In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of R∩R−1 does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we...

We show that with any finite partially ordered set, P , one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.

In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of R∩R does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we d...

This article describes the solvability of HornSAT and CNFSAT. Unsatisfiable HornCNF have partially ordered set that is made by causation of each clauses. In this partially ordered set, Truth value assignment that is false in each clauses become simply connected space. Therefore, if we reduce CNFSAT to HornSAT, we must make such partially ordered set in HornSAT. But CNFSAT have correlations of e...

We report the direct soft chemical synthesis and characterization of a family of face centered cubic (fcc) and partially ordered face centered tetragonal (fct) FePt nanoparticles (NPs) suitable for biomedical applications. Both fcc and partially ordered fct-FePt NPs are synthesized by employing a simple polyol method. By using polyvinyl pyrolidone (PVP) as a stabilizer in various ratios during ...

We report the direct soft chemical synthesis and characterization of a family of face centered cubic (fcc) and partially ordered face centered tetragonal (fct) FePt nanoparticles (NPs) suitable for biomedical applications. Both fcc and partially ordered fct-FePt NPs are synthesized by employing a simple polyol method. By using polyvinyl pyrolidone (PVP) as a stabilizer in various ratios during ...

Molodtsov [2] introduced the soft set theory. Moreover Babitha and Sunil [5], [6] introduced partially ordered soft set. In this study we improve orderings on soft sets by giving new definitions such as filtered soft set, soft lattice, complete soft lattice, and some results related these definitions are studied.