Ranking Fuzzy Number And Priority Of The Fuzzy Judgment Matrices

Ranking fuzzy number is an important issue in the process of fuzzy optimization. Considering the definition and quality of fuzzy sets, the sequence of fuzzy numbers is not the entire-sequence but semi-sequence under lattice structures, which makes both the comparison and discrimination of fuzzy numbers become important and hardship tasks in the decision-makers.In recent years, various methods of ranking fuzzy number have been proposed. A sequence formula of interval numbers which is based on left and right imitated preceding degrees of fuzzy numbers is provided in this paper. This new index, which is obtained by constructing consistent positive reciprocal judgment matrix, satisfies five axioms of reasonable ranking fuzzy number, including the completeness of sequence, the property of uncross fuzzy quantity, the independence of misrelated fuzzy quantity, the transitivity of sequence and the compatibility to addition. Subsequently, triangle fuzzy numbers are converted toα-cut sets, and the sequence of triangle fuzzy numbers underα-level is determined by the new sequence formula of interval numbers. Finally, the sequence of triangle fuzzy numbers is determined by weighted integral. This sort of approach takes account of the impact of fuzzy-numbers' cut-set levels on the outcome of the sequence, and adjusts the value of pessimistic coefficientλto make the sequence more flexible and the outcome more scientific.The Analytic Hierarchy Process (AHP) is the most common method of decision-making. The key of AHP is to construct the judgment matrices by obtaining decision-makers' complete favorable information, and determine priority vectors with appropriate method. In the AHP method, the consistency of the judgment matrices is the precondition of their application. In this paper, a new approach to determine priority vectors of consistent positive reciprocal judgment matrix is provided. After that, the logic relationship between elements of consistent positive reciprocal judgment matrix with the parameter and the priority is revealed. It could not only take full advantage of the judgment of known information, but also take use of information preference of decision-makers to a large extent. The priority determined by this new logic relationship contains parameters can help the decision-makers choose parameters and meet the requirement of priority resolution.