Two new methods for deriving the priority vector from interval multiplicative preference relations

Two new methods to derive the interval priority vector are developed.To obtain the interval priority vector, the associated models are constructed.Some concepts of acceptable consistency are defined, and some properties are discussed.An improved interval ranking method is presented, and two algorithms are introduced.Three examples are offered, and comparisons with other existing procedures are made. Interval preference relations are widely used in the analytic hierarchy process (AHP) for their ability to express the expert's uncertainty. The most crucial issue arises when deriving the interval priority vector from the interval preference relations. Based on two of the most commonly used prioritization methods (the eigenvalue method (EM) and the row geometric mean method (RGMM)), two new methods for obtaining the interval priority vector from interval multiplicative preference relations are developed, which endow the expert with different risk preferences for his/her interval judgments. In contrast to existing methods, new approaches calculate the interval priority weights of alternatives separately. Then, several concepts of acceptable consistency for interval multiplicative preference relations are defined. Using a convex combination method, the acceptable consistency of interval multiplicative preference relations can be derived from the associated and exact numerical relations. To increase the distinction of intervals, an improved interval ranking method is presented. After that, two algorithms that can cope with acceptably and unacceptably consistent cases are introduced. Meanwhile, three numerical examples are examined to show the application of the new approaches, and comparisons with several other methods are also made.