Abstract
This paper examines rough sets in hypervector spaces and provides a few examples and results in this regard. We also investigate the congruence relations-based unification of rough set theory in hypervector spaces. We introduce the concepts of lower and upper approximations in hypervector spaces.
Highlights
Giuseppe Peano [1], an Italian mathematician, was the first to define vector space as an abstract algebraic structure in 1888
The most basic example of vector space in the plane is R2. More studies extended this to Euclidean space ðRnÞ
This paper created a bond between rough sets and hypervector space
Summary
Giuseppe Peano [1], an Italian mathematician, was the first to define vector space as an abstract algebraic structure in 1888. The most basic example of vector space in the plane is R2 More studies extended this to Euclidean space ðRnÞ. In 1982, Pawlak introduced the rough set theory [5]. In 2009, Wu et al [12, 13] had explored a new idea of roughness in vector spaces by using congruence relations. Taghavi and Hosseinzadeh [19–21] added very useful results to the theory of Journal of Function Spaces hypervector spaces. Muhiuddin and Al-Roqi [27] studied the concept of double-framed soft sets in hypervector spaces. Muhiuddin [28] applied intersectional soft sets theory to generalized hypervector spaces, see [29, 30]. We introduced the concept of lower and upper rough subsets in hypervector spaces.
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