Journal
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B
Volume 37, Issue 4, Pages 563-582Publisher
ZHEJIANG UNIV PRESS
DOI: 10.1007/s11766-022-4100-y
Keywords
fuzzy rough set; fuzzy approximation space; fuzzy ideal approximation space; r-fuzzy separation axioms; r-fuzzy connectedness; r-fuzzy compactness
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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.
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.
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