A subresiduated lattice is a pair (A, D), where bounded distributive lattice, D sublattice of and for every $$a,b\in A$$ there $$c\in D$$ such that all $$d\in , $$d\wedge a\le b$$ if only $$d\le c$$ . This c denoted by $$a\rightarrow can be regarded as an algebra $$\left$$ type (2, 2, 0, 0) $$D=\{a\in A\mid 1\rightarrow a=a\}$$ The class lattices variety ...

In this paper a new class of fuzzy sets, namely r-(τi, τj)-θ-generalized fuzzy closed sets is introduced for smooth bitopological spaces. This class falls strictly in between the class of r-(τj, τi)fuzzy θ-closed sets and the class of r-(τi, τj)generalized fuzzy closed sets. Furthermore, by using the class of r-(τi, τj)-θgeneralized fuzzy closed sets we establish a new fuzzy closure operator wh...

We explore a pointfree theory of bitopological spaces (that is, sets equipped with two topologies). In particular, here we regard finitary biframes as duals spaces. particular for biframe $$\mathcal {L}$$ the ordered collection all its bisubspaces (i.e. biquotients) is studied. It shown that this in three meaningful ways. it that, apart from assembly , there are other structures $$\mathsf {A}_{...