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On Regular, Intra-regular Ordered and Fuzzy Ordered Hypersemigroups in Terms of Ideals

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Fuzzy Information and Engineering-2019

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1094))

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Abstract

In this paper, the concepts of ordered and (fuzzy) ordered hypersemigroups are introduced, and several related properties are investigated. In particular, we give the characterization of regular, intra-regular, and quasi-regular (fuzzy) ordered hypersemigroups in terms of ideals. Furthermore, we define and discuss the semisimple (fuzzy) ordered hypersemigroups.

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Acknowledgements

The authors are very much grateful to the anonymous reviewers for their helpful comments and suggestions for improving the paper. The work is supported by the National Natural Science Foundation (No. 11271040, No. 11361027), Guangdong Province Natural Science Foundation of China (No. 2014A030313625, No. 2018A030313063).

Funding

This paper is recommended by Xi-lin Tang who is a professor of the South China University of Technology in China.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Wuyi University, Jiangmen, 529020, Guangdong, People’s Republic of China

    Xiang-yun Xie, Lian-fei Gao & Min Li

Authors
  1. Xiang-yun Xie
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  2. Lian-fei Gao
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  3. Min Li
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Corresponding author

Correspondence to Xiang-yun Xie .

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Editors and Affiliations

  1. Foshan University, Foshan, Guangdong, China

    Bing-yuan Cao

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Xie, Xy., Gao, Lf., Li, M. (2020). On Regular, Intra-regular Ordered and Fuzzy Ordered Hypersemigroups in Terms of Ideals. In: Cao, By. (eds) Fuzzy Information and Engineering-2019. Advances in Intelligent Systems and Computing, vol 1094. Springer, Singapore. https://doi.org/10.1007/978-981-15-2459-2_16

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