert or fuzzy linguistic data. 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 focused 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.