Refined Labels

A paper on 'refined neutrosophic set' has been published in 2013, but a ‘refined COMPLEX neutrosophic set’ was never done – upon the best of my knowledge. In refined neutrosophic set, T is split into T1, T2, ...; and I is split into I1, I2, ...; and F is split into F1, F2, ... [http://fs.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf]. We can either refine only the amplitude part of the CNS, or only the phase part of CNS, or both.

Refined Labels

To Le Hoang Son On the paper: F. Smarandache, J. Dezert, Xinde Li, Refined Labels for Qualitative

Information Fusion in Decision-Making Support System, 12th

International Conference on Information Fusion, Seattle,

WA, USA, July 6-9, 1203-1210, 2009 [http://fs.unm.edu/FLARL.pdf]. It is shown that we can approximate the addition, subtraction, multiplication, power of labels si and sj by similar operations of their indexes i and j. Since we do not need a linear algebra of labels in the label neutrosophic set, because we need to limit the labels' values to [0, 1], when we add, subtract etc. we can set such restrictions (not above 1, nor below 0). Commutativity & Associativity If a law * is commutative, it does not involve that the law * is associative, nor reciprocally.