Geodesic
More Generalizations of Union Soft Hyperideals of Ordered Semihypergroups
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 2, p. 287 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
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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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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/