t-closure Operators


Ince M. A. , KARAÇAL F.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, cilt.48, ss.139-156, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 48 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/03081079.2018.1549041
  • Dergi Adı: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Sayfa Sayıları: ss.139-156

Özet

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.