On the property of T-distributivity
FIXED POINT THEORY AND APPLICATIONS, 2013 (SCI-Expanded, Scopus)
- 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.