Representations of L-fuzzy rough approximation operators

In recent years, there has been tremendous interest in developing lattice-valued rough set theory. In this framework, we primarily take into account the following two problems. Firstly, we include the well-known intuitionistic, interval-valued, neutrosophic and Pythagorean fuzzy rough sets into the framework of lattice-valued rough sets. Specifically, the four kinds of rough sets can be considered as special lattice-valued rough sets. Secondly, based on a completely distributive lattice L, we provide representations of the upper and lower L-fuzzy rough approximation operators by using four kinds of cut sets of an L-fuzzy set and an L-fuzzy relation, which generalizes the existing results in the case that L = [0, 1]. In particular, we show that representations of intuitionistic and interval-valued fuzzy rough approximation operators provided by Zhou and Sun are special examples of our proposed representations.

Automated summary

There has been a growing interest in the development of lattice-valued rough set theory in recent years. This framework includes various types of rough sets, such as intuitionistic, interval-valued, neutrosophic, and Pythagorean fuzzy rough sets. Additionally, representations of fuzzy rough approximation operators based on a completely distributive lattice are provided, extending the existing results for the case when the lattice is [0,1]. It is shown that the representations of intuitionistic and interval-valued fuzzy rough approximation operators proposed by Zhou and Sun are special cases of the proposed representations.