Compatible Relatively dual weakly complemented lattice

Key Points

• The aim is to introduce and analyze the properties of relatively dual weakly complemented lattices, particularly focusing on compatibility and filters.
• Defined relatively dual weakly complemented (RDWC) lattices within bounded lattices.
• Investigated algebraic properties of RDWC and compatible RDWC lattices.
• Studied relative closed and dense sets of elements.
• Defined various types of filters on compatible RDWC lattices and explored their relationships.
• Introduced the concept of compatible RDWC lattices and their defining characteristics.
• Established relationships between different types of filters in compatible RDWC lattices.
• Outlined the fundamental algebraic properties of the newly defined lattices.