Residuated Multilattice as set of Truth Values for Fuzzy Rough Sets

TL;DR

This paper extends fuzzy rough set theory by introducing residuated multilattices as the set of truth values, enabling more flexible modeling of uncertainty in fuzzy rough sets.

Contribution

It generalizes previous work by using residuated multilattices instead of lattices, defining new classes of fuzzy rough sets, and exploring their properties.

Findings

Defined $M$-fuzzy rough sets using residuated multilattices.

Introduced multiple classes of $M$-fuzzy rough sets based on binary relations.

Analyzed properties of these classes.

Abstract

In 2004 Anna Maria Radzikowska et al \cite{RK2004} investigated the fuzzy rough sets where the set of truth values is an arbitrary residuated lattice. In this paper, we extend their work by considering a residuated multilattice $M$ as the set of truth values. $M$-fuzzy rough sets are defined using the residuation operators provided by residuated multilattice $M$. Depending on classes of binary fuzzy relations, we define several classes of $M$-fuzzy rough sets and investigate some properties of these classes.