# Bounded Fuzzy Possibilistic Method

## TL;DR

The paper introduces the Bounded Fuzzy Possibilistic Method (BFPM), a novel clustering approach that relaxes traditional membership constraints, allowing objects to have full memberships in multiple clusters, enhancing overlap handling and data object tracking.

## Contribution

BFPM is a new clustering method that relaxes membership restrictions, enabling objects to fully belong to multiple clusters, improving overlap analysis and data behavior tracking.

## Key findings

- BFPM effectively handles overlapping clusters.
- BFPM improves accuracy in various application domains.
- BFPM enables analysis of object movement between clusters.

## Abstract

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.