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Appendix B. Consensus Index
Appendix B. Consensus Index
For a given goal, a regional manager/branch manager makes a judgment on weighting
For a given goal, a regional manager/branch manager makes a judgment on weighting
Appendix B. Consensus Index
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
Appendix B. Consensus Index
For a given goal, a regional manager/branch manager makes a judgment on weighting
Appendix B. Consensus Index
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
For a given goal, a regional manager/branch manager makes a judgment on weighting
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
NTU Management Review Vol. 33 No. 3 Dec. 2023
For a given goal, a regional manager/branch manager makes a judgment on weighting
number of elements; in our case, it is four × four.
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
number of elements; in our case, it is four × four.
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
Appendix B. Consensus Index
Appendix B. Consensus Index
rankings are pre
number of elements; in our case, it is four × four. sented in a matrix form. The size of the matrix (n×m) depends on the
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
For a given goal, a regional manager/branch manager makes a judgment on weighting
For a given goal, a regional manager/branch manager makes a judgment on weighting
Appendix B. Consensus Index
number of elements; in our case, it is four × four.
number of elements; in our case, it is four × four.
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
1
⋯ 1
1
⋯
For a given goal, a regional manager/branch manager makes a judgment on weighting
� (1)
��
⋮
⋱
⋮
X=[xij]=�
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
� (1)
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
⋮
⋱
⋮
X=[xij]=�
the four goals with the scale ranging from one to nine, as shown in Appendix A; these
⋯ 1 ⋯
1 1/ 1
1
number of elements; in our case, it is four × four.
number of elements; in our case, it is four × four.
� (1)
1
⋯
1/
⋮
⋮ ��
⋱
X=[xij]=�
1
⋯ 1
rankings are presented in a matrix form. The size of the matrix (n×m) depends on the
1
1
⋯
⋯
1/ 1
��
number of elements; in our case, it is four × four. ⋮ � (1) ⋮ ⋱ ⋮ � (1)
X=[xij]=�
⋱
⋮
X=[xij]=�
1/ hich represents X=[xij]; the comparison element
Equation (1) demonstrates matrix X, w 1 ⋯ ⋯ 1 1/ 1 ⋯ 1
1
Equation (1) demonstrates matrix X, which represents X=[xij]; th
� (1) e comparison element
��
⋮
⋱
⋯ ⋮
1
X=[xij]=�
for i≠j, where i is the n-th column of the matrix and j is the m-th
��
1
value is [xij]= �
� (1)
1
1/ 1
1
⋯
for i≠j, where i is the n-th column of the matrix and j is the m-th
Equation (1) demonstrates matrix X, which represents X=[xij] . .; the comparison element
⋮
⋱
⋮
X=[xij]=�
��
value is [xij]= �
⋯ score is calculated, the individual score is
row of the matrix. After the individual
��
1
1/
for i≠j, where i is the n-th column of the matrix and j is the m-th
Equation (1) demonstrates matrix X, which represents X=[xij]; the comparison element
row of
value is [xij]= � the matrix. After the individual score is calculated, the individual score is
1
��
Equation (1) demonstrates matrix X, which represents X=[xij]; the comparison element
aggregated into group decision making. The formula is as follows:
��
row of the matrix. After the individual score is calculated, the individual score is
Equation (1) demonstrates matrix X, which represents X=[x ]; the comparison
for i≠j, where i is the n-th column of the matrix and j is the m-th
aggregated into group decision making. The formula is as follows:
1
Equation (1) demonstrates matrix X, which represents X=[xij]; the comparison element
for i≠j, where i is the n-th column of the matrix and j is the m-th
value is [xij]= �
ij
1
��
value is [xij]= �
for i≠j, where i is the n-th column of the matrix and j is the m-th
element value is [x ]= for i ≠ j, where i is the n-th column of the matrix and j is the
aggregated into group decision making. The formula is as follows:
row of the matrix. After the individual score is calculated, the individual score is
��
1
value is [xij]= �
Equation (1) demonstrates matrix X, which represents X=[xij]; the comparison element is
row of the matrix. After the individual score is calculated, the individual score
ij
��
) (2)
G
G
row of the matrix. After the individual score is calculated, the individual score is
�
(�)
�
m-th row of the matrix. After the individual score is calculated, the individual score is
aggregated into group decision making. The formula is as follows:
aggregated into group decision making. The formula is as follows:
X =[xij] =∏
(
G
) (2)
G
� ���
��
�
(�)
for i≠j, where i is the n-th column of the matrix and j is the m-th
X =[xij] =∏
(
1
aggregated into group decision making. The formula is as follows:
���
��
value is [xij]= �
G
aggregated into group decision making. The formula is as follows:
��
) (2)
G
row of the matrix. After the individual score is calculated, the individual score is
�
(�)
�
(
X =[xij] =∏
��
���
G
G
� (�) X
�
� =[xij] =∏
