Fuzzy rough sets in Sostak sense

In this paper, we defined the fuzzy operator Phi(lambda), in a fuzzy ideal approximation space (X, R, I) associated with a fuzzy rough set lambda in Sostak sense. Associated with Phi (lambda) , there are fuzzy ideal interior and closure operators int Phi (lambda), and cl Phi (lambda) respectively. r-fuzzy separation axioms, r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces. There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces. Lastly, using a fuzzy grill, we will get the same results given during the context.

Automated summary

This paper investigates the fuzzy operator Phi(lambda) and its associated fuzzy ideal interior and closure operators in a fuzzy ideal approximation space. It compares these concepts with their counterparts in fuzzy approximation spaces and highlights the differences. The paper also defines and examines r-fuzzy separation axioms, r-fuzzy connectedness, and r-fuzzy compactness in fuzzy ideal approximation spaces.