Interval-valued neutrosophic AHP with possibility degree method

The Analytic Hierarchy Process (AHP) is one of the most widely used methods in multi criteria decision making (MCDM) in many areas. The method has been extended with hesitant fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, and type -2 fuzzy sets etc. These extended methods can consider the vagueness in decision making problems through different definitions of membership functions. Each of them tries to increase the effectiveness of AHP under uncertainty. Decision makers can fully express their judgments through neutrosophic sets (NS) since NS are based on three independent parameters, truthiness (T), indeterminancy (I) and falsity (F), providing a distinction between a 'relative truth' and an 'absolute truth'. In this paper, we employ the possibility degree method for ranking interval numbers in our neutrosophic AHP approach by utilizing NS' representation power. Besides, we employ interval-valued NS since a larger domain for the definition of T, I, and F is provided. Pairwise comparison matrices can be filled in by using linguistic terms such as weakly more important, moderately more important or extremely important. Then, we obtain the relative importance degrees of criteria by using the possibility degree method. In order to show the effectiveness of our method, a MCDM application is given in energy planning. Comparative and sensitivity analyses are also presented in the paper.