• Korean Journal of Mathematics
• /
• v.19 no.2
• /
• pp.219-232
• /
• 2011

We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.4
• /
• pp.299-304
• /
• 2011

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.2
• /
• pp.135-148
• /
• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.

• Korean Journal of Mathematics
• /
• v.20 no.1
• /
• pp.61-75
• /
• 2012

We investigate the properties of various frames and connections on partially ordered sets. In particular, we study the relations between various connections and various frames.

• Honam Mathematical Journal
• /
• v.22 no.1
• /
• pp.77-82
• /
• 2000

After considering an equivalence relation on a directed preordered set, we construct an isomorphism between derived limits of inverse systems indexed by the directed (pre)ordered sets.