Congruence Relations and Direct Decomposition of Uninorms on Bounded Lattices


KARAÇAL F., ERTUĞRUL Ü., Arpaci S., Kesicioglu M. N.

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol.31, no.06, pp.1033-1059, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 06
  • Publication Date: 2023
  • Doi Number: 10.1142/s0218488523500460
  • Journal Name: INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, zbMATH
  • Page Numbers: pp.1033-1059
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, the concept of U-compatible congruence and its related properties are studied. We also focus on homomorphism theorems for uninorms. Decomposition of uninorms is investigated via factor congruences, at first. Subsequently, we investigate decomposition of conjunctive and disjunctive uninorms, respectively. After all, we determine necessary and sufficient conditions for decomposition of some uninorms that are neither conjunctive nor disjunctive. In addition to all these, we shed light on the application of our results with the examples.