Abstract
In this paper, the notions of soft hypervector space and fuzzy soft hypervector space are introduced, and several basic properties are provided. Also, we define and analyze the concept of image and pre-image of fuzzy soft hypervector space.
Highlights
The concept of soft set has been introduced in 1999 by Molodtsov [15] as a general mathematical tool for dealing with uncertainties and imprecision
After Molodtsovs work, some research papers have appeared on the algebraic structures of soft set theory
In 2007, Aktas and Cagman [2] studied the basic concepts of soft sets theory and soft groups, providing examples to clarify their differences
Summary
The concept of soft set has been introduced in 1999 by Molodtsov [15] as a general mathematical tool for dealing with uncertainties and imprecision. After Molodtsovs work, some research papers have appeared on the algebraic structures of soft set theory. In 2007, Aktas and Cagman [2] studied the basic concepts of soft sets theory and soft groups, providing examples to clarify their differences. In [12] Maji et al presented the concept of fuzzy soft sets. Fuzzy soft set theory has been investigated by some researchers, for examples, see [6], [12], [13] and [20]. In this paper, applying the notions of soft sets and fuzzy soft sets to the theory of hypervector spaces, we introduce soft hypervector spaces and fuzzy soft set to hypervector spaces, and study some properties of them
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