On the property of T-distributivity

Kesicioglu M. N.

FIXED POINT THEORY AND APPLICATIONS, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1687-1812-2013-32
  • Dergi Adı: FIXED POINT THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

In this paper, we introduce the notion of T-distributivity for any t-norm on a bounded lattice. We determine a relation between the t-norms T and T', where T' is a T-distributive t-norm. Also, for an arbitrary t-norm T, we give a necessary and sufficient condition for T-D to be T-distributive and for T to be T-boolean AND-distributive. Moreover, we investigate the relation between the T-distributivity and the concepts of the T-partial order, the divisibility of t-norms. We also determine that the T-distributivity is preserved under the isomorphism. Finally, we construct a family of t-norms which are not distributive over each other with the help of incomparable elements in a bounded lattice.