One axiom characterization for (L, M)-fuzzy rough approximation operators

Document Type : Regular Articles

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Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt.

10.21608/sjsci.2025.408231.1298

Abstract

A thorough comprehension of the single axiomatic characterization governing fuzzy rough approximation operators is crucial for delving deeper into the foundational principles of rough set theory. By analyzing these operators through an axiomatic lens, researchers can gain valuable insights into the structural and theoretical underpinnings of rough sets, enabling more rigorous exploration of their conceptual framework. This paper focuses on developing a single axiom to characterize each kind of M-level L-rough approximation operators or (L, M)-fuzzy rough approximation operators (LM-Rapprox operators for short) produced by non-increasing, unary, reflexive, serial, and transitive LM-fuzzy G neighborhood system (LM-fgns for short), as well as their compositions. Finally, we discuss the relationship between the LM-Rapprox operators and the LM-quasi fuzzy topologies. Specifically, it demonstrates that the lower and upper LM-Rapprox operators derived from LM-fgns correspond to a pair of LM-quasi-fuzzy interior and LM-fuzzy closure operators, respectively.

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