Refined Neutrosophic Complex Set

while (R,#) is, with respect to the law #, well-defined, nonassociative, such that for each x ∊ R, there is a neut(x) ∊ R, such that x # neut(x) = neut(x) # x = x, where neut(x) is different from the classical unitary algebraic unit; also there is no anti(x). And an Associative Neutrosophic Triplet Ring, where (R,#) is, with respect to the law #, well-defined, associative, with neut(x), but no anti(x).

Refined Neutrosophic Complex Set

To: Le Hoang Son, Mumtaz Ali, Luu Quoc Dat In extension of our previous paper on Neutrosophic

Complex Set, we may do the Refined Neutrosophic

Complex Set never done before. In 2013, I published a paper on neutrosophic refinement: http://fs.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf. We have for Neutrosophic Complex Set <a∙ejT, b∙ejI, c∙ejF>, where j = √(-1), and T, I, F are the neutrosophic components. Then: "a" and "T" are refined as a1, a2, ..., ap and T1, T2, ..., Tp respectively; similarly: "b" and "I" are refined as b1, b2, ..., br and I1, I2, ..., Ir respectively,

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