Abstract
The notion of int-soft subfields, int-soft algebras over int-soft subfields, and int-soft hypervector spaces are introduced, and their properties and characterizations are considered. In connection with linear transformations, int-soft hypervector spaces are discussed.
Highlights
The hyperstructure theory was introduced by Marty [1] at the 8th congress of Scandinavian Mathematicians in 1934
A soft set theory is introduced by Molodtsov [7], and Cagman and Enginoglu [25] provided new definitions and various results on soft set theory
A soft set (f, F) over F is called an int-soft subfield of F if the following conditions are satisfied: (1) (∀a, b ∈ F) (f(a + b) ⊇ f(a) ∩ f(b)), (2) (∀a ∈ F) (f(−a) ⊇ f(a)), (3) (∀a, b ∈ F) (f(a) ∩ f(b) ⊆ f(ab)), (4) (∀a ∈ F) (a ≠ 0 ⇒ f(a) ⊆ f(a−1))
Summary
The hyperstructure theory was introduced by Marty [1] at the 8th congress of Scandinavian Mathematicians in 1934. Uncertainties cannot be handled using traditional mathematical tools but may be dealt with using a wide range of existing theories such as probability theory, theory of (intuitionistic) fuzzy sets, theory of vague sets, theory of interval mathematics, and theory of rough sets All of these theories have their own difficulties which are pointed out in [7]. Cagman et al [11] introduced fuzzy parameterized (FP) soft sets and their related properties They proposed a decision making method based on FP-soft set theory and provided an example which shows that the method can be successfully applied to the problems that contain uncertainties. Aktas and Cagman [13] studied the basic concepts of soft set theory and compared soft sets to fuzzy and rough sets, providing examples to clarify their differences They discussed the notion of soft groups. In connection with linear transformations, we discuss int-soft hypervector spaces
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