Behaviour of Fuzzy Agents within a Collaborative Design Platform
Alain-Jérôme Fougères
1,2
and Egon Ostrosi
2
1
ESTA, School of Business and Engineering, Belfort, France
2
Research Laboratory M3M, University of Technology of Belfort-Montbéliard, Belfort, France
Keywords: Fuzzy Agents, Fuzzy Agent Modelling, Fuzzy Agent Behaviour, Collaborative Design Platform.
Abstract: This paper presents first a fuzzy agent-based approach for assisting collaborative design, and then, an
analysis of behaviours of fuzzy agents evolving within a collaborative design platform. In a collaborative
design platform, more effective design decisions can be made by fuzzy agents when fuzzy design
information is considered in a fuzzy interaction based process and fuzzy evolving systems. The modelling
of fuzzy agents, their fuzzy interactions, their fuzzy roles, and their fuzzy organization, are presented.
During design process, fuzzy agents grouped in communities interact and play fuzzy roles for converging to
solutions of design. A case study of product configuration illustrates the analysis of fuzzy agents’ behaviour.
1 INTRODUCTION
Our research focuses on computer support for
distributed design activities. These activities are
inherently distributed, and then we proposed the
multi-agent systems as efficient computing
paradigm. Furthermore, many agent-based systems
have been proposed in many industrial fields,
especially in concurrent engineering and
collaborative and intelligent manufacturing
(Monostori et al., 2006).
During the collaborative design process,
designers deal with some distinct forms of
uncertainty such as imprecision, randomness,
fuzziness, ambiguity and incompleteness.
Imprecision is caused by the non-precise nature of
design information. Therefore we assume that more
effective design decisions can be made by fuzzy
agents when fuzzy design information is considered
in a fuzzy interaction based process.
Fuzzy agents are reactive to their environment
and they interact between them to adjust their
actions with their fuzzy knowledge (Ghasem-
Aghaee and Ören, 2007). Their evolution is fuzzy
(Lughofer, 2011), when they are designed to
interpret fuzzy information and to adopt a fuzzy
behaviour (Ostrosi et al., 2012; Fougères and
Ostrosi, 2013). Indeed, they interpret the fuzzy
information that they either receive or perceive. So
they interact in a fuzzy way.
Fuzzy agents are well adapted to respond to
heterogeneity and evolving of some organizations
(Fougères, 2012). So, we propose to analyse both the
evolution of their fuzzy roles and the change of their
distribution in different communities of an
organization, within a collaborative design platform.
This paper is organized as follows: in following
section, a fuzzy agent modelling is proposed; in third
section, an agentification of a product configuration
model is presented; in fourth section an illustration
of a fuzzy agent-based product configuration and an
analysis of fuzzy roles of fuzzy agents during this
configuration process are proposed; finally,
conclusions of this research are presented.
2 FUZZY AGENT MODELING
2.1 Fuzzy Agent Model
An agent-based system is fuzzy if the agents that
compose it are fuzzy:
 Knowledge of an agent is fuzzy (defined by fuzzy
values).
 Behaviour of an agent (Fig. 1, 2) depends on the
fuzzy evaluation of its fuzzy perceptions, its fuzzy
decisions, and its fuzzy actions.
 Interactions between agents are fuzzy, since 1) the
relationship or affinities between agents are
weighted by a fuzzy value, and 2) interactions
provide a relative interest (fuzzy evaluation) to
agents based on roles that they play at a given
241
Fougères A. and Ostrosi E..
Behaviour of Fuzzy Agents within a Collaborative Design Platform.
DOI: 10.5220/0004551802410248
In Proceedings of the 5th International Joint Conference on Computational Intelligence (FCTA-2013), pages 241-248
ISBN: 978-989-8565-77-8
Copyright
c
 2013 SCITEPRESS (Science and Technology Publications, Lda.)

