Compatible congruences defined via triangular norms and triangular conorms

İnce M. A.

International Journal of General Systems, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1080/03081079.2025.2510460
  • Journal Name: International Journal of General Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Congruence, S-compatible, T-compatible, t-conorm, t-norm
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

The main aim of this paper is to investigate relationship between ideals or filters of a bounded lattice and T-compatible or S-compatible congruences which are obtained by using the definition of compatible aggregation functions. Additionally, we introduce some congruences and characterize the conditions under which they belong to the sets of T-compatible or S-compatible congruences, denoted as (Formula presented.) and (Formula presented.), respectively. We define an equivalence class denoted by (Formula presented.) (A is an aggregation function and I is a nonempty set) and elaborate on the properties of this class when A is t-norm or t-conorm.