T-closure Operators. Issue 2 (17th February 2019)

• Record Type: Journal Article
• Authors: İnce, Mehmet Akif; Karaçal, Funda
• Is Part Of: International journal of general systems. Volume 48:Issue 2(2019)
• Page Start: 139
• Page End: 156
• Publication Date: 2019-02-17
• Subjects: Closure operator -- triangular norm -- bounded lattice; 06B99 -- 06A15; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2018.1549041
• Languages: English
• ISSNs: 0308-1079

Abstract

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.