Abstract
We first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets (IVIF-soft rough sets).
Highlights
In 1999, Smarandache introduced the theory of neutrosophic set (NS) [1], which is the generalization of the classical sets, conventional fuzzy set [2], intuitionistic fuzzy set [3], interval-valued fuzzy set [4], and so on
For an interval-valued neutrosophic set σ ∈ IVNSU, the lower and upper soft rough approximations of σ with respect to S are denoted by NS(σ) and NS(σ), respectively, which are intervalvalued neutrosophic sets in U given by NS (σ) = {⟨x, [⋀ {inf μσ (y) : ∃a ∈ A ({x, y} ⊆ f (a))}, ⋀ { sup μσ (y) : ∃a ∈ A ({x, y} ⊆ f (a)) }]
It is easy to see that the primary evaluation result of the whole expert group G can be represented as an interval-valued neutrosophic evaluation soft set S∗ = (F∗, G) over U, where F∗ : G → IVNSU is given by F∗(Ti) = Xi, for i = 1, 2, . . . , n
Summary
In 1999, Smarandache introduced the theory of neutrosophic set (NS) [1], which is the generalization of the classical sets, conventional fuzzy set [2], intuitionistic fuzzy set [3], interval-valued fuzzy set [4], and so on. Saha and Mukherjee [48] proposed the concept of the notion of soft interval-valued intuitionistic fuzzy rough sets. Broumi et al [49] combined neutrosophic sets with rough sets in a new hybrid mathematical structure called “rough neutrosophic sets” handling incomplete and indeterminate information. Based on the equivalence relation on the universe of discourse, Mukherjee et al [51] introduced soft lower and upper approximation of interval-valued intuitionistic fuzzy set in Pawlak’s approximation space. Motivated by the idea of interval-valued intuitionistic fuzzy soft rough sets introduced in [52], we extend the interval intuitionistic fuzzy lower and upper approximations to the case of an intervalvalued neutrosophic set.
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