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Justification of I2 = I
For example, if T = 0.90, then F can be even bigger, let's say F = 0.95. So, T and F are not complementary in neutrosophic theory. I recall that T+I+F ≤ 3. Now, going to neutrosophic algebraic research, if
T(xy) ≥ min{T(x), T(y)} it does not mean that F(xy) ≤ max{F(x), F(y)}. See this counter-example: Let A = {2(0.1, 0.4, 0.3), 3(0.2, 0.5, 0.4), 6(0.3, 0.6, 0.5)}. T(2 3) = T(6) = 0.3 ≥ min{T(2), T(3)} = min{0.1, 0.2} = 0.2. But
F(2 3) = F(6) = 0.5 is not smaller than max{F(2), F(3)} = max{0.3, 0.4} = 0.4.
Similarly
I(2 3) = I(6) = 0.6
is not smaller than max{I(2), I(3)} = max{0.4, 0.5} = 0.5.
Justification of I2 = I
In the previous neutrosophic algebraic structures (started by W. B. Vasantha Kandasamy & F. Smarandache in 2003) we have neutrosophic numbers of the form:
