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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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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Communicated by Regivan Hugo Nunes Santiago.
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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
- Ordered \(*\)-semihypergroup
- Fuzzy hyperideal
- Prime (weakly prime, semiprime) fuzzy hyperideal
- Intra-regular ordered \(*\)-semihypergroup
- Semisimple ordered \(*\)-semihypergroup
Mathematics Subject Classification