Abstract

This paper solves the imperfect triplets problem in refined neutrosophic rings, where it presents the necessary and sufficient conditions for a triple (x,y,z) to be an imperfect triplet in any refined neutrosophic ring. Also, this work introduces a full description of the structure of imperfect triplets in numerical refined neutrosophic rings such as refined neutrosophic ring of integers Z(I1,I2) , refined neutrosophic ring of rationales Q(I1,I2), and refined neutrosophic ring or real numbers (R(I1,I2).

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