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Complex Neutrosophic Cubic Set
Even <A> <antiA> = nonempty set, since for example some elements from <A> may be sympathizers (or hidden spies) working for <antiA>, and/or reciprocally. We may also have: <A> <neutA> <antiA> = nonempty set, since for example there may be a double spy in <neutA> that works for both <A> and <antiA>, and other situations. But we may consider the cases when some (or all intersections) are empty, depending on applications and experts. For example, let <A> be a small family, <antiA> another small enemy family, and <neutA> a neutral family, and we choose all intersections be empty. We may connect somehow the neutrosophic triplet sets with the neutrosophic crisp sets. What about such paper, but getting some applications?
You had a good intuition to ask about NCS.
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Complex Neutrosophic Cubic Set
To Said Broumi, Surapati Pramanik, Young Bae Jun Dr. Surapati Pramanik is right, the Neutrosophic Cubic Set is a combination (hybrid) of Interval-Valued
Neutrosophic Set and Single-Valued Neutrosophic Set. By the way, we can extend the Complex Neutrosophic Set to
Complex Neutrosophic Cubic Set - as a combination
Scilogs, V: joining the dots
(hybridization) of Interval-Valued Complex Neutrosophic
Set and Single-Valued Complex Neutrosophic Set. There are several published articles about NCS. Prof. Dr.
Young Bae Jun from South Korea was the first I think who proposed the NCS. Some idea of applications would be, for example, when we know that the degree of truth is between [0.2, 0.5] according to a source of information, but another source of information says that the degree of truth is mostly closer to 0.3. Similarly for the degrees of indeterminacy and falsehood. Therefore, we may have two (sometimes even more) independent sources of information providing information about the same thing. Another interpretation could be using classical statistics: For example, the degree of truth is 0.4, with a standard deviation (approximation) of 0.1 { meaning that the degree of truth is between [0.3, 0.5], also meaning that it is a higher chance that the degree of truth be close to the mean 0.4, and lower chance for the degree of truth be further from 0.4 }. Similarly for the degrees of indeterminacy and falsehood. Y. B. Jun has used NCSs especially in neutrosophic algebraic structures.