time.
 Roles of agents are fuzzy, which means that a
fuzzy value is associated to all roles a fuzzy agent
plays. At a given time, it is possible to determine
what roles an agent plays based on fuzzy values of
its roles and a threshold value setting the minimum
value an agent should invest in these roles.
 Organization of the agent-based system is fuzzy,
insofar as the distribution of roles played by fuzzy
agents is continually evolving – this defines a self-
organizing agents which is the result both of their
fuzzy multiple interactions and the continuing
evolution of their roles in the general activity of
the agent-based system.
Fuzzy actions
goals
Fuzzy informations
Fuzzy
Observation
Fuzzy
Executio
n
Situation
recognition
Association
state/task
Procedure /
fuzzy rules
Fuzzy
interpretation
Planning
Level 1: Fuzzy
skill-based
behaviour
Level 2: Fuzzy
rule-based
behaviour
Level 3: Fuzzy
knowledge-based
behaviour
sign reflex
Fuzzy
decision
Fuzzy cognitive agent
Fuzzy routine agent
Fuzzy reactive agent
Figure 1: Variable agent behaviour and fuzzy agent
behaviour, based on Rasmussen’s model.
A fuzzy agent-based system is described by the
following tuple (1):

~
,
~
,
~
,
~
~

(1)
where

~
is a fuzzy set of agents,

~
is the fuzzy set
of interactions between agents fuzzy set of

~
,

~
is
the fuzzy set of roles that fuzzy agents of

~
can
play, and

~
is the fuzzy set of organizations (or
communities) defined for fuzzy agents of

~
. We
can then affirm the plasticity of these organizations.
However this plasticity is most pronounced in matrix
organizations than in hierarchical organizations. If
the agents that compose it are fuzzy: agents have the
knowledge and behaviour fuzzy, their interactions
are fuzzy, their roles are fuzzy, and the resulting
organizations are themselves fuzzy.
Agents developed in our various projects can
perform reflex actions (automatic), routine actions,
and actions in new situations (creative or
cooperative situations). Thus, a fuzzy agent

~
~
i
 is
described by the following tuple (2):


i
 

(


i
)
,

(


i
)
,

(


i
)
,




i

(2)
Global algorithms of


(


i
)
,


(


i
)
,


(


i
)
respectively functions of observation, decision and
action, are given in figure 2. The set of fuzzy
knowledge




i
includes decision rules, values of
the domain, acquaintances (networks of affinities
between agents), along with dynamic knowledge
(observed events, internal states, etc.).
Figure 2: Functional algorithms of a fuzzy agents
i

~
.
2.2 Fuzzy Agents Organization
Problems due to the partial view of agents (local
goals, interleaving activities, etc.), require the
development of strong coordination mechanisms
(Kubera et al., 2011). The organization shall allow
an agent-based system to behave as a coherent
whole, to solve a problem unequivocally. It controls
and coordinates the interaction between agents of the
system, thus structuring their activities with the goal
of convergence. Ferber et al. (2009) distinguish
between "organizational structure" and
"organization", corresponding to the process of
designing the structure. Wooldridge (1997) proposed
a more practical definition: “a collection of roles that
stand in certain relationships to one another and that

~
~

// a fuzzy event
Tt

// a courant task

~
~

// a fuzzy observation

~
~

// a fuzzy rule

~
~

// a fuzzy decision

~
~

// a fuzzy act
i) Fuzzy agent observation function (


(


i
)
)
if
)
~
(
~



= true then // fuzzy observation
if t = true then
if relation(

~
, t) = true then


~
~

;
)
~
(
~



else insert(

~
, Agenda) endif
else
t  true


~
~

;
)
~
(
~



endif
endif
ii) Fuzzy agent decision function (


(


i
)
)
if
)
~
(
~



= true then // fuzzy decision
if find_rule(

~
,

~
) = true then

~
~

;
)
~
(
~



else


~
(null) endif
endif
iii) Fuzzy agent action function (


(


i
)
)
if
)
~
(
~



= true then // fuzzy action

~
 extract_conclusions(

~
)
process(

~
)
else
process(null)
endif
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242

take part in systematic institutionalised patterns of
interactions with other roles”. From these
definitions, we extract the following characteristics:
 Organization includes active entities having
behaviour and defined functionalities.
 An organization can be partitioned into groups or
communities of agents.
 A group (or community) is comprised of agents
sharing a goal and characteristics.
 An agent can play one or more roles within the
group or groups to which he belongs.
 An agent interacts with agents of its community
and/or other communities to carry out its roles.
 A role corresponds to a function to be performed
by an agent in a group.
Figure 3: Different distributions of agents in communities
based on the roles they play at a given time.
In a dynamic organizational structure, the roles of
agents can become dynamic, variable and
determined by the actions to be done (Fig. 3). We
proposed that the roles of agents are considered
fuzzy. An agent in this organization can have several
fuzzy roles at a given time. Thus a fuzzy set of roles
is defined as follows (3):


q

~
,...,
~
,
~
~
21

(3)
Then, the fuzzy set of roles played by an agent is
defined by (4):




