**5. Conclusions**

The main objective of this document is to present the new BON-PrIHOWA operator. The main features of this new proposition are that one can combine a nonrestricted to one weighting vector, an induced vector that assigns weights to the attributes and a prioritized vector that unifies the opinions of the decision makers in a group decision-making process, where not all stakeholders have the same importance in the computation.

Additionally, in this document, the main definitions of the BON-PrIHOWA operator are included, and it is important to mention that the BON-PrIHOWA can be reduced to the PrIOWA, PrHOWA, IHOWA, and OWA. This is suggested when the complexity of the problem is minimal and not very extensive. However, the design of this operator, its functionality and its operability are intended for complex phenomena with highly dynamic information. This is the case, e.g., when a combination of expert information is required to assess open governmen<sup>t</sup> initiatives and public policies.

The complete design of the BON-PrIHOWA operator uses a ranking of transparency websites for Mexico. Among the main results, it was possible to identify that the top and bottom four states remained the same even when the weights, operators and experts changed. This is important because their positions cannot change easily. However, other positions can also change drastically depending on the operator or expert and, because of that, the perception of transparency of the citizens and governors. The main component that changes the ranking is the importance that is given to each component of transparency websites. When the weights assigned to each result are not 1 *n* , but rather they depend on the focus and goals of each government, the score can change drastically. This change in the weights is important because not all information can be treated in the same way since

the characteristics, objectives and goals of the states are not always the same. They are derived from their demographic, economic, and geographic characteristics, among others, in such a way that treating similar information is not appropriate. The idea of identifying changes in the ranking can improve the public policies that are established because the ranking can be established not only by using the average of the components but also by using a specific operator depending on the individual characteristics of the state.

For future research, more extensions of the OWA operator can be conceived with the use of distance operators [43], Bonferroni means [17,29,44], moving averages [45–48], forgotten effects [47,49], the least square deviation [50,51] or logarithmic operators [52,53]. This is important when the subjectivity and the uncertainty of the decision–making process are presented. With the use of aggregation operators and other fuzzy techniques, it is possible to generate new scenarios based on the expertise and expectations of the decision makers. Additionally, the use of different coefficients to test the similarity between the rankings will be useful to compare rankings in decision-making fields [54]. Finally, these new techniques can be applied in different areas such as economics, finance, engineering, social science and other areas [55] where the idea and characteristics of fuzzy logic and fuzzy sets can be used [56,57].

**Author Contributions:** Conceptualization, V.A.-G.; Data curation, L.A.P.-A.; Formal analysis, F.B.-M.; Methodology, E.L.-C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Author Leon-Castro acknowledges support from the Chilean governmen<sup>t</sup> through FONDECYT initiation gran<sup>t</sup> No. 11190056.

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