Methods and apparatus for decision making
Abstract
There is disclosed a multiple criteria decision analysing method in which a plurality L of basic criteria are assessed in order to a general criterion, comprising the steps of: making an assessment {(K m,l ,γ m,l ),m=1, . . . , M} of the l th basic criteria under a set of grades {K m,l ,m=1, . . . , M}; and transforming the assessment {(K m,l ,γ m,l ),m=1, . . . ,M} to an assessment {(H n ,β n,l ),n=1, . . . ,N} of the general criterion under a set of grades {H n ,n=1, . . . N} using the matrix equation: [ β 1 , l β 2 , l ⋮ β N , l ] = [ α 1 , 1 α 1 , 2 … α 1 , M α 2 , 1 α 2 , 2 … α 2 , M ⋮ ⋮ ⋰ ⋮ α N , 1 α N , 2 … α N , M ] = [ γ 1 , l γ 2 , l ⋮ γ M , l ] wherein: H n is the n th grade for assessment of the general criterion; K m,l is the m th grade for assessment of the l th basic criterion; α n,m is the m th degree to which K m,l implies H n ; γ m,l is the degree to which the l th basic criterion is assessed to K m,l ; β n,l is the degree to which the th basic criterion is assessed to H n ; and ∑ n = 1 N α n , m = 1
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A multiple criteria decision analysis method in which a plurality L of basic criteria are assessed in order to a general criterion, comprising the steps of:
making an assessment {(K m,l ,γ m,l ),m=1, . . . ,M} of the l th basic criteria under a set of grades {K m,l , Im=1, . . . ,M}; and transforming the assessment {(K m,l γ m,l ),m=1, . . . , M} to an assessment {(H n ,β n,l ),n=1, . . . ,N} of the general criterion undera set of grades {H n , n=1, . . . ,N} using the matrix equation: [ β 1 , l β 2 , l ⋮ β N , l ] = [ α 1 , 1 α 1 , 2 ⋯ α 1 , M α 2 , 1 α 2 , 2 ⋯ α 2 , M ⋮ ⋮ ⋰ ⋮ α N , 1 α N , 2 ⋯ α N , M ] = [ γ 1 , l γ 2 , l ⋮ γ M , l ] wherein:
H n is the n th grade for assessment of the general criterion;
K m,l is the m th grade for assessment of the l th basic criterion;
α n,m is the degree to which K m,l implies H n ;
γ m,l is the degree to which the l th basic criterion is assessed to K m,l ;
β n,l is the degree to which the th basic criterion is assessed to H n ; and
∑ n = 1 N α n , m = 1.
2 . A method according to claim 1 in which the values of α n,m (m=1, . . . , M and n=1, . . . ,N) are assigned by a decision maker.
3 . A method according to claim 2 in which a grade K m,l implies a grade H n to a degree of α n,m wherein m=1, . . . ,M.
4 . A method according to claim 1 in which the values of α n,m (m=1, . . . ,M and n=1, . . . ,N) are determined using the following equations:
α
n
,
m
=
u
(
H
n
+
1
)
-
u
(
K
m
,
l
)
u
(
H
n
+
1
)
-
u
(
H
n
)
,
α
n
+
1
,
m
=
1
-
α
n
,
m
,
α i,m =0(i=1, . . . ,N,i≠n,n+1)
if u(H n )≦u(K m,l )≦u(H n+1 ) for n=1, . . . ,N−1;m=1, . . . ,M where u(H n ) and u(K m,l ) are utilities of H n and K m,l , respectively.
5 . A method according to claim 4 in which at least one of u(H n ) and u(K m,l ) are estimated by a decision maker.
6 . A method according to claim 4 in which at least one of u(H n ) and u(K m,l ) are determined using one or more of the equations:
u
(
H
n
)
=
n
-
1
N
-
1
for
n
=
1
,
…
,
N
if
H
n
+
1
is preferred to H n ; and
u
(
K
m
,
l
)
=
m
-
1
M
-
1
for
m
=
1
,
…
,
M
if
K
m
+
1
,
l
is preferred to K m,l .
