Method and system for analytic network process (ANP) rank influence analysis
An apparatus includes an analytic network process (ANP) storage memory that stores an ANP model with feedback connections in place among nodes within the ANP model and with at least preliminary input of data stored in the ANP model, and a processor in communication with the ANP storage memory. The process performs a rank influence analysis on the ANP model, wherein the rank influence analysis determines one or more nodes among the nodes in the ANP model in which a smallest upward or downward change in importance will change a rank among the nodes in the ANP model, so as to determine which one or more nodes have the most influence on the rank among the nodes in the ANP model.
1. An apparatus comprising:
an analytic network process (ANP) storage memory that stores an ANP model with feedback connections in place among nodes within the ANP model and with at least preliminary input of data stored in the ANP model; and
a processor in communication with the ANP storage memory, the processor being configured to facilitate
performing a rank influence analysis on the ANP model, wherein the rank influence analysis determines one or more nodes among the nodes in the ANP model in which a smallest upward or downward change in importance will change a rank among the nodes in the ANP model, so as to determine which one or more nodes have the most influence on the rank among the nodes in the ANP model.
2. The apparatus of claim 1 , wherein the processor is configured to facilitate determining a rank score for the nodes among the nodes in the ANP model based on an amount of upward or downward change in importance that causes a change in the rank among the nodes in the ANP model.
3. The apparatus of claim 1 , wherein the processor is configured to indicate the nodes determined to have the most influence.
4. The apparatus of claim 1 , wherein the processor is configured to prompt a user to input refined data for the nodes determined to have the most influence while skipping input for other nodes in the ANP model.
5. The apparatus of claim 1 , wherein the processor is configured to provide, for output to a user, a display showing a magnitude of rank influence for the nodes in the ANP model.
6. The apparatus of claim 1 , wherein the processor is configured to base the rank of each node in the ANP model on an amount of influence each said node has on rankings of alternatives in the ANP model.
7. The apparatus of claim 1 , wherein the rank influence analysis is performed by finding upper and lower rank change parameter values for alternatives ordered in a weighted supermatrix representing the ANP model.
8. The apparatus of claim 1 , further comprising
an input unit configured to input, from an input device to the processor, pairwise comparisons, ANP ratings, or ANP client data, which are stored as the data in the ANP model, the pairwise comparisons representing a judgment of priority between ANP alternatives in the pair, the ANP ratings representing a rating of a choice, and the ANP client data representing real world values.
9. A method, comprising:
storing, in an analytic network process (ANP) storage memory, an ANP model with feedback connections in place among nodes within the ANP model and with at least preliminary input of data stored in the ANP model; and
in a processor in communication with the ANP storage memory, performing a rank influence analysis on the ANP model, wherein the rank influence analysis determines one or more nodes among the nodes in the ANP model in which a smallest upward or downward change in importance will change a rank among the nodes in the ANP model, so as to determine which one or more nodes have the most influence on the rank among the nodes in the ANP model.
10. The method of claim 9 , further comprising determining a rank score for the nodes among the nodes in the ANP model based on an amount of upward or downward change in importance that causes a change in the rank among the nodes in the ANP model.
11. The method of claim 9 , further comprising outputting, to an output unit in communication with the processor, an indication of the nodes determined to have the most influence.
12. The method of claim 9 , further comprising prompting a user to input refined data for the nodes determined to have the most influence while skipping input for other nodes in the ANP model.
13. The method of claim 9 , further comprising providing, for output to a user, a display showing a magnitude of rank influence for the nodes in the ANP model.
14. The method of claim 9 , wherein the rank of each node in the ANP model is based on an amount of influence each said node has on rankings of alternatives in the ANP model.
15. The method of claim 9 , wherein the rank influence analysis is performed by finding upper and lower rank change parameter values for alternatives ordered in a weighted supermatrix representing the ANP model.
16. The method of claim 9 , further comprising
inputting, from an input device, pairwise comparisons, ANP ratings, or ANP client data, which are transformed into priority vectors and stored as the data stored in the ANP model, the pairwise comparisons representing a judgment of priority between ANP alternatives in the pair, the ANP ratings representing a rating of a choice, and the ANP client data representing real world values.
17. A non-transitory computer-readable storage medium encoded with a computer executable instructions, wherein execution of said computer executable instructions by one or more processors causes a computer to perform the steps of:
storing, in an analytic network process (ANP) storage memory, an ANP model with feedback connections in place among nodes within the ANP model and with at least preliminary input of data stored in the ANP model; and
in a processor in communication with the ANP storage memory, performing a rank influence analysis on the ANP model, wherein the rank influence analysis determines one or more nodes among the nodes in the ANP model in which a smallest upward or downward change in importance will change a rank among the nodes in the ANP model, so as to determine which one or more nodes have the most influence on the rank among the nodes in the ANP model.
