More Generalization of Union Soft Hyperideals of Ordered Semihypergroups
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Authors: M. FAROOQ, M. KHALAF AND A. KHAN
DOI: 10.46793/KgJMat2402.287F
Abstract:
In this paper, we introduce the notions of
-union soft hyperideals
and 
-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 
-union soft hyperideals and 
-union soft interior
hyperideals. We prove that every 
-union soft hyperideal is an
-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
-union soft hyperideals and 
-union soft interior hyperideals
coincide in a regular as well as in intra-regular ordered semihypergroups.
Moreover we introduce the notion of 
-union soft simple ordered
semihypergroups. Finally, we characterize 
-union soft simple
ordered semihypergroups by means of 
-union soft hyperideals and
-union soft interior hyperideals.
Keywords:
Regular ordered semihypergroup, intra-regular ordered semihypergroup,
-union soft hyperideal, 
-union soft interior hyperideal,
-union soft simple ordered semihypergroup.
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