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

作     者：Palangetić, Marko Cornelis, Chris Greco, Salvatore Slowiński, Roman 

作者机构：Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Department of Economics and Business University of Catania Catania Italy  University of Portsmouth Portsmouth United Kingdom Institute of Computing Science Poznań University of Technology Poznań Poland Systems Research Institute Polish Academy of Sciences Warsaw Poland 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Fuzzy sets 

摘      要：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 Lukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts. Copyright © 2022, The Authors. All rights reserved.