Analytical Hierarchy Process based on intuitionistic interval approximation of trapezoidal intuitionistic fuzzy numbers

The fuzzy Analytical Hierarchy Process (AHP) is a method in fuzzy decision-making, which helps decision makers make the best choice of alternatives when dealing with uncertainty. The objective of this paper is to propose a conversion method of trapezoidal intuitionistic fuzzy numbers (TrIFN) into interval-valued intuitionistic fuzzy numbers (IVIFN), followed by a new fuzzy AHP based on the proposed approximation. The linguistic judgments of decision makers are converted into TrIFN before being transformed into IVIFN using the nearest weighted intuitionistic interval approximation (NWIIA). The proposed model is implemented in supplier selection problems by taking into account five criteria comprising cost, quality, service, cycle time, and reputation. The results showed that the proposed model simplifies the fuzzy AHP using TrIFN without affecting the consistency of the solutions from the existing method, thus supporting the fact that TrIFN has a better capability of processing ill-defined quantities. This is because TrIFN entails a generalization of the triangular intuitionistic fuzzy number (TIFN), making it a better form of representation of linguistic variables for reducing the inexactness.