Neutrosophic Notions

Neutrosophic Notions

To Mumtaz Ali, John Mordeson The adopted fuzzy notions to neutrosophic notions are correct. I think we can say in a more general way. Let's use the notations: NS(x) = < T(x), I(x), F(x)>, where NS means neutrosophic set values, NS(y) = < T(y), I(y), F(y)>, NS(xy) = < T(xy), I(xy), F(xy)>. Then one has a Neutrosophic Fuzzy Subgroupoid A of a groupoid (G, .) if for all x, y in G one has: NS(xy) ≥ NS(x)∧NS(y). And the definition of the Neutrosophic Fuzzy Subgroup can be written as: For x, y in A one has: NS(xy) ≥ NS(x)∧NS(y) NS(x) ≥ NS(x-1). We may have classes of neutrosophic fuzzy subgroupoids, and neutrosophic fuzzy subgroups, since there are classes of neutrosophic conjunctions, i.e.: NS(x)∧NS(y) = <min{T(x), T(y)}, max{I(x), I(y)}, max{F(x), F(y)}>

or

NS(x)∧NS(y) = <min{T(x), T(y)}, min{I(x), I(y)}, max{F(x), F(y)}>

or

or NS(x)∧NS(y) = <T(x)T(y), 1-I(x)I(y), 1-F(x)F(y)>

NS(x)∧NS(y) = <T(x)T(y), I(x)I(y), 1-F(x)F(y)>

etc. And we also have two types of neutrosophic inequalities of sets:

<T1, I1, F1> ≥ <T2, I2, F2>, if T1 ≥ T2 and I1 ≤ I2 and F1 ≤ F2, or

<T1, I1, F1> ≥ <T2, I2, F2> if T1 ≥ T2 and I1 ≥ I2 and F1 ≥ F2. *

An direct edge of a graph, let's say from A to B (i.e. how

A influences B), may have a neutrosophic value (t, i, f), where t means the positive influence of A on B, i means the indeterminate influence of A on B, and f means the negative influence of A on B. Then, if we have, let's say: A→B→C, such that A→B has the neutrosophic value (t1, i1, f1), and B→C has the neutrosophic value (t2, i2, f2), then A→C has the neutrosophic value (t1, i1, f1)∧N(t2, i2, f2), where ∧N is the

AND neutrosophic operator. What do you think about new interpretation of the neutrosophic graphs, neutrosophic trees? Can we apply it to neutrosophic cognitive maps as well?