)
~
(),...,
~
(),
~
(
~
~
~~~
21
i
q
iii



(4)
Fuzzy agent interacts by sending messages within its
initial community (in this case, it plays its main
role), but it also interacts with fuzzy agents from
other communities (in this case it plays other roles).
A fuzzy agent
i

~
by interacting with a fuzzy agent
j

~
of another community then participates in the
same role as
j

~
(5):
)]
~
,
~
()
~
,,
~
,
~
(
~
)
~
,
~
(,
~
~
~
:[
~
~
~
,
~
xijiji
xjxjxi
x






(5)
2.3 Fuzzy Agents Interactions
In multi-agent systems, as in human organizations,
actions, interactions and communications, are
closely linked and interdependent (Jennings, 2000).
Interaction is an exchange between agents and their
environment. This exchange depends on the intrinsic
properties of the world in which agents are active.
Perception of agents may be passive when receiving
messages/signals, or active, when it is the result of
voluntary actions. Communication is an exchange
between the agents themselves, using a language.
A fuzzy interaction


i



between two fuzzy
agents is defined by the following tuple (6):

irsi
s


~
,
~
,
~
,
~
~
~
(6)
where


s
is the fuzzy agent source of the fuzzy
interaction,


r
is the fuzzy agent destination,
s

~
~

is
the fuzzy set of roles played by


s
, and
i

~
is a
fuzzy act of cooperation, and has a goal. Interactions
are fuzzy; also the recipient agent always evaluates
an interaction (fuzzy value) to determine the interest
this interaction can take for it.
For cooperating, agents can express their
intentions using a language derived from the speech
acts theory. In most agent platforms we developed,
fuzzy agents perform five main speech acts:

~
=
{inform, diffuse, ask, reply, confirm}. For
interacting, a fuzzy agent chooses its fuzzy
destination agent according to its intentions, the
context-solving and the state of its acquaintances. A
fuzzy communication act
rs,
~

between two fuzzy
BehaviourofFuzzyAgentswithinaCollaborativeDesignPlatform
243

agents is defined by (7):
 

~
,,
~
,
~
,
~
,
~~
~
,
s
rsrs
(7)
where

~
~

is a fuzzy speech act denoted by a
performative verb,
s

~
is the fuzzy source agent of
communication,
r

~
is the fuzzy receiver agent,

is
a type of message,
s

~
~

is the fuzzy set of roles
played by
s

~
, and

~
is the fuzzy message, which
can be a question, a response, etc.
A fuzzy agent plays roles evolving in function of
its knowledge, its fuzzy competences and its fuzzy
interactions. Thus, fuzzy decision rules
i

~
~

of fuzzy
agent
i

~
are defined by (8):

iiii
~~~~
~
,
~
,
~
~

(8)
where
i

~
~

,
i

~
~

,
i

~
~

,are respectively the set of fuzzy
events that
i

~
can observe, the set of fuzzy
conditions associated to the internal states of
i

