The weighted arithmetical mean complex judgement matrix （WAMCJM） is the most common method for aggregating group opinions, but it has a shortcoming, namely the WAMCJM of the perfectly consistent judgement matrices g...The weighted arithmetical mean complex judgement matrix （WAMCJM） is the most common method for aggregating group opinions, but it has a shortcoming, namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency. An upper bound of the WAMCJM＇s consistency is presented. Simultaneously, a compatibility index of judging the aggregating extent of group opinions is also introduced. The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency. These conclusions are important to group decision making.展开更多
This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invarian...This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invariance under change of scale, and also gives a simple convergent iterativealgorithm and some numerical examples. The well-known eigenvector method(EM) is then compared.Theoretical analysis and the numerical results show that the iterative times of the GMLSM are generallyfewer than that of the MLSM, and the GMLSM are preferable to the EM in several important respects.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
基金the National Natural Science Foundation of China (705250047047103570121001).
文摘The weighted arithmetical mean complex judgement matrix （WAMCJM） is the most common method for aggregating group opinions, but it has a shortcoming, namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency. An upper bound of the WAMCJM＇s consistency is presented. Simultaneously, a compatibility index of judging the aggregating extent of group opinions is also introduced. The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency. These conclusions are important to group decision making.
文摘This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invariance under change of scale, and also gives a simple convergent iterativealgorithm and some numerical examples. The well-known eigenvector method(EM) is then compared.Theoretical analysis and the numerical results show that the iterative times of the GMLSM are generallyfewer than that of the MLSM, and the GMLSM are preferable to the EM in several important respects.
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.
