t-closure Operators

Ince M. A., Karaçal F.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.48, no.2, pp.139-156, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1080/03081079.2018.1549041
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.139-156
  • Keywords: Closure operator, triangular norm, bounded lattice, NORMS
  • Recep Tayyip Erdoğan University Affiliated: Yes


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 by , and by using this set, we investigate under which conditions L can be embedded into . We obtain a topology by using t-closure operators and examine some properties of this topology. Lastly, we generalize partial order.