Geodesic
More Generalizations of Union Soft Hyperideals of Ordered Semihypergroups
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 2, p. 287

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we introduce the notions of$(\mathit{M,N}) $-union soft hyperideals and $(\mathit{M,N}) $-union soft interior hyperideals of ordered semihypergroups. Some basic operations are investigated and some related properties are also studied. We present characterizations of ordered semihypergroups in terms of $(\mathit{M,N})$-union soft hyperideals and $(\mathit{M,N})$-union soft interior hyperideals. We prove that every $(\mathit{M,N})$-union soft hyperideal is an $(\mathit{M,N})$-union soft interior hyperideal but the converse is not true which is shown with help of an example. However we show that the notions of $(\mathit{M,N})$-union soft hyperideals and $(\mathit{M,N})$-union soft interior hyperideals coincide in a regular as well as in intra-regular ordered semihypergroups. Moreover we introduce the notion of $(\mathit{M,N})$-union soft simple ordered semihypergroups. Finally, we characterize $(\mathit{M,N})$-union soft simple ordered semihypergroups by means of $(\mathit{M,N})$-union soft hyperideals and $(\mathit{M,N})$-union soft interior hyperideals.
Classification : 03D40, 08Q70, 47D03
Keywords: regular ordered semihypergroup, intra-regular ordered semihypergroup, (M;N)-union soft hyperideal, (M;N)-union soft interior hyperideal, (M;N)-union soft simple ordered semihypergroup 
Muhammad Farooq; Mohammad Khalaf; Asghar Khan. More Generalizations of Union Soft Hyperideals of Ordered Semihypergroups. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 2, p. 287 . http://geodesic.mathdoc.fr/item/KJM_2024_48_2_a7/
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     author = {Muhammad Farooq and Mohammad Khalaf and Asghar Khan},
     title = {More {Generalizations} of {Union} {Soft} {Hyperideals} of {Ordered} {Semihypergroups}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {287 },
     year = {2024},
     volume = {48},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2024_48_2_a7/}
}
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