18. The non-transitory computer-readable storage medium of claim 17 , further comprising determining a rank score for the nodes among the nodes in the ANP model based on an amount of upward or downward change in importance that causes a change in the rank among the nodes in the ANP model.
19. The non-transitory computer-readable storage medium of claim 17 , further comprising outputting an indication of the nodes determined to have the most influence.
20. The non-transitory computer-readable storage medium of claim 17 , further comprising prompting a user to input refined data for the nodes determined to have the most influence while skipping input for other nodes in the ANP model.
21. The non-transitory computer-readable storage medium of claim 17 , further comprising providing, for output to a user, a display showing a magnitude of rank influence for the nodes in the ANP model.
22. The non-transitory computer-readable storage medium of claim 17 , wherein the rank of each node in the ANP model is based on an amount of influence each said node has on rankings of alternatives in the ANP model.
23. The non-transitory computer-readable storage medium of claim 17 , wherein the rank influence analysis is performed by finding upper and lower rank change parameter values for alternatives ordered in a weighted supermatrix representing the ANP model.
24. The non-transitory computer-readable medium of claim 17 , further comprising instructions for:
prompting a user to input refined data for the nodes determined to have the most influence while skipping input for other nodes in the ANP model.
25. The non-transitory computer-readable storage medium of claim 17 , further comprising instructions for:
inputting, from an input device, pairwise comparisons, ANP ratings, or ANP client data, which are transformed into priority vectors and stored as the data stored in the ANP model, the pairwise comparisons representing a judgment of priority between ANP alternatives in the pair, the ANP ratings representing a rating of a choice, and the ANP client data representing real world values.
26. An apparatus comprising:
an analytic network process (ANP) storage memory that stores an ANP model with feedback connections in place among nodes within the ANP model and with at least preliminary input of data stored in the ANP model; and
a processor in communication with the ANP storage memory, the processor being configured to:
perform a rank influence analysis on the ANP model, wherein the rank influence analysis determines one or more nodes among the nodes in the ANP model in which a smallest upward or downward change in importance will change a rank among the nodes in the ANP model, so as to determine which one or more nodes have the most influence on the rank among the nodes in the ANP model;
determine a rank score for the nodes among the nodes in the ANP model based on an amount of upward or downward change in importance that causes a change in the rank among the nodes in the ANP model;
indicate the nodes determined to have the most influence;
prompt a user to input refined data for the nodes determined to have the most influence while skipping input for other nodes in the ANP model;
provide, for output to a user, a display showing a magnitude of rank influence for the nodes in the ANP model;
base the rank of each node in the ANP model on an amount of influence each said node has on rankings of alternatives in the ANP model;
and
an input unit configured to input, from an input device to the processor, pairwise comparisons, ANP ratings, or ANP client data, which are stored as the data in the ANP model, the pairwise comparisons representing a judgment of priority between ANP alternatives in the pair, the ANP ratings representing a rating of a choice, and the ANP client data representing real world values,
wherein the rank influence analysis is performed by finding upper and lower rank change parameter values for alternatives ordered in a weighted supermatrix representing the ANP model,
wherein the amount of upward or downward change in importance that causes a change in the rank among the nodes in the ANP model is obtained by an upper rank influence score and a lower rank influence score.
27. The apparatus of claim 26 , comprising performing row perturbations in the weighted supermatrix representing the ANP model, so as to determine for the first p + above fixed point p 0 where an upper rank change occurs and p − below p 0 where a lower rank change occurs, and using the first p + and p − to construct a value that indicates the upper and lower rank influence of the rows throughout the weighted supermatrix.
28. The apparatus of claim 26 , wherein the upper rank influence score rki + A,W,r is defined by
rki
A
,
W
,
r
+
=
1
-
p
A
,
W
,
r
+
1
-
p
o
,
and the lower rank influence score rki − A,W,r is defined by
rki
A
,
W
,
r
-
=
1
-
p
A
,
W
,
r
-
p
o
,
where
A is the ANP model,
W is the weighted supermatrix of A(of dimensions n×n),
1≦r≦n is a row of W,
k is column of W,
i is an alternative in A,
W(p) is a family of row perturbations for row r of W with p 0 as the fixed point,
p 0 represents returning the node values to the original weights,
p + is above p 0 where the upper rank change occurs, and
p − is below p 0 where the lower rank change occurs.