A note on multi-criteria decision-making using a complete ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers is an inevitable task in solving multi-criteria decision-making problems modelling under a fuzzy environment. Generalized trapezoidal fuzzy numbers are used in the literature for modelling real-life problems involving incomplete information. Many researchers worldwide are looking for a standard method that can be used to discriminate arbitrary GTrFNs. However, most of them do not define a total ordering on the class of generalized trapezoidal fuzzy numbers. Recently, Marimuthu and Mahapatra (2020) defined various ranking functions on the class of GTrFNs and tried to define a complete ranking principle on the set of GTrFNs. But their method also has some drawbacks in comparing arbitrary GTrFNs. The main aim of this paper is to discuss some issues of the complete ranking principle introduced in Marimuthu and Mahapatra (2020). Also, we discuss the limitations of a few theorems and give the correct version of them. Further, we improve a complete ranking principle by discussing a membership score of a GTrFN. Finally, we prove that the proposed (improved) ranking principle defines a complete ranking in the class of GTrFNs.