A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary jud...A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.展开更多
In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection f...In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.展开更多
文摘A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.
文摘In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.
