Neutrosophic sets, expanded from the constructs of fuzzy and intuitionistic fuzzy sets, can accommodate degrees of truth, indeterminacy, and falsity for each element. This attribute equips them with an aptitude for a more refined interpretation of ambiguous or uncertain data. This study presents an innovative application of Neutrosophic Data Envelopment Analysis (Neu-DEA), incorporating pentagonal neutrosophic numbers in both input and output data. This novel methodology involves the transformation of traditional DEA models into a Pentagonal neutrosophic DEA model, subsequently converting it into a Crisp Linear Programming (CrLP) model. A unique ranking function is integral to this process. Performance evaluation of decision-making units (DMUs) is accomplished through the resolution of the CrLP model, with subsequent ranking of the DMUs based on their relative efficiency scores. The utility and effectiveness of this novel technique is validated through a numerical example.

The development and competition in educational facilities, are gradually increasing the importance of the quality of service. In order to accommodate this fast process, the educational organisations attempt to increase the quality of their service and to measure their performance. In general, the organisation's performance should not depend only on one criterion, but it should be evaluated basically on multi criteria. In this study, the academic performance of the departments in the Engineering Faculty of Gazi University have been compared by using one of the multi attribute decision making methods, called TOPSIS. In contrast to the most of the previous studies, in this study the necessary criteria for TOPSIS method and their weights were obtained not relatively, but based on the views of the specialists. For this purpose, in order to prevent the loss of information in the areas of the group decision making, linguistic variables have been utilized and criterion weights have been obtained by using a fuzzy Delphi method.