Nullnorms on bounded lattices derived from t-norms and t-conorms


INFORMATION SCIENCES, vol.512, pp.1134-1154, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 512
  • Publication Date: 2020
  • Doi Number: 10.1016/j.ins.2019.10.059
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts, Library, Information Science & Technology Abstracts (LISTA)
  • Page Numbers: pp.1134-1154
  • Keywords: Bounded lattice, Annihilator, Nullnorm, Idempotent nullnorm, t-norm, t-conorm, IDEMPOTENT NULLNORMS, TRIANGULAR NORMS, UNINORMS, DISTRIBUTIVITY, OPERATORS, EQUATIONS, ORDER
  • Karadeniz Technical University Affiliated: Yes


Nullnorms with an annihilator a in any point of a bounded lattice are generalizations and unifications of t-norms and t-conorms. This study continues to investigate the construction of nullnorms on bounded lattices. We propose some methods to construct nullnorms derived from t-norms and t-conorms on bounded lattices, where some sufficient and necessary conditions on theirs annihilator are required. As a by-product of these constructions, idempotent nullnorms on bounded lattices are obtained. Further, we provide some illustrative examples of the new classes of nullnorms (idempotent nullnorms) on bounded lattices. (C) 2019 Elsevier Inc. All rights reserved.