July 2006 Volume 9 Number 3 - CiteSeerX

B, C and D, who rate the portfolio by defining fuzzy constraints after identifying their own evaluation concepts.
The role of the assessment agent is to negotiate the assessment of students A, B, C and D and to achieve an
agreement. Based on this process, the assessment agent is considered a distributed fuzzy constraint network (Lai
and Lin, 2004). Assessment criteria are regarded as negotiation issues or constrained objects and student
assessments are fuzzy constraints. Figure 3 presents the workflow of the assessment agent.
Define Fuzzy
constraints
In the first step of the assessment process, students evaluate the portfolios submitted by the other students and
use their own fuzzy membership functions to mark. These fuzzy membership functions for assessment criteria
are regarded as fuzzy constraints. After defining fuzzy constraints, the assessment agent applies concession
and/or trade-off strategies to negotiate. Trough offers generation and evaluation, if an agreement cannot be
reached, the fuzzy constraints or negotiation strategies must be adjusted. Conversely, if an agreement is reached,
the interests of all students are considered to produce the final results. Then, the student submitting portfolio to
be assessed by other students receives final scores, understands the peer assessments, and can reflect upon the
assessment and revise the portfolio.
During the negotiation process, each agent begins negotiating by proposing an ideal offer. However, when an
offer is unacceptable to the other agents, these agents make concessions using a concession strategy or derive
new alternatives using a trade-off strategy to move toward an agreement. Adopted from the framework in (Lai
and Lin, 2004), the fuzzy constraint-based negotiation context is formalized as follows.
ℜ is a set of agents involved in the negotiation, ℜ p ∈ℜ
is the one of members inℜwhere 1 ≤ p ≤ m and
m is the number of ℜ .
p
C is a distributed fuzzy constraint network that represents an agent ℜ . p
p
Π is the intent of a distributed fuzzy constraint network p
C and represents the set of all potential
C
agreements for agent ℜ . p
μ (u ) is the overall degree of satisfaction reached with a solution u.
Π
p
C
Apply negotiation
strategy
Negotiation
(Offer generation)
(Offer evaluation)
Self-reflection and
improvement
Figure 3. The workflow of the assessment agent
p
wq
μΠ
= min (( μ p ( u))
)
(1)
C
p q=
1,..,
n Cq
p
where n is the number of negotiation issues, w is the weight of issue q in agent q
ℜ , and p μ p (.) is the
Cq
degree of satisfaction for agent ℜ and issue q.
p
The process of negotiation is a series of determining how agents evaluate and generate alternatives
from a possible designated space. ( ,
p )
i C Π ℜ ℑ denotes to find a final agreement for all agents in ℜ
α
from p
i C Π . If α ( ,
p )
i C Π ℜ ℑ holds, the negotiation is complete and terminates; otherwise, threshold
α
α will move to next lower threshold i
α and repeatedly applies i+
1
( ,
p )
i 1 C Π ℜ ℑ to achieve an agreement.
α +
As the next lower threshold q
q
α over issue q is smaller than the minimal satisfaction degree δ for
i+ 1
issue q, the set of potential agreements over issue q would be j Π and that of other issues is k k
δ C j
i C j
Π .
α +1
Then, ( ,
p )
i C Π ℜ ℑ will be false and the negotiation terminates until the next lower threshold α α is i+
1
lower than the overall minimal satisfaction degree, that is,
q
αi
+ 1 arg minδ
q=
1..
n
< .
No
Reach an
agreement
Yes
Produce the final
results
19