Quality & Quantity 36: 239–257, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
A Fuzzy Clustering Algorithm Based on the
Analogy with Mechanical Physics: MeccFuz
and FABRIZIO GUERRISI
Genoa University, Italy
Abstract. This paper presents a new algorithm of fuzzy clustering, based on analogy with mechanics
physics. The vectors x
are compared with ‘material points’ and the clusters can be looked on as
material points clouds, that are characterized by speciﬁc units. The choice is based on a study of
potential energy. Once a speciﬁc unit is chosen, we calculated the membership of the other units whit
A study of a sociology test is performed and the results are very encouraging, though an further
deepening is needed like a thermodynamics analogy application.
Key words: fuzzy clustering, cluster analysis, fuzzy logic, social research, membership ranks,
gerarchical agglomerative techniques, graphs theory, human sciences
Cluster analysis, or analysis of sets, is a family of tools that bases its hypo-
theses on the similarity between elements membership of the same subset and the
dissimilarity of these elements from cases membership of other subsets.
The widespread dissatisfaction for traditional cluster analysis techniques, which
entail an exclusive pertinence to the clusters, led to the creation of algorithms
able to overcome this limitation. In other words, it is not more a matter of Aris-
tothelic or Boolean logic, on which the classical techniques of cluster analysis are
based on, but a matter of fuzzy logic. This last approach avoids considering the
non-contradiction principle and the third-excluded principle, resulting in a more
‘elastic’ logic. Fuzzy logic implies that a certain element is not forced to be a
member of a set in an entire or null way, but it can be partially included in the set
Owing to the fact that the human being cannot be easily bounded into closed
categories excluding one from another, but is something more complex as well
as different from the classiﬁcation, when dealing with social research a cluster
analysis, which has to start from assumptions being as realistic as possible. The
risk linked to reducing people interviewed in clusters being similar to the ones that
This paper belongs to thesis disputed in the Faculty of Formation Sciences of Genoa University