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Subtraction and Division of Neutrosophic Numbers Florentin Smarandache 1
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University of New Mexico, Gallup, NM, USA smarand@unm.edu
Abstract In this paper, we define the subtraction and the division of neutrosophic single-valued numbers. The restrictions for these operations are presented for neutrosophic singlevalued numbers and neutrosophic single-valued overnumbers / undernumbers / offnumbers. Afterwards, several numeral examples are presented.
Keywords neutrosophic calculus, neutrosophic numbers, neutrosophic summation, neutrosophic multiplication, neutrosophic scalar multiplication, neutrosophic power, neutrosophic subtraction, neutrosophic division.
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Introduction
Let đ??´ = (đ?‘Ą1 , đ?‘–1 , đ?‘“1 ) and đ??ľ = (đ?‘Ą2 , đ?‘–2 , đ?‘“2 ) be two single-valued neutrosophic numbers, where đ?‘Ą1 , đ?‘–1 , đ?‘“1 , đ?‘Ą2 , đ?‘–2 , đ?‘“2 ∈ [0, 1] , and 0 ≤ đ?‘Ą1 , đ?‘–1 , đ?‘“1 ≤ 3 and 0 ≤ đ?‘Ą2 , đ?‘–2 , đ?‘“2 ≤ 3. The following operational relations have been defined and mostly used in the neutrosophic scientific literature: 1.1
Neutrosophic Summation (1)
đ??´ ⊕ đ??ľ = (đ?‘Ą1 + đ?‘Ą2 − đ?‘Ą1 đ?‘Ą2 , đ?‘–1 đ?‘–2 , đ?‘“1 đ?‘“2 ) 1.2
Neutrosophic Multiplication A ⊗ đ??ľ = (đ?‘Ą1 đ?‘Ą2 , đ?‘–1 + đ?‘–2 − đ?‘–1 đ?‘–2 , đ?‘“1 + đ?‘“2 − đ?‘“1 đ?‘“2 )
1.3
(2)
Neutrosophic Scalar Multiplication â‹‹ đ??´ = (1 − (1 − đ?‘Ą1 )â‹‹ , đ?‘–1â‹‹ , đ?‘“1â‹‹ ),
(3)
where ⋋∈ �, and ⋋> 0. Critical Review. Volume XIII, 2016