Geometric approach for ranking generalized trapezoidal fuzzy numbers and its application in selecting security guard service company

In many mathematical and real-life situations, the classical set theory is not applicable where there is ambiguity, imprecision, uncertainty, and qualitative information. The fuzzy set theory plays an instrumental role in these real-life situations. Fuzzy numbers are a particular class of fuzzy sets. To rank fuzzy numbers, a multitude of methods exists in the literature. Various ranking method has a few limitations in comparing generalized trapezoidal fuzzy numbers (GTrFNs). This paper presents a new geometric approach to rank generalized trapezoidal fuzzy numbers (GTrFNs) which can overcome the drawbacks of many familiar ranking methods. This ranking principle uses the concept of centroid, the distance between the centroids and the mid-point of diagonals. The potentiality of the proposed ranking principle examines using illustrative numerical examples and comparing the results with the existing approaches. The Multi-criteria decision-making (MCDM) problem has been solved using the modified Fuzzy TOPSIS, modified Fuzzy ARAS, and modified Fuzzy WASPAS approaches to examine the efficacy of the proposed ranking principle. Finally, a case problem has been considered in choosing the best security guard service provider for an educational institute. This example illustrates the effectiveness of the proposed model in solving fuzzy MCDM problems and selecting the best service provider. Also, we discuss the sensitivity analysis of the proposed algorithm by considering different weights of the criteria, which makes the proposed work more reliable in comparing familiar methods.