Commutative, associative and non-decreasing functions continuous around diagonal
Publish place: Iranian Journal of Fuzzy Systems، Vol: 19، Issue: 2
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-19-2_004
تاریخ نمایه سازی: 18 فروردین 1401
Abstract:
We characterize all functions that can be obtained as a z-ordinal sum of semigroups related to continuous t-norms, t-conorms, representable uninorms and idempotent semigroups. We show that this class of functions is bigger than the class of n-uninorms with continuous underlying functions. Vice versa, we show that the characterization of n-uninorms with continuous underlying functions via z-ordinal sum can be extendedto any commutative, associative and non-decreasing binary function on the unit interval, which has continuous Archimedean components and is continuous on the diagonal.
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Authors
A. Mesiarová-Zemánková
Mathematical Institute, Slovak Academy of Sciences, ۸۱۴۷۳ Bratislava, Slovakia