A new ranking principle for ordering generalized trapezoidal fuzzy numbers based on diagonal distance, mean and its applications to supplier selection

The ranking of fuzzy numbers is vital in decision-making problems involving qualitative information and some fuzzy mathematical models. With the classical set theory, decision-making is challenging when it involves many uncertainties or qualitative information. This paper uses the proposed ranking principle for generalized trapezoidal fuzzy numbers (GTrFNs) to solve problems with imprecise information or uncertainty. There are multitudes of methods available for ranking generalized fuzzy numbers (GFNs), some of which have shortcomings. A few recent approaches involving centroid point, magnitude, distance, etc., to ordering GFNs have some drawbacks in ranking arbitrary GTrFNs. In this paper, we propose a new ranking principle based on the mean score and diagonal distance score function to overcome the shortcomings of a few existing ranking approaches. In this paper, we also demonstrate how well the suggested model works as a tool for selecting suppliers for an MCDM under a fuzzy environment. In addition, we show the effectiveness of the proposed ranking principle in solving multi-criteria decision-making problems using the modified fuzzy TOPSIS method. For this, an illustrative example of a hotel supplier section of electrical appliances illustrates the effectiveness of the proposed ranking principle.