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The construction of \(\Theta \)–\(\Xi \) functions on complete lattices

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Abstract

The \(\Theta \)–\(\Xi \) function is a unified framework for 0-overlap functions and 1-grouping functions on the unit interval. Building upon this, the present article extends the concept to complete lattices and provides constructions of \(\Theta \)–\(\Xi \) functions on complete lattices. Additionally, our paper explores the algebraic relationship between 0-overlap functions and 1-grouping functions on a totally ordered complete lattice, demonstrating that the set of all 0-overlap functions and the set of all 1-grouping functions on a totally ordered complete lattice are isomorphic as lattices.

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Acknowledgements

The authors are highly grateful to the editor and anonymous referees for their careful reading and valuable suggestions which helped to improve the paper. This research is supported by a grant of Guangxi Science and Technology Program (Nos. AD23023001 and AA24010005), National Natural Science Foundation of China (11901371), Postdoctoral Science Foundation of China (2019M660054XB).

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, China

    Xulong An & Jiang Yang

  2. School of Mathematics Sciences, Guangxi Minzu University, Nanning, 530006, China

    Heng Liu

Authors
  1. Xulong An
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  2. Heng Liu
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  3. Jiang Yang
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Contributions

Xulong An: Writing-original draft, Writing-review & editing. Heng Liu: Writing-review & editing, Funding acquisition, Formal analysis. Jiang Yang: Writing-review & editing, Funding acquisition, Supervision.

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Correspondence to Jiang Yang.

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An, X., Liu, H. & Yang, J. The construction of \(\Theta \)–\(\Xi \) functions on complete lattices. Comp. Appl. Math. 44, 85 (2025). https://doi.org/10.1007/s40314-024-03046-1

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  • DOI: https://doi.org/10.1007/s40314-024-03046-1

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