![](bg8.png)
5.4 Quality Criteria for
{none < few < much < a lot}
The value set {none < few < much < a lot} is a to-
tally ordered set of values. With such a value set, the
propagated influence on a path is usually defined as a
min and the propagated influence as a max. Since this
value set contains very few values, the notion of com-
patible values may not be as useful for this value set
as for the value set [−1; 1]. However, we can still list
the values that are compatible with a specific value,
as we did for the set {+, ⊕, 0, , −, ?}. One easy way
to do this is to use the total order between the values.
This order can indeed by used to define a distance be-
tween the values. We can then use again a threshold
such that, if the distance between two values is lesser
than or equal to this threshold, then these two values
are compatible according to this threshold.
6 CONCLUSIONS
We have presented a way to validate cognitive maps
by introducing four different kinds of quality criteria
for cognitive maps defined on the value set {+, −}.
We have so introduced two kinds of verification cri-
teria, the cleanliness and the non-ambiguity and two
kinds of test criteria, the coherency and the compat-
ibility. We have also proposed a way to adapt these
criteria to other value sets such as [−1; 1].
We have tested our criteria on cognitive maps rel-
ative to fishing (Christiansen, 2011). Our criteria de-
tect the contradictions spotted by the authors as well
as others contradictions that may be interesting to
study. To do so, we developed a software that im-
plements the quality criteria in order to automatically
validate a cognitive map (Le Dorze, 2013).
As for now, our approach can only inform a de-
signer that its map does or does not validate a specific
quality criterion. It does not tell the user where are
the contradictions spotted by the criterion and how to
correct them. Our current research are leading on this
point.
REFERENCES
Axelrod, R. M. (1976). Structure of decision: the cognitive
maps of political elites. Princeton, NJ, USA.
Ayel, M. and Laurent, J.-P. (1991). Validation, verification
and test of knowledge-based systems. John Wiley &
Sons, Inc., New York, NY, USA.
Celik, F. D., Ozesmi, U., and Akdogan, A. (2005). Par-
ticipatory Ecosystem Management Planning at Tu-
zla Lake (Turkey) Using Fuzzy Cognitive Mapping.
eprint arXiv:q-bio/0510015.
Chauvin, L., Genest, D., and Loiseau, S. (2009). Ontologi-
cal Cognitive Map. International Journal on Artificial
Intelligence Tools, 18(5):697–716.
Christiansen, G. (2011). Modélisation du savoir portée par
les acteurs d’un système : application aux pêcheurs à
la coquille en rade de Brest. Master’s thesis, Agro-
campus Ouest, Saint-Brieuc, France.
Dibie-Barthélemy, J., Haemmerlé, O., and Loiseau, S.
(2001). Refinement of Conceptual Graphs. In Del-
ugach, H. S. and Stumme, G., editors, ICCS 2001,
volume 2120 of Lecture Notes in Computer Science,
pages 216–230. Springer.
Dickerson, J. A. and Bart, K. (1994). Virtual Worlds as
Fuzzy Cognitive Maps. Presence, 3(2):73–89.
Ginsberg, A. (1988). Knowledge-Base Reduction: A New
Approach to Checking knowledge Bases for Inconsis-
tency and Redundancy. In Shrobe, H. E., Mitchell,
T. M., and Smith, R. G., editors, AAAI 1988, pages
585–589. AAAI Press / The MIT Press.
Kosko, B. (1986). Fuzzy cognitive maps. International
Journal of Man-Machines Studies, 24:65–75.
Le Dorze, A. (2013). Validation, synthèse et paramétrage
des cartes cognitives. PhD thesis, LERIA, Université
d’Angers, France.
Levi, A. and Tetlock, P. E. (1980). A Cognitive Analysis of
Japan’s 1941 Decision for War. The Journal of Con-
flict Resolution, 24(2):195–211.
Poignonec, D. (2006). Apport de la combinaison cartogra-
phie cognitive/ontologie dans la compréhension de la
perception du fonctionnement d’un écosystème récifo-
lagonaire de Nouvelle-Calédonie par les acteurs lo-
caux. PhD thesis, ENSA Rennes, France.
Satur, R. and Liu, Z.-Q. (1999). A Contextual Fuzzy Cogni-
tive Map Framework for Geographic Information Sys-
tems. IEEE Transactions on Fuzzy Systems, 7(5):481–
494.
Tolman, E. C. (1948). Cognitive maps in rats and men. The
Psychological Review, 55(4):189–208.
Wellman, M. P. (1994). Inference in cognitive maps. Math-
ematics and Computers in Simulation, 36(2):137–148.
Zhou, S., Zhang, J. Y., and Liu, Z.-Q. (2003). Quotient
FCMs – A Decomposition Theory for Fuzzy Cog-
nitive Maps. IEEE Transactions on Fuzzy Systems,
11(5):593–604.
ValidationofaCognitiveMap-DefinitionofQualityCriteriatoDetectContradictionsinaCognitiveMap
327