Single Valued Neutrosophic Numbers

For example: Z3 = {0, 1, 2}, with respect to the classical multiplication modulo 3, is a neutrosophic triplet week set, but it is not a neutrosophic triplet strong set. Because all neutrosophic triplets are: <0, 0, 0>, <0, 0, 1>, <0, 0, 2>. Z3 is not a neutrosophic triplet strong set, since for example 2 ∈ Z3, but there is no neut(2) nor anti(2) in Z3. Several Chinese professors told me that there might be no neutrosophic triplet group such that at least one element has two or more neutrals. They believe that in all neutrosophic triplet groups an element has only a neutral (different from the classical unit). Yet, there are many neutrosophic triplet groups whose elements have many anti’s.

Single Valued Neutrosophic Numbers

Question from Amin Vafadarnikjoo I am a PhD student at the University of East Anglia. (…) How can I get the inverse of a simplified Single Valued

Neutrosophic Number (SVNN)? I mean if A = <T(x), I(x), F(x)> then what is the inverse(A) = A−1? Florentin Smarandache Please see this paper: F. Smarandache, Subtraction and Division of Neutrosophic

Numbers, Critical Review, Volume XIII, 103-110, 2016;

http://fs.unm.edu/CR/SubtractionAndDivision.pdf . It works for all subtractions and divisions, because of the below remark: for both, subtraction and division, if a component result is < 0, we put 0, and if a component result is > 1, we put 1. It works even when we have divisions by 0 (since the above remark changes +∞ to 1, and -∞ to 0. By the way, the general multiplication of SV neutrosophic numbers is defined as follows [see in my previous article]: <t1, i1, f1>  <t2, i2, f2> = <t1 ∧F t2, i1 ∧F i2, f1 ∨F f2>, where ∧F can be ANY fuzzy t-norm, and ∨F can be ANY fuzzy t-conorm. Therefore, you may get different formulas for addition and multiplication of neutrosophic numbers, and implicitly different formulas for subtraction and division, and implicitly different results for the neutrosophic inverse. So far, researchers have been used only: x ∧F y = xy, and x ∨F y = x+y-xy within the neutrosophic framework. You might try to check other t-norms / t-conorms (min/max, Lukasiewicz etc.), but I am not confident that the "inverse" would be what you expect.