Using Sieve of Eratosthenes for the Factor Analysis of Neutrosophic Form of the Five Facet Mindfulness Questionnaire as an Alternative Confirmatory Factor Analysis
  • Volkan Duran1, Selçuk Topal2,*, Florentin Smarandache3, Said Broumi4
1 Igdır University, Campus, Igdır, 76000, Turkey
2 Department of Mathematics, Arts and Sciences Faculty, Bitlis Eren University, Bitlis, Turkey
3 Department of Mathematics, University of New Mexico, Gallup, 87301, NM, USA
4 Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco
* Corresponding Author: Selc¸uk Topal. Email:
(This article belongs to this Special Issue:Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))
Received 17 March 2021; Accepted 08 July 2021 ; Published online 02 September 2021
In this study, the Five Facet Mindfulness Questionnaire which was adapted from the short form of the Five Facet Mindfulness Questionnaire was evaluated and this scale into neutrosophic form was converted and the results of the scale were compared for proposing new type confirmatory analysis procedure as well as developing neutrosophic scales. The exploratory factor analysis was used in the analysis of the data. Besides, test results were analyzed for Kaiser–Meyer–Olkin and Bartlett values, common factor variance values, scree plot graphs, and the principal component analysis results. The sample of the study consists of 194 students in mathematics departments at Bitlis Eren University and I˘gdır University in Turkey by convenience sampling method. A convenience sampling is a kind of non-probability sampling procedure in which the sample is obtained from a group of individuals easily accessible or reachable. The convenience sampling method was chosen in this study because the study aims to examine the structure of the measurement tool rather than the psychological characteristics of a particular population. First of all, it is observed that if any classical scale can be converted into a neutrosophic one. It is observed that the sub-dimensions of a neutrosophic scale as agree, disagree, and undecided might not have a similar factor structure to the classical one. Interestingly, in the factor analysis of the neutrosophic scale, both classical and the agreement part of the neutrosophic scales have the same factors, implying that the one-dimensional classical scale measures the agreement degree of the participants. When the factor analysis was conducted to disagreement and vagueness dimensions, it seemed that some factors were eliminated and even some new factors emerged, indicating that in human cognition those three dimensions can be taken as independent of each other, just as assumed by neutrosophic logic. The another important implication of the factor analysis is that the neutrosophic forms of any questionnaire can be used for the validity of the classical ones. Loads of items or their accumulation into factors are compared to the classical scale and the three-dimensional neutrosophic scale in the factor, so that the corresponding ones in the same factors and the items or factors that do not correspond to each other are eliminated. It is very similar to the Sieve of Eratosthenes, which is an ancient algorithm for finding prime numbers up to any given limit where each prime is taken as an independent base or dimension and multiples of the selected primes in a given interval are eliminated until there are only prime numbers left. Finally, the reliability of three independent dimensions of the neutrosophic forms of any questionnaire can also be used to check whether the measurement tool is reliable. Low-reliability results in any dimensions may imply that the scale has some problems in terms of meaning, language, or other factors.
Neutrosophic scales; factor analysis; scale development; explanatory analysis; reliability analysis