A novel investigation on fuzzy hyperideals in ordered \(*\)-semihypergroups

Abstract

In this paper, we study the ordered \(*\)-semihypergroups in terms of fuzzy subsets in detail and define a unary operation \(\star \) on the set of all the fuzzy subsets of an ordered \(*\)-semihypergroup. To begin with, we define and study the fuzzy hyperideals of an ordered \(*\)-semihypergroup. In particular, we investigate the properties of fuzzy hyperideals generated by ordered fuzzy points of an ordered \(*\)-semihypergroup. Furthermore, we introduce the concepts of prime, weakly prime and semiprime fuzzy hyperideals of ordered \(*\)-semihypergroups. Especially, the relationships among these three types of fuzzy hyperideals are established. In the sequel, we give some characterizations of intra-regular ordered \(*\)-semihypergroups and semisimple ordered \(*\)-semihypergroups in terms of fuzzy hyperideals. Especially, we prove that an ordered \(*\)-semihypergroup S is semisimple if and only if every fuzzy hyperideal of S can be expressed as the intersection of all weakly prime fuzzy hyperideals of S containing it.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11801081), the Demonstration Project of Grass-roots Teaching and Research Section in Anhui Province (No. 2018jyssf053), Anhui Provincial Excellent Youth Talent Foundation (No. gxyqZD2019043) and the University Natural Science Project of Anhui Province (No. KJ2019A0543).

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Correspondence to Jian Tang.

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Tang, J., Yaqoob, N. A novel investigation on fuzzy hyperideals in ordered \(*\)-semihypergroups. Comp. Appl. Math. 40, 43 (2021). https://doi.org/10.1007/s40314-020-01388-0

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Keywords

  • Ordered \(*\)-semihypergroup
  • Fuzzy hyperideal
  • Prime (weakly prime, semiprime)  fuzzy hyperideal
  • Intra-regular ordered \(*\)-semihypergroup
  • Semisimple ordered \(*\)-semihypergroup

Mathematics Subject Classification

  • 08A72
  • 20N20
  • 06F05