**6. Conclusions**

The objective of this study was to present the Pythagorean membership grade induced ordered weighted moving average (PMGIOWMA) operator. The main characteristic of this new proposition is that it combines a weighting vector with a Pythagorean membership grade to include the knowledge, expertise, and expectations of the decision-maker, as well as a reordering step based on induced values and the application of a series of data based on moving averages.

Additionally, the main definitions and theorems of the PMGIOWMA operator are provided here, as well as some other extensions that are less complex, such as the PMGOWMA or PMGIOWA operators. These two extensions are considered less complex because in the first, the reordering is not based on induced values, and in the second, there is not a moving average. The main idea of presenting fewer complex formulations is based on the problem that needs to be solved. To reduce the uncertainty, it is possible to use a simpler formula. Moreover, sometimes not all the information needed for using the most complex operator can be obtained and the analysis must be carried out with another operator.

The PMGIOWMA operator was used to visualize the perceptions of and relationship between savings and credit based on a survey of 1914 people from 13 provinces of the department of Boyacá, Colombia. Among the main results, it was possible to see that the three different groups had the same perceptions of saving and credits, and the relationship degree was also the same. This idea is important, considering that the groups were based on their educational level, and it was possible to see that, regarding the financial topics of saving and credits, their perceptions were the same. Another interesting result was that the perception of saving in Group 1 (people with no and primary education) was 50% higher with the PMGOWA operator.

Futures research should focus on fuzzy decision-making [64] to propose more extension of the Pythagorean membership grade and OWA operator [65], possibly through the use of distance operators [40], linguistic variables [8,66], logarithmic operators [67], heavy operators [33] or prioritized operators [68].

**Author Contributions:** Conceptualization, J.R.-M. and F.B.-M.; methodology, F.B.-M. and E.L.-C.; formal analysis, F.B.-M. and E.L.-C.; writing—original draft preparation, J.R.-M. and F.B.-M.; writing— review and editing, F.B.-M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Universidad Pedagogica y Tecnologica de Colombia (grant number SGI-2589). Author Number 2 acknowledges support from the Chilean Government through FONDECYT initiation gran<sup>t</sup> No. 11190056.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Universidad Pedagogica y Tecnologica de Colombia.

**Informed Consent Statement:** All subjects gave their informed consent for inclusion before they participated in the study. The study was conducted in accordance with the Declaration of Helsinki.

**Data Availability Statement:** The database used is from a secondary source provided by the Eugene Fama research group of the Financial Literacy in Boyacá project (2018–2019).

**Conflicts of Interest:** The authors declare no conflict of interest.
