**6. Conclusions**

In this paper, we surveyed the literature on mathematical programming with fuzzy numbers from a perspective that emphasizes the necessity of using the extension principle within the whole optimization process, not only within the fuzzy arithmetic evaluation.

Since our review showed that the extension principle was widely present through the fuzzy arithmetic, but much less involved in the foundations of the solution concepts, we advanced the idea that the rehabilitation of the extension principle when deriving relevant fuzzy descriptions to optimal solutions is highly needed. Our opinion was supported by several recent studies showing that better and more effective solutions can be obtained when the algebraic aggregation of the fuzzy quantities and optimization are unified and together conduce to a solution concept that complies to the extension principle.

We discussed the similarities between optimization problems with fuzzy coefficients and full fuzzy optimization problems, and concluded about the unification of their subclass of optimization problems with fuzzy coefficients that assume fuzzy decision variables but with a priori unknown shapes. The solution approaches to this subclass of optimization problems with fuzzy numbers are expected to follow the extension principle, and a posteriori disclose the shapes of the decision variables.

We believe that this study advances relevant ideas to initiate the revitalization of the extension principle in mathematical optimization with fuzzy numbers. Due to its critical view on the basis of the methodology used to solve certain classes of fuzzy optimization problems, and since its implementation in various fields is able to provide more accurate and reliable optimal solutions, we expect that our conclusions will have an impact on solving practical industrial problems. As it has been said, the impact should be effective on the methodology level, and could be seen as a subtle attempt to filling the gap between the academic researches with their theoretical results and the relevant solutions needed in practice.

Our future research will be focused on deriving analytic solutions to full fuzzy optimization problems that are in accordance to the extension principle, and also simple enough to be able to replace the existing solution approaches. We will follow the research directions proposed in the previous section in order to enlarge the class of problems approachable via the extension principle.

**Author Contributions:** Conceptualization and methodology, B.S. and M.S.; writing—original draft and visualization, B.S.; writing—review and editing, validation, S.N.; supervision, M.S. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to record their sincere gratitude to professor I. Dzitac for his generous help in the preparation of this paper, and also for many valuable and constructive suggestions that guided them for years. This work was partly supported by the Serbian Ministry of Education, Science and Technological Development through Mathematical Institute of the Serbian Academy of Sciences and Arts and Faculty of Organizational Sciences of the University of Belgrade.

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