aggregated into group decision making. The formula is as follows: � ( �� (�) ) (2)
G
. ) (2)
( ) (2)
G
G
G
G
,
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
�
(�) �
X =[xij] =∏
���
(
X =[xij] =∏
G
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
���
��
��
���
are considered to have different weight vectors , which have values between 0 and
�
are considered to have different weight vectors , which have values between 0 and
where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers are
G
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
G
�
1. In the event where the decision maker considers weights to be equally important,
) (2)
G
G
(�)
�
�
G
X =[xij] =∏
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
(
1. In the event where the decision maker considers weights to be equally important,
are considered to have different weight vectors , which have values between 0 and
considered to have different weight vectors , which have values between 0 and 1. In the
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
G
��
����
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
G
� (RGMM) is selected for the
then =1/m. Then, the row geometric mean method
�
are considered to have different weight vectors , which have values between 0 and
then =1/m. Then, the row geometric mean method (RGMM) is selected
event where the decision maker considers weights to be equally important, then =1/m. the
1. In the event where the decision maker considers weights to be equally important, , which have values between 0 and
are considered to have different weight vectors for
�
�
are considered to have different weight vectors , which have values between 0 and
�
prioritization group decision method using the following formula:
1. In the event where the decision maker considers weights to be equally important,
prioritization group decision method using the following formula:
Then, the row geometric mean method (RGMM) is selected for the prioritization group
then =1/m. Then, the row geometric mean method (RGMM) is selected for the
1. In the event where the decision maker considers weights to be equally important,
�
1. In the event where the decision maker considers weights to be equally important,
then =1/m. Then, the row geometric mean method (RGMM) is selected for the
Where X is the group matrix for all decision makers (n = 1,2,….,m), decision makers
G
�
prioritization group decision method using the following formula:
decision method using the following formula: Then, the row geometric mean method (RGMM) is selected for the
then =1/m.
�
prioritization group decision method using the following formula:
then =1/m. Then, the row geometric mean method (RGMM) is selected for the
are considered to have different weight vectors , which have values between 0 and
�
�
prioritization group decision method using the following formula:
prioritization group decision method using the following formula:
�/�
1. In the event where the decision maker considers weights to be equally important,
�
�/� ∏
�
�
��
� ���
�∏
�
� (3)
��
then =1/m. Then, the row geometric mean method (RGMM) is selected for the
���
�/� =
�
�/�
� (3)
�
. .
�
�
�∏
�
= ∑
(∏
�
��
�∏
�
���
��
� � ���
� ���
��
prioritization group decision method using the following formula:
���
∑
�∏
� �
=
��
(3) �/�
� ���
� ���
�
= � �/� ∑ (3) �∏ � � ��
���
(∏
�
�
�
�
��
���
�∏ �
∑ ��� (∏ ��� �� � �� ��� (3)
���
In equation (3), the collective weight is w where i = 1,2,…,n, and the group
=
=ve weight is wi, where i
In equation (3), the collecti i, (3) = 1,2,…,n, and the group
�
�
�
∑ weight is wi, where i = 1,2,…,n, and the group
In equation (3), the collective � �∏ � � � ∑ ��� (∏ ��� � ��
�
In equation (3), the collective weight is wi, where i = 1,2,…,n, and the group
consistency score is measured using the geometric consistency index GCI:
consistency score is measured using the geometric consistency index GCI:
��
�/�
���
���
�
consistency score is measured using the geometric consistency index GCI:
��� where i = 1,2,…,n, and the group
�∏
consistency score is measured using the geometric consistency index GCI:
In equation (3), the collective weight is wi, � ��
(3)
=
GCI(X)=
� ( ) � � �)�� (4)
�
� � In equation (3), the collective weight
consistency score is measured using the geometric consistency index GCI: . . is wi, where i = 1,2,…,n, and the group
∑
(� ��
GCI(X)= collective
� � ( ) � � �)�� (4)
∑ ∑ weight is wi, where i = 1,2,…,n, and the group
�
�
��� �� ( ) � � �)�� (4)
���
�
��
�∏
�
In equation (3), the ∑ ��� (� (� �� � � � �
GCI(X)= (���)(���)
��� ��
��
��� ��
(���)(���)
(���)(���) consistency score is measured using the geometric consistency index GCI:
consistency score is measured using the geometric consistency index GCI:
(� �� ( ) � � �)�� (4)
GCI(X)=
�
∑
(���)(���) ��� �� � �
In equation (3), the collective weight is wi, where i = 1,2,…,n, and the group �)�� (4)
�
GCI(X)=
∑
(� �� ( ) � � �)�� (4)
(� �� ( ) � �
GCI(X)=
�
���
�
��
�
∑
(���)(���)
�
���
��
�
consistency score is measured using the geometric consistency index GCI:
(���)(���)
GCI(X)= � ∑ (� �� ( ) � � �)�� (4)
(���)(���) ��� �� � �
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