~
,
and the set of fuzzy actions that
i

~
can perform.
3 A DESIGN PLATFORM
3.1 Product Configuration Model
Configuration tasks consist of selection,
arrangement of components, and evaluation test: the
configuration is a design problem (Deciu et al.,
2005). Product configuration must consider
explicitly different domain actors and their
perspectives influencing simultaneously the design
of configurable products. Moreover, during the
design for configuration process each product is
customized according to customer’s preferences.
Therefore, product configuration must be able to
deal with various, instable and imprecise
requirements coming from fuzziness of design
problems (Agard and Barajas, 2012). In order to
capture the uncertainty aspects that characterize
design for configuration, the fuzzy sets (Zadeh,
1965) approach can be used.
Configurable product design is a mapping
process between product requirement view,
functional view, physical solution view, process
view and fuzziness of collaborative design process.
Thus a fuzzy approach for searching configuration
structures, performing into three phases, is proposed
(Ostrosi et al., 2012) (Fig. 4):
 Phase 1. Fuzzy relationships in engineering
design: the engineering design models, from
requirements to solutions, necessary for the
configuration of a product, are built.
 Phase 2. Searching the fuzzy set of consensual
solutions: a designer customizes the product based
on particular customer’s requirements and specific
domains’ constraints involved in its production.
Result is a fuzzy set of consensual solutions.
 Phase 3. Fuzzy optimal solution agents based
product configuration: the result is a fuzzy set of
consensus solutions.
Building fuzzy
relationships in
product
configuration
(1)
R, F,
C, S
Fuzzy
consensual
solutions
S
~
Fuzzy optimal
configurations
G
~
Customer
Searching the
fuzzy set of
consensual
solutions
(2)
Generating
fuzzy optimal
product
confi
g
uration
Fuzzy relationships {
i

~
}
R
~
F
~
C
~
S
~
Domains’
expertise
Co-designers
Figure 4: Product configuration approach.
3.2 Fuzzy Agent-based Configuration
Requirements, functions, solutions and constraints
are fuzzy agents, with a degree of membership in
each community defined for the configuration:
specification community, function community,
solution community and constraint community.
Cooperative interactions can occur between fuzzy
agents in the communities of functions and solutions
(intra-communities interactions), or between fuzzy
agents of different communities (inter-communities
interaction).
A fuzzy agent-based platform called FAPIC
(Fuzzy Agents for Product Integrated Configuration)
was developed for product configuration (Fig. 5). In
FAPIC, fuzzy agents are organized in four
communities (9):

~
~
,
~
~
,
~
~
,
~
~
scfr
(9)
Each community has a clear objective, which
determines the main role that fuzzy agents play in
this community (Fougères and Ostrosi, 2013). This
means that each fuzzy agent belongs to a community
of reference in which it plays its main role (10):

 )]
~
,
~
(
~
~
,,,,[
~
~
~
xx
scfrx 


(10)
IJCCI2013-InternationalJointConferenceonComputationalIntelligence
244

C
ommunityoffuzzy
functionagents
C
ommunityoffuzzy
requirementagents
Communityoffuzzy
solutionagents
Communityoffuzzy
constraintagents
Requirements
Constraints
Customer
Domainexperts
Figure 5: Agent-based architecture of FAPIC platform.
4 CASE STUDY
To illustrate the fuzzy agent configuration approach,
a “chair configurable product” is chosen because of
both the simplicity and accessibility of this
illustration. Though a chair is composed of a few
elements, it can be configured in multiple ways
satisfying both customer's requirements and different
experts’ process views (Production, Recycling,
Maintenance, Assembly, and Design).
4.1 Product Configuration
This section gives a detailed illustration for the three
phases of the proposed approach (Fig. 4).
In the first phase (fuzzy agents based systems
building) communities of fuzzy agents are built. In
this case study, 11 fuzzy requirement agents, 4 fuzzy
function agents, 20 fuzzy solution agents, and 44
fuzzy constraint agents, are built. Then, interactions
between fuzzy agents of all communities are built.
The second phase (searching fuzzy set of
consensual solution, see Fig. 8) comprised six steps:
 Step 1: Definition of fuzzy set of requirements.
The fuzzy set of requirements

