  This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing
several issues that previous clustering/classification methods have not
considered. In fuzzy clustering, object's membership values should sum to 1.
Hence, any object may obtain full membership in at most one cluster.
Possibilistic clustering methods remove this restriction. However, BFPM differs
from previous fuzzy and possibilistic clustering approaches by allowing the
membership function to take larger values with respect to all clusters.
Furthermore, in BFPM, a data object can have full membership in multiple
clusters or even in all clusters. BFPM relaxes the boundary conditions
(restrictions) in membership assignment. The proposed methodology satisfies the
necessity of obtaining full memberships and overcomes the issues with
conventional methods on dealing with overlapping. Analysing the objects'
movements from their own cluster to another (mutation) is also proposed in this
paper. BFPM has been applied in different domains in geometry, set theory,
anomaly detection, risk management, diagnosis diseases, and other disciplines.
Validity and comparison indexes have been also used to evaluate the accuracy of
BFPM. BFPM has been evaluated in terms of accuracy, fuzzification constant
(different norms), objects' movement analysis, and covering diversity. The
promising results prove the importance of considering the proposed methodology
in learning methods to track the behaviour of data objects, in addition to
obtain accurate results.
