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General L-fuzzy aggregation functions based on complete residuated lattices

  • Yexing Dan
  • Bao Qing HuEmail author
  • Junsheng Qiao
Foundations
  • 19 Downloads

Abstract

As a vital tool in data analysis, aggregation functions have been widely studied in many papers. In particular, one of the recent research topics for aggregation functions is the study of the various extension forms of those useful functions. This paper continues to research this topic from the theoretical point of view. First, we introduce the notions of L-fuzzy aggregation functions and general L-fuzzy aggregation functions based on complete residuated lattices. Then we present the upper and lower general L-fuzzy aggregation approximation functions of the general L-fuzzy aggregation functions, which are the pointwise extension of an L-fuzzy aggregation function. Moreover, we consider some vital properties of those aggregation approximation functions and investigate the relationship between those aggregation approximation functions and the corresponding L-fuzzy relations. Finally, we show that the approach of axiomatizations of the upper and lower general L-fuzzy aggregation approximation functions ensures the existence of corresponding L-fuzzy relations which generate the functions.

Keywords

General L-fuzzy aggregation functions L-fuzzy relations Complete residuated lattices Upper and lower general L-fuzzy aggregation approximation functions 

Notes

Acknowledgements

The authors express their sincere thanks to the editors and anonymous reviewers for their most valuable comments and suggestions for greatly improving this article. Yexing Dan and Bao Qing Hu acknowledge support by grants from the National Natural Science Foundation of China (Grant Nos. 11971365 and 11571010) and the Natural Science Foundation of Hubei Province (Grant No. 2019CFA007). Junsheng Qiao acknowledges support by the National Natural Science Foundation of China (11901465), the Scientific Research Fund for Young Teachers of Northwest Normal University (5007/384) and the Doctoral Research Fund of Northwest Normal University (6014/0002020202).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Hubei Key Laboratory of Computational ScienceWuhan UniversityWuhanPeople’s Republic of China
  3. 3.College of Mathematics and StatisticsNorthwest Normal UniversityLanzhouPeople’s Republic of China

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