i
r
~
R
~

for a
particular customer is defined. The fuzzy
requirement agents observe what the requirements
of a particular customer are, and take the
corresponding fuzzy values.
 Step 2: Emergence of fuzzy product functions. It
spells out functions that configuration product will
support. Given the fuzzy set of customer
requirements, the fuzzy set of product function
agents are computed using the fuzzy relationship
between requirement agents and product function
agents. These agents are called active functions.
 Step 3: Emergence of fuzzy set of solutions.
Solutions agents will be activating as soon as the
set of active function agents emerge. Agents
interact to compute the fuzzy set of solutions,
called active solutions. Active solutions are
computed from interaction between the set of
active function agents and solution agents.
 Steps 4 and 5: Definition and integration of fuzzy
set of constraints. Constraints of different process
views are defined. The constraints agents observe
what the requirements of a particular process view
are and they decide to take the corresponding
fuzzy values.
 Step 6: Emergence of consensual fuzzy set of
solutions. Constraint agents interact with active
solution agents to converge towards a consensual
fuzzy set of solutions (respecting both of
requirements through functions and constraints).
In the third phase (fuzzy optimal solution for
configuration), the consensual solution agents
through their interactions, using their affinities from
the fuzzy solution agents’ structure, are structured
into modules. The fuzzy optimal solution agents
represent a network of fuzzy solution agents which
maximise the objective function. Results of this
phase are given in Fig. 6. For instance, considering
the solution agent s1 as solution for the class Cl
1
, its
optimal network is formed by the solution agents
[s1, s6,
, s16], with value of objective equal to 1.8.
O
p
timal confi
g
uration
<s1>
0.6
<s6>
0.6
<s16>
0.6
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20
[s1  s
i
] = [ 0 0 0 0 0 0.7 0.6 0.5 0.5 0.5 0 0 0 0 0 0.7 0.7 0.6 0.7 0.6 ]
s6 - Square
s1 - Square
s16 – Staight_a
<s1> Agent’s local
point of view

a) Configuration 4 : {s
1
, s
6
, s
16
}

Figure 6: Configuration: local point of view of agent <s1>.
4.2 Fuzzy Roles
Considering the set


scfr
~
,
~
,
~
,
~
~
 
of four roles
defined in FAPIC: roles of specification, function,
constraint, and solution. Then, the fuzzy set of roles
an agent
i

~
plays is defined by (11):


