More Generalizations of Union Soft Hyperideals of Ordered Semihypergroups


Muhammad Farooq, Mohammad Khalaf, Asghar Khan




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.