Multi-class granular approximation by means of disjoint and adjacent fuzzy granules

TL;DR

This paper introduces disjoint and adjacent fuzzy granules for multi-class granular approximation, enhancing classification by maintaining decision region separation and coverage, with efficient computation methods demonstrated.

Contribution

It presents new concepts of disjoint and adjacent granules, extending granular approximations to multi-class classification and providing efficient calculation methods.

Findings

Disjoint and adjacent granules improve class separation and coverage.

Multi-class granular approximation effectively handles multi-class problems.

Efficient algorithms for Lukasiewicz fuzzy connectives are provided.

Abstract

In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multi-class granular approximations for {\L}ukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.