)
~
(),
~
(),
~
(),
~
()
~
(
~
i
s
i
c
i
f
i
r
i
~~~~



(11)
BehaviourofFuzzyAgentswithinaCollaborativeDesignPlatform
245

Figure 7 shows one of the typical partitioning
proposed for the six fuzzy roles of product
configuration: the repartition for the role “solution”.
0 1 2 4 8 12 20 30 50 80 180 1000
1
0
µ
1s
(
i

~
)
Nb of exchanges of 
i
with agents of the solution community
µ
2s
(
i

~
) µ
3s
(
i

~
)
Figure 7: Membership function of
i

~
to the role
“solution”.
In this diagram, the universe Us is defined by the
number of exchanges of
i

~
with agents of the
solution community. 3 fuzzy subsets 1
s
, 2
s
and 3
s
are defined, meaning respectively “fuzzy agent plays
little role”, “fuzzy agent plays moderate role” and
“fuzzy agent plays important role” (12-14):







0/1000 0/180, 0/80, 0/50, 0/30,
0.1/20, 0.3/12, 0.6/8, 1/4, 1/2, 0.8/1, 0/0,
1
s

(12)







0/1000 0/180, 0.1/80, 0.5/50, 1/30,
0.5/20, 0.3/12, 0.1/8, 0/4, 0/2, 0/1, 0/0,
2
s

(13)







0/1000 0.8/180, 0.4/80, 0.1/50,
0/20,0/30, 0/12, 0/8, 0/4, 0/2, 0/1, 0/0,
3
s

(14)
with µ
1s
(
i
), the membership function of
i

~
in the
fuzzy subsets "little role"; µ
2s
(
i

~
), the membership
function of
i

~
in the fuzzy subsets "moderate role"
and µ
3s
(
i

~
), the membership function of
i

~
in the
fuzzy subsets “strong role”.
Table 1 illustrates the behaviour of fuzzy agents.
For instance, let us consider the decision rule
i

~
:
(i)
1
~

:= <inform,
i
f
~
 ,
k
r
~
 , t = 2, V> ;
(ii)
1
~

:= <V = sup(0.4)> ;
(iii)
1
~

:= <diffuse,
i
f

~
,
F
~
, t=2, V>.
This rule means that: (i) depending on fuzzy
event
1
~

: the fuzzy agent
i
f

~
(

~~
,
~
~
FF
i
f

, is a
function agent) receives a message of type t whose
value is equal to 2 by which a fuzzy agent
k
r

~
(

~
R
~
,R
~
~
k
r

, is a requirement agent) informs
i
f

~
of its value V; (ii) under condition
1
~

“V must be
greater than the threshold value 0.4”; (iii) then action
1
~

is triggered: agent
i
f

~
communicates this
information to all function agents of the set
F
~
.
Let us consider the Phase 2 of the configuration
Table 1: Behaviour of fuzzy agents and evolution of fuzzy roles during the step 2 of phase 2.
Behaviour of a fuzzy agent
Illustration with the fuzzy function agent
1
f
~

1) Receiving a message OR
observing its environment
1) Event
1
~

: receiving “inform
)8.0)
~
(,7.0,V,
~
,
~
(
1
1
r11
r
~
fr






”
2) Computing interest (fuzzy
degree) of the message or the
observation
2) Knowledge of
1
f
~
 :


1
f
~
 = 0.9 ; )
~
,
~
(
11
fr
 = 0.7 ;












0
~
,5.0
~
,1
~
,5.0
~~
~
1c1s1f1r1
f
~
f
~
f
~
f
~
f
 

Interest =






)
~
(,
~
),
~
,
~
(,
~
min
11r111
rf
~
frf


= 0.5
3) Updating fuzzy values of roles
from the cooperative activity of the
message sender, or in connection
with observation
3) Message interest > 0.4 then changing fuzzy value of role “Requirement” :






6.0)
~
,
~
(,
~
moy
~
111r1r
frf
~
f
~
 

4) Consulting fuzzy rule-base and
selecting fuzzy rules to be
triggered (see scenario below)
4) Two kinds of rules can be triggered after the event
1
~

:
4.1) related to the communication protocol: inform/confirm ;
4.2) related to the conditions : message interest (> 0.4), roles




)4.0
~
4.0
~
(
1f1r
f
~
f
~








, transmitted value
)4.0)
~
(4.0V(
1
1
r
r
~






5) Triggering fuzzy rules:
construction and implementation
of actions associated with the
selected fuzzy rules
5) 2 communication acts are performed :
5.1) confirm
)1)
~
(,7.0,V,
~
,
~
(
1
1
r11
f
~
rf






5.2) diffuse
)6.0)
~
(,7.0,V,F
~
,
~
(
1
1
r1
f
~
f
 

IJCCI2013-InternationalJointConferenceonComputationalIntelligence
246

process and the fuzzy agents r1, f1, c1 and s1 (traced
agents) (Fig. 8). The fuzzy values of roles played by
an agent
i

~
are calculated by the formula (15):

1
aeae
nnnn
(15)
where n
e
is the number of exchanges between
i

~
and agents of the community corresponding to
the target role and n
a
is the number of agents in the
community corresponding to the target role.
F
–
{f
1
}
S
–
{s
1
}
:r
1
:
f
1
:
c
11
:s
1
1
2
2
3
3
5
4
5
R
–
{
r
1
}
C
–
{c
11
}
6
Figure 8: Illustration of Phase 2: Searching the fuzzy set of
consensual solution agents.
The following tables (Table 2-7) show the change
step by step of the fuzzy values of agents’ roles
during the Phase 2. These tables indicate for each
step of the Phase 2 and each of the four tracks agents


