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Rough Sets: Introduction, History and Selected Applications (Tutorial Lecture — Extended Abstract)

Dutta Soma, Ciucci Davide

Annals of Computer Science and Information Systems

2023

Vol. 35

69--70

The aim of this tutorial is to present a brief overview of the theory of rough sets from the perspective of its mathematical foundations, history of development, as well as connections with other branches of mathematics and informatics. The content concerns both the theoretical and practical aspects of applications. The above mentioned target of the tutorial will be covered in two parts. In the first part we would aim to present the introduction to rough sets and the second part will focus on the connections with other branches of mathematics and informatics. In particular, in the second part, we will discuss the connections of rough sets with logics, topology and algebra, and graph theory (when it comes to mathematics), as well as knowledge representation, machine learning and data mining, and theoretical computer science (when it comes to informatics).

Three-way Learnability: A Learning Theoretic Perspective on Three-way Decision

Campagner Andrea, Ciucci Davide

Annals of Computer Science and Information Systems

2022

Vol. 30

243--246

In this article we study the theoretical properties of Three-way Decision (TWD) based Machine Learning, from the perspective of Computational Learning Theory, as a first attempt to bridge the gap between Machine Learning theory and Uncertainty Representation theory. Drawing on the mathematical theory of orthopairs, we provide a generalization of the PAC learning framework to the TWD setting, and we use this framework to prove a generalization of the Fundamental Theorem of Statistical Learning. We then show, by means of our main result, a connection between TWD and selective prediction.