Some programming models to derive priority weights from additive interval fuzzy preference relation

Deriving priority weights from fuzzy preference relations is a significant issue in decision making problems. In this paper, based on the definition of additive consistent fuzzy preference relations proposed by Tanino, a new approach with a parameter is developed to obtain priority weights, and properties of the new approach are explored. Then, a method for correcting inconsistent fuzzy preference relations is derived, and a new definition for the additive consistent interval fuzzy preference relations is obtained for the interval complementary pairwise comparison matrix. From these, linear programming models for generating interval priority weights from additive consistent or inconsistent interval fuzzy preference relations are established. Finally, three numerical examples are examined to show the feasibility of the developed method, and comparisons are also made between this new approach and the methods proposed by Xu and Chen [15]. Through the numerical examples, the ranking of interval priority weights using the different methods was found to be the same but with a slightly different degree of possibility. However, for the same interval complementary pairwise comparison matrix, the new definition for additive consistent interval fuzzy preference relations proposed in this paper was found to have more consistent information.