On the T-partial order and properties


AŞICI E. , KARAÇAL F.

INFORMATION SCIENCES, cilt.267, ss.323-333, 2014 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Cilt numarası: 267
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.ins.2014.01.032
  • Dergi Adı: INFORMATION SCIENCES
  • Sayfa Sayıları: ss.323-333

Özet

For a t-norm Ton [0, 1], a partial order T was recently defined and studied. In this study, for any fixed cc (0, I), we define the set of incomparable elements according to <=(T) and this set is deeply investigated. By means of the equivalence relation, defined in [14], it is shown the set [0,1]/ similar to, denoting the set of all equivalence classes on t-norms on [0,1] is uncountably infinite. Finally, with the help of any t-norm Ton [0, 1], it is obtained that the family (T-lambda)(lambda is an element of(0,1)) of t-norms on [0,1]. If T is a divisible t-norm, then it is obtained that ([0, 1], <=(T),) is a lattice. Thus, we give an answer to an open problem in [10]. (C) 2014 Elsevier Inc. All rights reserved.