11111
s
~
andc
~
,f
~
,r
~
: 1) the number of exchanges
between these fuzzy agents and other fuzzy agents
of FAPIC (inter or intra-community interactions)
S
~
/S
~
,S
~
/C
~
,C
~
/C
~
,S
~
/F
~
,F
~
/F
~
,F
~
/R
~
,R
~
/R
~
), and 2) the
fuzzy values of the different fuzzy roles played by
the fuzzy agents (a vector of fuzzy roles
corresponding to

scfr
~
,
~
,
~
,
~
~
 
).
Table 2: Fuzzy values of agents’ roles during the step 1.
Agent R/R R/F F/F F/S
C
/C C/S S/S Roles
1
r
~
10 - - - - - - [0.5,0,0,0]
1
f
~
- - - - - - - [0,0,0,0]
11
c
~
- - - - - - - [0,0,0,0]
1
s
~
- - - - - - - [0,0,0,0]
Table 3: Fuzzy values of agents’ roles during the step 2.
Agent R/R R/F F/F F/S
C
/C C/S S/S Roles
1
r
~
10 1 - - - - - [0.5,0.2,0,0]
1
f
~
- 1 3 - - - - [0.1,0.5,0,0]
11
c
~
- - - - - - - [0,0,0,0]
1
s
~
- - - - - - - [0,0,0,0]
Table 4: Fuzzy values of agents’ roles during the step 3.
Agent R/R R/F F/F F/S C/C
C
/S S/S Roles
1
r
~
10 1 - - - - - [0.5,0.2,0,0]
1
f
~
- 1 3 1 - - - [0.1,0.6,0,0.1]
11
c
~
- - - - - - - [0,0,0,0]
1
s
~
- - - 1 - - 19 [0,0.2,0,0.5]
Table 5: Fuzzy values of agents’ roles during the step 4.
Agent R/R R/F F/F F/S C/C C/S S/S Roles
1
r
~
10 1 - - - - - [0.5,0.2,0,0]
1
f
~
- 1 3 1 - - - [0.1,0.6,0,0.1]
11
c
~
- - - - 27 - - [0,0,0.5,0]
1
s
~
- - - 1 - - 19 [0,0.2,0,0.5]
Table 6: Fuzzy values of agents’ roles during the step 5.
Agent R/R R/F F/F F/S C/C C/S S/S Roles
1
r
~
10 1 - - - - - [0.5,0.2,0,0]
1
f
~
- 1 3 1 - - - [0.1,0.6,0,0.1
]
11
c
~
- - - - 27 1 - [0,0,0.5,0.1]
1
s
~
- - - 1 - 1 38 [0,0.2,0.1,0.7
]
Table 7: Fuzzy values of agents’ roles during the step 6.
Agent R/R R/F F/F F/S C/C C/S S/S Roles
1
r
~
10 1 - - - - - [0.5,0.2,0,0]
1
f
~
- 1 3 1 - - - [0.1,0.6,0,0.1]
11
c
~
- - - - 27 1 - [0,0,0.5,0.1]
1
s
~
- - - 1 - 1 57 [0,0.2,0.1,0.8]
Finally, after a full configuration, we get for fuzzy
agents r
1
, f
1
, c
11
and s
1
(our reference agents), the
number of inter/intra-communities exchanges and
the fuzzy values of roles given in Table 8.
Table 8: Fuzzy values of roles at the end of process.
Agent R/R R/F F/F F/S C/C C/S S/S Roles
1
r
~
220 44 - - - - - [1,0.9,0,0]
1
f
~
- 11 66 220 - - - [0.5,1,0,0.9]
11
c
~
- - - - 1512 560 - [0,0,1,0.9]
1
s
~
- - - 80 - 560 12800 [0,0.9,0.9,1]
This analysis shows that organizations in the
proposed agent-based system FAPIC are fuzzy
evolving systems. Indeed, dynamic adaptive
BehaviourofFuzzyAgentswithinaCollaborativeDesignPlatform
247

organizations emerge from the fuzzy interaction of
heterogeneous fuzzy agents and their fuzzy roles.
The analysis of the behaviour of fuzzy agents during
design collaborations has shown that the distribution
of roles played by fuzzy agents is continually
changing. Fuzzy agents are characterised by fuzzy
organizations. The last one is the result of agents’
fuzzy roles and their fuzzy interactions.
5 CONCLUSIONS
In previous work we have already shown that
collaborative design is characterized by fuzzy
interactions, heterogeneous, and evolving
organizations (Fougères and Ostrosi, 2011). In this
paper, the modelling of fuzzy agents, their fuzzy
interactions, their fuzzy roles, and their fuzzy
organization, are presented. During the collaborative
design process, fuzzy agents grouped in
communities interact and play fuzzy roles for
converging to solutions of design.
A simple case study of “chair configuration”
illustrates clearly our fuzzy agent-based approach.
The analysis of fuzzy agents’ roles during the
collaborative configuration process shows that
organizations within FAPIC platform are fuzzy
evolving systems. Indeed, dynamic adaptive
organizations emerge from the fuzzy interactions of
heterogeneous fuzzy agents and their fuzzy roles.
Furthermore, the analysis of fuzzy agents’ behaviour
during this collaborative design shows that the
distribution of roles played by fuzzy agents is
continually changing. Fuzzy agents are characterised
by fuzzy organization which is the result of fuzzy
roles of fuzzy agents and their fuzzy interactions.
We continue to work on a better understanding
of self-organization of fuzzy agents and on the level
changes of their behaviour during collaborative
design activities. The current extension of FAPIC
platform to other design tasks offers an experimental
context to test the evolution of our model.
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