4.7 Article

On the monotonicity of functions constructed via z-ordinal sum construction

Journal

FUZZY SETS AND SYSTEMS
Volume 466, Issue -, Pages -

Publisher

ELSEVIER
DOI: 10.1016/j.fss.2023.01.006

Keywords

Ordinal sum; z -Ordinal sum; Tosab; t -Norm; n-Uninorm

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This paper is the second part of a two-part series, focusing on the monotonicity of functions defined on the unit interval using (z)-ordinal construction. In Part I, we characterized all non-decreasing functions constructed by a non-trivial ordinal sum of semigroups and provided necessary and sufficient conditions for a function constructed via ordinal sum to be monotone. In Part II, we explore the structure of monotone functions constructed via z-ordinal sum with respect to a finite branching set, and we present necessary and sufficient conditions for monotonicity when the intermediate condition is fulfilled. We also discuss the case when the intermediate condition is not fulfilled.
This is the second part of a two-part paper which discusses monotonicity of functions defined on the unit interval, constructed via (z)-ordinal. In Part I we characterized all non-decreasing functions defined on the unit interval which are constructed by a non-trivial ordinal sum of semigroups and gave necessary and sufficient conditions for a function constructed via ordinal sum to be monotone. In the present Part II we describe the structure of a monotone function defined on the unit interval which is constructed via z-ordinal sum construction with respect to a finite branching set and we give necessary and sufficient conditions for a function constructed via z-ordinal sum to be monotone in the case when the intermediate condition is fulfilled. The case when the intermediate condition is not fulfilled is discussed as well. & COPY; 2023 Elsevier B.V. All rights reserved.

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