M3 {FuzzyStatTraEOO}

69 trapezoidal fuzzy numbers.

Description

A dataset containing 69 trapezoidal fuzzy numbers. The data correspond to the well-knows questionaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question M3 "Mathematics is harder for me than any other subject" are collected in this dataset.

Usage

M3

Format

A matrix with 69 rows and 4 columns:

inf0

infimum of support of the trapezoidal fuzzy numbers, real number

inf1

infimum of core of the trapezoidal fuzzy numbers, real number

sup1

supremum of core of the trapezoidal fuzzy numbers, real number

sup0

supremum of support of the trapezoidal fuzzy numbers, real number

Source

http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

References

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, 131-148 (2016)

[3] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, 918-929 (2016)

[4] Lubiano, M.A.; Salas, A.; Carleos, C.; De la Rosa de Sáa, S.; Gil, M.Á.: Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88, 128-147 (2017)

Examples

M3