7 . A method according to claim 1 in which:
a basic criterion is assessed using the set {(k j , p j ),=1, . . . ,P}, where k j is a number and p j is the probability of the basic criterion taking the number k j ; and
the values of γ m,l in the assessment {(K m,l , γ m,l ),m=1, . . . ,M} are calculated using the equation
γ m , l = ∑ j = 1 P S m , j p j for m = 1 , … , M wherein : S m , j = K m + 1 , l - k j K m + 1 , l - K m , l , S m + 1 , j = 1 - S m , j , S i , j = 0 ;
m=M, . . . ,M−1; j=1, . . . ,P; i=1, . . . ,M,i≠m,m+1 if K m,i ≦k≦K m+1,l
8 . A multiple criteria decision analysis method in which a plurality L of basic criteria are assessed in order to assess a general criterion, comprising the steps of:
assigning weights W i (i=1, . . . L) to the L basic criteria; normalising the weights using the equations ω i = W i ∑ j = 1 L W j ( i = 1 , … L ) ; determining β n,l , wherein β n,i is the degree to which the i th basic criterion is assessed to H n , and H n is the n th grade for assessment of the general criterion, the general criterion being assessed into N grades; calculating weighted degrees of belief n i from the equation m n,i =ω i β n,i )=ω i β n,i ,( n= 1 , . . . , N; i=. . . , 1);and calculating a remaining probability mass m H,i from the equation m H , i = 1 - ∑ n = 1 N m n , i ( i = 1 , … , L ) .
9 . A method according to claim 8 in which m H,i is decomposed into {overscore (m)} H,i and {tilde over (m)} H,i , wherein:
m H,i ={overscore (m)} H,i +{tilde over (m)} H,i ; {overscore (m)} H,i =1−ω i ;and m ~ H , i = ω i ( 1 - ∑ n = 1 N β n , i ) for i = 1 , … , L .
10 . A method according to claim 9 in which m n,i ,{overscore (m)} H,i and {tilde over (m)} H,i (i=1, . . . ,L) are aggregated into combined probability masses I n,L ,{overscore (I)} H,L and Ĩ H,L , respectively, using equations i) to ix) in a recursive manner
I n,1=m n,l (n=1,2, . . . ,N) i) I H,l =m H,l ii) Ĩ H,l ={tilde over (m)} H,l iii) {overscore (I)} H,l ={overscore (m)} H,l iv) K i + 1 = [ 1 - ∑ t = 1 N ∑ j = 1 j ≠ t N I t , i m j , i + 1 ] - 1 v ) I n,i+1 =K i+1 [I n,i m n,i+1 +I H,i m n,i+1 +I n,i m H,i+1 ]( n= 1,2 . . . , N) vi) Ĩ H,i+1 =+K i+1 [Ĩ H,i {tilde over (m)} H,i+1 +{overscore (I)} H,i+1 {tilde over (m)} H,i+1 +Ĩ H,i+1 {overscore (m)} H,i+1 ] vii) {overscore (I)} H,i+1 =K i+1 [{overscore (H)} H,i+1 {overscore (m)} H,i+1 ] viii) I H,i+1 ={overscore (I)} H,i+1 +{overscore (I)} H,i+1 ix) i={1,2, . . . ,L−1}
11 . A method according to claim 10 in which combined degrees of belief β n and β H are generated using the equations:
β
n
=
I
n
,
L
1
-
I
_
H
,
L
n
=
1
,
2
,
…
,
N
β
H
=
I
~
H
,
L
1
-
I
_
H
,
L
wherein β n is a degree of belief to which the general criterion is assessed to the n th grade H n and β H is a remaining degree of belief which is not assigned to any specific grade.
12 . A method according to claim 11 wherein each grade H n+1 is more favourable than H n and performance indicators of a general criterion are generated using the equations:
u
max
=
∑
n
=
1
N
-
1
β
n
u
(
H
n
)
+
(
β
N
+
β
H
)
u
(
H
N
)
u
min
=
(
β
1
+
β
H
)
u
(
H
1
)
+
∑
n
=
2
N
β
n
u
(
H
n
)
u
avg
=
u
max
+
u
min
2
and wherein u max , u min and u avg are the best possible, worst possible and average performance indicators respectively, and u(H n )(n=1, . . . N) is optionally defined by
u
(
H
n
)
=
n
-
1
N
-
1
13 . A method according to claim 8 in which the values of β n,i are determined using a method according to claim 1 .
14 . A carrier medium storing a computer program, which computer program performs a method according to claim 1 .
15 . A computer adapted to perform a method according to claim 1 .
16 . A carrier medium storing a computer program, which computer program performs a method according to claim 8 .
17 . A computer adapted to perform a method according to claim 8.Join the waitlist — get patent alerts
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