Systems, Man & Cybernetics - October 2015 - 11

◆ Definition 5: A message [15], [16], [20], [21] (symbolized

by a music note) is defined a s
:: = < id, r,
f, P, l, a, b >, where: id is the identification of the message; r is null or the receiver (role) of the message
expressed by an identification of the role; f is the pattern of a message (function), specifying the types,
sequence, and number of parameters; P is a set of
objects taken as parameters with the message pattern
f, where P 1 O; l is a label that expresses any, some,
or all to mean the type of the message; a is the space
limit for this message to be processed; b is the time
limit for this message to be processed.
We use to express a specific message and M a set
of all the messages. A message is a way to facilitate
interactions among the components of the E-CARGO
model. Note that, in RBC, we emphasize that messages
are sent to roles. Messages are exchanged among roles,
and a role is also a message dispatcher to the agents that
are playing this role. Therefore, in E-CARGO, objects are
passive entities that are accessed by agents through
roles. Objects cannot process messages. Role players,
i.e., agents, are the only components to process messages. This idea clearly clarifies the differences among
agents, roles, and objects.
◆ Definition 6: For group g, a tuple  of g. J [20] is
called a role assignment, also called an agent assignment.
◆ Definition 7: A role range vector [20] is a vector of the
lower ranges of roles in environment e of group g. Suppose that roles in g.e are numbered as j (0 # j # n - 1)
and B [j] means the range tuple for role j, then L[j] =
g.e. B [j].q.l. The role range vector is denoted as L[j]
! N, 0 # j # n - 1.
◆ Definition 8: A role weight vector [20] is a vector of the
weights of roles in environment e of group g. Suppose
that roles in g.e are numbered as j (0 # j # n - 1) and
B [j] means the role requirement tuple for role j, then
W[j] = g.e. B [j].w. The role weight vector is denoted as
W[j] ! [0, 1], 0 # j # n - 1.
◆ Definition 9: A qualification matrix [20] is an m × n
matrix Q: A # R " [0, 1], where Q[i, j] ! [0, 1]
expresses the qualification value of agent i for role j
(0 # i # m - 1, 0 # j # n - 1), 0 means the lowest and
1 the highest.
In E-CARGO, an environment regulates the performance of groups built in it. A group is mainly built by
assigning roles to agents. It is the environment that points
out the importance of role assignment. In fact, L and Q are
both discovered by investigating the internal properties of
an environment. L and Q change timely and point out the
importance of dynamic role assignment.
◆ Definition 10: Agent evaluation (AE) [17] is a function
to obtain the Q matrix of group g with agent set A and
role set R; i.e., Q = AE (A, R).
◆ Definition 11: A role assignment matrix [20] is defined as
an m × n matrix T: A # R " {0, 1}, where T[i, j] = 1
expresses that agent i is assigned to role j (i.e., 

! g. J) and agent i is called an assigned agent, while
T [i, j] = 0 means not (i.e.,  z g. J) .
For example, Figure 2(a) shows a Q matrix and Figure
2(b) a T matrix.
◆ Definition 12: The group qualification v of group g
[20] is defined as the sum of the assigned agents' qualifications, shown as follows:
m-1 n-1

i.e., v (Q, W, T) = | | Q [i, j] # W [j] # T [i, j] .
i=0 j=0

Note that L is used in producing T but not v directly.
◆ Definition 13: Role j is workable [20] in group g if it is

assigned with enough agents, i.e., | i = 0 T [i, j] $ L [ j].
◆ Definition 14: T is workable [20] if each role j is workm-1
able, i.e., 6 (0 # j 1 n) | i = 0 T [i, j] $ L [ j]. Group g is
workable if T is workable.
◆ Definition 15: The optimal assignment matrix [20] T*
is a workable T to make the following:
m-1

m=1 n=1

| | Q [i, j] # W [|
j] (|
t) #QT[i*, j[]i,#j]W=[j] (t) # T * [i, j] =
m=1 n=1

i=0 j=0

i=0 j=0

m=1 n=1

m=1 n=1

i=1 j=1

i=1 j=1

max { | | Q [i, j]max
# W{[|
j] (|
t) #QT[i[,ij,]j#
]},W [ j] (t) # T [i, j]},
where T is workable.
◆ Definition 16: Group role assignment (GRA) [20] is to

find T* subject to the following:
T [i, j] ! {0, 1} (0 # i 1 m, 0 # j 1 n),
m=1

| T [i, j] = L [j] (0 # j 1 n),

(1)
(2)

i=0

n-1

| T [i, j] # 1 (0 # i 1 m),

(3)

i=0

where (1) tells that an agent is either assigned or not; (2)
makes the group workable with the smallest number of
agents; and (3) means that each agent can only be
assigned to one role.
This GRA problem has been solved with an efficient
algorithm by adopting the Kuhn-Munkres algorithm for
general assignment problems [6], [7]. The results of the
experiments in this paper are based on the efficient algorithm for the GRA problem [20].
◆ Definition 17: A group state (GS) [18] for group g at
time t is defined as GS(t) ::= < A (t), R (t), L(t), W(t)>.
With the aforementioned definitions, we may view
other parameters as a function of time t. For example,

0.71
0.29
0.69
0.0
0.97
0.58

0.6
0.67
0.92
0.0
0.51
0.64

0.0
0.44
0.92
0.53
0.77
0.24

(a)

0.22
0.76
0.6
0.0
0.65
0.0

1
0
0
0
1
0

0
0
0
0
0
1

0
0
0
1
0
0

0
1
1
0
0
0

(b)

Figure 2. (a) a qualification matrix Q and (b) an
assignment matrix T.

O c tob e r 2015

IEEE SyStEmS, man, & CybErnEtICS magazInE

11



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - October 2015

Systems, Man & Cybernetics - October 2015 - Cover1
Systems, Man & Cybernetics - October 2015 - Cover2
Systems, Man & Cybernetics - October 2015 - 1
Systems, Man & Cybernetics - October 2015 - 2
Systems, Man & Cybernetics - October 2015 - 3
Systems, Man & Cybernetics - October 2015 - 4
Systems, Man & Cybernetics - October 2015 - 5
Systems, Man & Cybernetics - October 2015 - 6
Systems, Man & Cybernetics - October 2015 - 7
Systems, Man & Cybernetics - October 2015 - 8
Systems, Man & Cybernetics - October 2015 - 9
Systems, Man & Cybernetics - October 2015 - 10
Systems, Man & Cybernetics - October 2015 - 11
Systems, Man & Cybernetics - October 2015 - 12
Systems, Man & Cybernetics - October 2015 - 13
Systems, Man & Cybernetics - October 2015 - 14
Systems, Man & Cybernetics - October 2015 - 15
Systems, Man & Cybernetics - October 2015 - 16
Systems, Man & Cybernetics - October 2015 - 17
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Systems, Man & Cybernetics - October 2015 - 20
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Systems, Man & Cybernetics - October 2015 - 22
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Systems, Man & Cybernetics - October 2015 - Cover3
Systems, Man & Cybernetics - October 2015 - Cover4
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