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Many-Level Abstract Approximation Spaces
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DOI：10.22130/scma.2025.2058867.2160.png)
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Abstract
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A many-level abstract approximation system on a quantale L is introduced and studied. Based on this fact, a pair of lower quantic and upper quantic M-approximation operators is specified and discussed. In addition, the concepts of an Alexandrov M-Hutton quasi-fuzzy topology and an Alexandrov M-Hutton fuzzy co-topology on L are introduced. Moreover, the relationships between them and a lower quantic M-approximation operator (a lower QM-ApprX operator for short) and an upper quantic Mapproximation operator (an upper QM-ApprX operator for short) are discussed, respectively. Furthermore, the notion of an M-open structure and its relationships with a lower QM-ApprX operator and the concept of an M-closed structure are established.
Keywords:
Quantale
M-closed sets
Upper approximation oper-ator
Lower approximation operator
LM-fuzzy topological spaces
LM-fuzzy co-topological spaces
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