**6. Conclusions**

The results obtained in this article will facilitate the use of OFN in real object modelling.

In the face of conditions (7) and (8), the above-described approximation methods can be used for approximate FN by trapezoidal FN. The oriented energy index is then reduced to the energy measure.

Among other things, FN are applied in social choice and political sciences. In reference [47], FN describe imprecise linguistic evaluation labels used by voters. Each assessment can be irrationally undervalued or overvalued. Then, we can use OFN to describe the irrational deviations of the assessment. In [48], FN describe voters' opinion profiles. This is a static description of the population of voters. On the other side, voters' opinions are very dynamic. Replacement of FN by OFN would allow one to describe mentioned dynamics. The problems discussed in this paper can be a starting point for an attempt to create such approximation methods of OFN by TrOFN that such a constraint that a "vector of solution parameters is a monotonic sequence" will be included. Moreover, further research on the considered above approximation method should be devoted to the following problems:


Solutions obtained to the last three problems will allow estimation of the approximation error.

**Author Contributions:** Conceptualization, K.P.; Methodology, K.P. and A.Ł.H.; Validation, A.Ł.H.; Formal Analysis, A.Ł.H.; Writing—Original Draft Preparation, K.P.; Writing—Review & Editing, K.P. and A.Ł.H.

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

**Acknowledgments:** The authors are very grateful to the anonymous reviewers for their insightful and constructive comments and suggestions. We would like to thank to Professor José Carlos R. Alcantud for his valuable final remarks. Using these comments allowed us to improve this article.

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