Neutrosophic Ortogonal Set

linguistic labels, while the complex parts are singlevalued numbers in [0, 1], the operations are the same ! The distinction is that: instead of having min / max on labels, we have min / max on numbers! Pretty easy. And Pretty Nice! {Similarly, we can straightforwardly extend to Hesitant-

Valued Labels or Numbers, and Interval-Valued Labels or

Numbers - if you want.} The only change, in the paper, is instead of saying that the complex parts of the sets A and B belong to S (set of labels), we replace S by the interval [0, 1]. Therefore, one has to adjust as: T2A(x), I2A(x), F2A(x) in [0, 1]

and

T2B(x), I2B(x), F2B(x) in [0, 1].

Neutrosophic Ortogonal Set

To Mumtaz Ali If one has two neutrosophic sets A(t1, i1, f1) and B(t2, i2, f2), they are orthogonal if t1t2 = i1i2 = f1f2 = 0. But if we have neutrosophic complex numbers:

A( (t1, u1), (i1, v1), (f1, w1) ) and B( (t2, u2), (i2, v2), (f2, w2) ) then A and B are orthogonal if t1t2cos(|u1-u2|) = i1i2cos(|v1- v2|) = f1f2cos(|w1-w2|) = 0.

Even more, we may extend the definitions to subset (including intervals) of [0, 1], using the same formulas, but having multiplications and subtractions of sets. We say also that two neutrosophic undersets or offsets (which are sets that have negative neutrosophic components) are orthogonal, if: t1t2 + i1i2 + f1f2 = 0. This general formula actually works for any kind of neutrosophic set, overset, underset, offset, with singlevalued, interval-valued, or in general subset-valued from [0, 1]. Similarly we say that two neutrosophic complex undersets or offsets (which are sets that have negative neutrosophic amplitudes and phases)

A( (t1, u1), (i1, v1), (f1, w1) ) and B( (t2, u2), (i2, v2), (f2, w2) ) are orthogonal if t1t2cos(|u1-u2|) + i1i2cos(|v1- v2|) + f1f2cos(|w1-w2|) = 0. This general formula actually works for any kind of neutrosophic complex set, overset, underset, offset, with single-valued, interval-valued, or in general subset-valued from [0, 1]. In the case when t1, i1, f1, t2, i2, f2 are single numbers, intervals, or subsets included in [0, 1], we have that: t1t2 + i1i2 + f1f2 = 0 is equivalent to t1t2 = i1i2 = f1f2 = 0; and similarly: t1t2cos(|u1-u2|) + i1i2cos(|v1- v2|) + f1f2cos(|w1-w2|) = 0