boolean OR-distributive n-ary semicopulas on lattices

Khadjiev D., KARAÇAL F.

FUZZY SETS AND SYSTEMS, vol.284, pp.78-88, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 284
  • Publication Date: 2016
  • Doi Number: 10.1016/j.fss.2015.04.008
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.78-88
  • Karadeniz Technical University Affiliated: Yes

Abstract

In the present paper, definitions of an n-ary semicopula on a bounded lattice L, a boolean OR-distributive n-ary semicopula on L and an infinite boolean OR-distributive n-ary semicopula on L are introduced. A relation between the set of all bounded lattices L with a boolean OR-distributive n-ary semicopula on L and the set of all bounded lattices L with a boolean OR-distributive m-ary semicopula on L, where 2 <= n, 2 <= m, n not equal m, is obtained. The method is given for investigation of the following questions: a description of all bounded lattices L such that every n-ary semicopula on Lis boolean OR-distributive and a description of all complete lattices L such that every n-ary semicopula on Lis infinite boolean OR-distributive. (C) 2015 Elsevier B.V. All rights reserved.