A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process

The fuzzy analytic hierarchy process (FAHP) has been used to solve various multi-criteria decision-making problems where trapezoidal type-1 fuzzy sets are utilized in defining decision-makers' linguistic judgment. Previous theories have suggested that interval type-2 fuzzy sets (IT2 FS) can offer an alternative that can handle vagueness and uncertainty. This paper proposes a new FAHP characterized by IT2 FS for linguistic variables. Differently from the typical FAHP, which directly utilizes trapezoidal type-1 fuzzy numbers, this method introduces IT2 FS to enhance judgment in the fuzzy decision-making environment. This new model includes linguistic variables in IT2 FS and a rank value method for normalizing upper and lower memberships of IT2 FS. The proposed model is illustrated by a numerical example of work safety evaluation. Comparable results are also presented to check the feasibility of the proposed method. It is shown that the ranking order of the proposed method is consistent with the other two methods despite difference in weight priorities.