A convex combination approach for the weights of interval fuzzy preference relation

The weights of interval fuzzy preference relation generated in the analytic hierarchy process are investigated. Making use of a convex combination method, a family of real fuzzy preference relations are constructed. The aggregation of the weights of the family of real fuzzy preference relations is considered as the weights of interval fuzzy preference relation. In order to make any weight vector of the family of real fuzzy preference relations reliable, the sufficient and necessary conditions of their consistency and weak transitivity are given. When they are inconsistent, the method of repairing them to reach weak transitivity is also proposed. A numerical example is given to illustrate the validity and practicality of the developed methods.