The n-uninorms with continuous underlying t-norms and t-conorms. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Mesiarová-Zemánková, Andrea
• Is Part Of: International journal of general systems. Volume 50:Issue 1(2021)
• Page Start: 92
• Page End: 116
• Publication Date: 2021-01-02
• Subjects: n-uninorm -- uninorm -- ordinal sum -- t-norm -- t-conorm; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2020.1863395
• Languages: English
• ISSNs: 0308-1079

Abstract

ABSTRACT: The n -uninorms with continuous underlying t-norms and t-conorms are studied. We show that each 2-uninorm with continuous underlying functions can be expressed as an ordinal sum of a uninorm with continuous underlying functions (possibly also of a countable number of semigroups related to representable uninorms, continuous Archimedean t-norms, continuous Archimedean t-conorms and internal uninorms) and a 2-uninorm with continuous underlying functions such that U 2 ( 0, 1 ) = z 1 (possibly restricted to open or half-open unit square [ 0, 1 [ 2, ] 0, 1 ] 2 ). Similar results are shown for n -uninorms with continuous underlying functions, where n ∈ N, n > 2.