By the transformation relations between complementary judgement matrix and recip- rocal judgement matrix,this paper proposes two methods for improving the consistency of com- plementary judgement matrix and gives tw...By the transformation relations between complementary judgement matrix and recip- rocal judgement matrix,this paper proposes two methods for improving the consistency of com- plementary judgement matrix and gives two simple practical iterative algorithms.These two al- gorithms are easy to implementon computer,and the modified complementary judgementmatri- ces remain most information that original matrix contains.Thus the methods supplement and develop the theory and methodology for improving consistency of complementary judgement matrix展开更多
Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the correspon...Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.展开更多
In this paper,an approach to improving consistency of judgement matrix in the Analytic Hierarchy Process (AHP) is presented,which utilizes the eigenvector to revise a pair of entries of judgement matrix each time.By u...In this paper,an approach to improving consistency of judgement matrix in the Analytic Hierarchy Process (AHP) is presented,which utilizes the eigenvector to revise a pair of entries of judgement matrix each time.By using this method,any judgement matrix with a large C.R.can be modified to a matrix which can both tally with the consistency requirement and reserve the most information that the original matrix contains.An algorithm to derive a judgement matrix with acceptable consistency (i.e.,C.R.<0.1) and two criteria of evaluating modificatory effectiveness are also given.展开更多
The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency...The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency of the WGMM in group decision and prove that the weighted geometric mean complex interval judgement matrix (WGMIM) is of acceptable consistency under the condition that all interval matrices for the same decision\|making problem are of acceptable consistency. Thus, research on consistency of group decision in AHP is further developed and a theory basis for the application of the WGMM is also made.展开更多
We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.
Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(79970 0 93 ) and the Subject of PLAUniversity of Science and Technology
文摘By the transformation relations between complementary judgement matrix and recip- rocal judgement matrix,this paper proposes two methods for improving the consistency of com- plementary judgement matrix and gives two simple practical iterative algorithms.These two al- gorithms are easy to implementon computer,and the modified complementary judgementmatri- ces remain most information that original matrix contains.Thus the methods supplement and develop the theory and methodology for improving consistency of complementary judgement matrix
基金The Project of Shaanxi Provincial Natural Science Foundation of China (No.2004A05)the Project of Science and Research Foundation of Education Committee of Shaanxi Province (No.06JK324)
文摘Based on the concept of multiplicative fuzzy consistent complementary judgement matrix, the mixed least square method （MLSM） for priority of complementary judgement matrix is proposed and proved. Then, the corresponding convergent iterative algorithm is given and its convergence is proved. Finally, some main properties of the developed priority method, such as rank preservation under strong condition, etc., ate introduced. The theoretical analyses show that the MLSM can sufficiently reflect the preference information of the decision maker, and is easy to realize on a computer.
基金This research is supported by the National Natural Science Foundation of China under Project 79970093, the Ph.D. Dissertation Foundation of Southeast University-NARI-Relays Electric Co. Ltd.
文摘In this paper,an approach to improving consistency of judgement matrix in the Analytic Hierarchy Process (AHP) is presented,which utilizes the eigenvector to revise a pair of entries of judgement matrix each time.By using this method,any judgement matrix with a large C.R.can be modified to a matrix which can both tally with the consistency requirement and reserve the most information that the original matrix contains.An algorithm to derive a judgement matrix with acceptable consistency (i.e.,C.R.<0.1) and two criteria of evaluating modificatory effectiveness are also given.
基金Research supported by National Science Foundation of China
文摘The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency of the WGMM in group decision and prove that the weighted geometric mean complex interval judgement matrix (WGMIM) is of acceptable consistency under the condition that all interval matrices for the same decision\|making problem are of acceptable consistency. Thus, research on consistency of group decision in AHP is further developed and a theory basis for the application of the WGMM is also made.
基金This research is supported by National Natural Science Foundation of China（10201007） and NSF of Shandong.
文摘We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.
文摘Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
