Study On Consistency Index And Prioritization Method Of Fuzzy Preference Relations

The basic mathematical tool of analytic hierarchy process is pairwise comparison matrix obtained by pairwisely comparing alternatives.The prioritization method is used to determines the ranking of alternatives and determine the optimal solution.When the 0-1 scale is used to measure the preference intensity of the decision maker based on the idea of fuzzy sets,the given matrix is called fuzzy preference relations.It is an important issue on how to obtain the priorities of alternatives from fuzzy preference relations.The main work and results are given as follows:(1)A new consistency index and a new prioritization method for fuzzy additive reciprocal matrices are proposed.Based on the relationship between two rows or two columns of fuzzy additive reciprocal matrices,the variance-based consistency index is established,and the threshold of acceptable additive consistency is determined according to computer simulation.Based on the proposed method of constructing consistency index,an optimization model for eliciting priorities is constructed and the exact solution is obtained.The validity and novelty of the proposed method are illustrated by carrying out numerical examples and comparing with other prioritization methods.(2)The consistency index and prioritization method of fuzzy non-reciprocal preference relations are proposed.By considering the non-reciprocal property of fuzzy preference relations,the variance similarity measures of two rows and two columns are proposed.The double variance consistency index is constructed and the thresholds of acceptable consistency are computed.The optimization model is proposed to elicit the priority vector of fuzzy non-reciprocal preference relations,which is further extended to interval additive reciprocal matrices.The novelty of the proposed method is illustrated by numerical examples compared with other prioritization methods.Based on the above results,a new additive consistency index and a prioritization method of fuzzy preference relations are proposed.The decision theory based on fuzzy preference relations has been developed.