Measuring perspective of a factor in a decision

1. An apparatus comprising:

an analytic network process (ANP) storage memory that stores an ANP weighted supermatrix representing an ANP model; and

a processor in communication with the ANP storage memory, the processor being configured to facilitate

measuring how alternatives synthesize with respect to a fixed node in the stored ANP weighted supermatrix to determine a perspective metric vector for the fixed node; and

maintaining a same proportionality in the stored ANP weighted supermatrix for the measuring of the perspective metric vector for the fixed node,

the perspective metric vector being measured consistent with at least one of the formulas:

a synthesized value of alternative i from the perspective of the fixed node r being

p

r

,

i

=

lim

p

→

1

⁢

s

r

,

i

⁡

(

p

)

;

and

a total synthesized vector being denoted by

p r =( p r,1 , . . . , p r,a )

A being the ANP model,

W being the weighted supermatrix of a single level of the ANP model (of dimensions n×n),

W(p) being a family of row perturbations of row 1<r<n of W,

s r,i (p) the synthesized score for alternative i for the family of ANP row perturbations of row r at parameter value p,

A(p) being the induced family of ANP models,

the ANP model having a alternatives.

2. The apparatus of claim 1 ,

wherein the measuring of the perspective metric vector comprises pushing an overall importance of the fixed node toward a value of 1, and then synthesizing over the stored ANP weighted supermatrix.

3. The apparatus of claim 2 , the pushing of the importance comprising inducing a family of ANP models by row perturbations of the fixed node in the stored ANP weighted supermatrix of plural predetermined amounts so as to take a limit as a priority of the fixed node goes toward the value of 1, the alternative score further being synthesized from alternative scores of the fixed node in the induced family of ANP models.

4. The apparatus of claim 1 , further comprising constructing a perspective matrix for the stored ANP weighted supermatrix, giving simultaneous perspective information for plural nodes in the network using the node scores of all of the plural nodes from the perspective of the fixed node.

5. The apparatus of claim 1 , further comprising:

an output unit in communication with the processor and configured to output, for a display to a user, the determined perspective metric vector.

6. The apparatus of claim 1 , further comprising

an input unit configured to input, from an input device, pairwise comparisons, ANP ratings, or ANP client data, which are transformed into priority vectors and stored into the ANP weighted supermatrix, 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.

7. A method, comprising:

storing, in an analytic network process (ANP) storage memory, an ANP weighted supermatrix representing an ANP model; and

in a processor in communication with the ANP storage memory,

measuring how alternatives synthesize with respect to a fixed node in the stored ANP weighted supermatrix to determine a perspective metric vector for the fixed node; and

maintaining a same proportionality in the stored ANP weighted supermatrix for the measuring of the perspective metric vector for the fixed nod;

the perspective metric vector being measured consistent with at least one of the formulas:

a synthesized value of alternative i from the perspective of the fixed node r being

p

r

,

i

=

lim

p

→

1

⁢

s

r

,

i

⁡

(

p

)

;

and

a total synthesized vector being denoted by

p r =( p r,1 , . . . , p r,a )

A being the ANP model,

W being the weighted supermatrix of a single level of the ANP model (of dimensions n×n),

W(p) being a family of row perturbations of row 1<r<n of W,

s r,i (p) being the synthesized score for alternative i for the family of ANP row perturbations of row r at parameter value p,

A(p) being the induced family of ANP models,

the ANP model having a alternatives.

8. The method of claim 7 ,

wherein the measuring of the perspective metric vector comprises pushing an overall importance of the fixed node toward a value of 1, and then synthesizing over the stored ANP weighted supermatrix.

9. The method of claim 8 , the pushing of the importance comprising inducing a family of ANP models by row perturbations of the fixed node in the stored ANP weighted supermatrix of plural predetermined amounts so as to take a limit as a priority of the fixed node goes toward the value of 1, the alternative score further being synthesized from alternative scores of the fixed node in the induced family of ANP models.

10. The method of claim 7 , further comprising constructing a perspective matrix for the stored ANP weighted supermatrix, giving simultaneous perspective information for plural nodes in the network using the node scores of all of the plural nodes from the perspective of the fixed node.

11. The method of claim 7 , further comprising:

outputting, to an output unit in communication with the processor, for a display to a user, the determined perspective metric vector.

12. The method of claim 7 , further comprising

inputting, from an input device, pairwise comparisons, ANP ratings, or ANP client data, which are transformed into priority vectors and stored into the ANP weighted supermatrix, 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.

13. A non-transitory computer-readable storage medium encoded with 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 weighted supermatrix representing an ANP model;

measuring how alternatives synthesize with respect to a fixed node in the stored ANP weighted supermatrix to determine a perspective metric vector for the fixed node; and

maintaining a same proportionality in the stored ANP weighted supermatrix for the measuring of the perspective metric vector for the fixed node,

the perspective metric vector being determined consistent with at least one of the formulas:

a synthesized value of alternative i from the perspective of the fixed node r being

p

r

,

i

=

lim

p

→

1

⁢

s

r

,

i

⁡

(

p

)

;

and

a total synthesized vector being denoted by

p r =( p r,1 , . . . , p r,a )

A being the ANP model,

W being the weighted supermatrix of a single level of the ANP model (of dimensions n×n),

W(p) being a family of row perturbations of row 1<r<n of W,

s r,i (p) being the synthesized score for alternative i for the family of ANP row perturbations of row r at parameter value p,

A(p) being the induced family of ANP models,

the ANP model having a alternatives.

14. The non-transitory computer-readable storage medium of claim 13 ,

wherein the measuring of the perspective metric vector comprises pushing an overall importance of the fixed node toward a value of 1, and then synthesizing over the stored ANP weighted supermatrix.

15. The non-transitory computer-readable storage medium of claim 14 , the pushing of the importance comprising inducing a family of ANP models by row perturbations of the fixed node in the stored ANP weighted supermatrix of plural predetermined amounts so as to take a limit as a priority of the fixed node goes toward the value of 1, the alternative score further being synthesized from alternative scores of the fixed node in the induced family of ANP models.

16. The non-transitory computer-readable storage medium of claim 13 , further comprising constructing a perspective matrix for the stored ANP weighted supermatrix, giving simultaneous perspective information for plural nodes in the network using the node scores of all of the plural nodes from the perspective of the fixed node.

17. The non-transitory computer-readable storage medium of claim 13 , further comprising:

outputting, to an output unit for a display to a user, the determined perspective metric vector.

18. The non-transitory computer-readable storage medium of claim 13 , further comprising

inputting, from an input device, pairwise comparisons, ANP ratings, or ANP client data, which are transformed into priority vectors and stored into the ANP weighted supermatrix, 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.