T-closure Operators. Issue 2 (17th February 2019) - İnce, Mehmet Akif; Karaçal, Funda
Abstract : In this study, based on the knowledge of the existence of t-norms on an arbitrary given bounded lattice, we introduce t-closure operators with the help of a t-norm on the lattice and a subset of the lattice including the top element. We define two equivalence relations by using t-closure operators. The first one is on the set of all t-norms on a bounded lattice. An important class is obtained according to this relation. We define a partially order on the set of all equivalent relations given as secondly. Further, we define a set, denoted byL ∗, and by using this set, we investigate under which conditions L can be embedded intoL C A, T . We obtain a topology by using t-closure operators and examine some properties of this topology. Lastly, we generalizeT − partial order.