The algebraic structures of the families of fuzzy sets that arise out of various notions of openness and closedness in a double fuzzy topological space are investigated. The collection of these families forms a bounded, associative lattice. The zero divisors and zero-divisor graph of this lattice are also identified.

中文翻译：

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与双模糊拓扑空间有关的某些代数结构

研究了在双重模糊拓扑空间中由各种开放性和封闭性概念引起的模糊集族的代数结构。这些族的集合形成了一个有界的，关联的格子。还确定该晶格的零除数和零除数图。