Neutrosophic MOORA

Cells. In crisp MOORA every cell is a single number. Here every cell consists of three independent degrees: truth (T), indeterminacy (I) and falsity (F); the three come from separate sources and their sum may exceed 1. Criterion weights are taken in DecisionMind as crisp, single numbers; indeterminacy is carried only in the cells of the decision matrix.

Scale equalisation. Crisp MOORA divides the raw cell value directly by the column's magnitude. N-MOORA first reduces every cell's T-I-F triple to a single score: the score is found by subtracting twice the indeterminacy and the falsity from the truth, then halving the result; the indeterminacy share enters with double weight, like a penalty that lowers the score. This scoring differs from Fuzzy MOORA's defuzzification by averaging in the final step: here defuzzification happens in the first step, and the rest of the calculation proceeds in exactly the same form as crisp MOORA. It resembles the way IF-MOORA scores the support-reject difference in its first step and then continues.

Score and ratio system. The score produced in the first step is normalised, exactly as in crisp MOORA, by dividing by the root of its own column magnitude; it is then weighted, and the sum over the "higher is better" criteria has the sum over the "lower is better" criteria subtracted from it.

Result and defuzzification. Defuzzification, the reduction of T-I-F to a single score, is MOORA's first step, not the outcome itself. The output is directly a single net score and a ranking; DecisionMind also computes an optional reference-point approach on the same scored matrix, for cross-checking.

DecisionMind fixes, for classic N-MOORA, the score function (1 + T − 2I − F)/2 and its computation in the first step; this is one of several score functions that have been proposed for single-valued neutrosophic sets, and a different score function can produce a different ranking.

The output is a net score and a ranking, as in crisp MOORA; it is read the same way. The difference is this: the score compresses three independent sources of information, namely favourable evidence, an unknown share and unfavourable evidence, into a single number. Two alternatives can share the same score; one may have reached it with low indeterminacy (T and F sharp, I small), the other with high indeterminacy (I large, T and F less reliable). The net score does not show this difference.

Thus instead of writing:

"N-MOORA found the most reliable alternative"

the report should read:

"According to N-MOORA, the alternative with the highest score is the following; how much of this score comes from strong evidence and how much from the indeterminacy penalty should be examined separately"

Use this extension when information about a criterion is missing, inconsistent or contradictory, and this matters for the decision itself: evaluating alternatives with no track record, expert opinions built on conflicting sources, early-stage decisions where the unknown share must be kept explicitly separate. If the evaluation rests on a reliable measurement, or experts do not report a separate indeterminacy share (only support or rejection is given), the intuitionistic fuzzy extension is sufficient and there is no need to move to neutrosophic data. The exit condition is the same as for crisp MOORA: if no compromise is acceptable on one criterion, this extension too is compensatory and will not eliminate anything below a threshold.

Forcing the sum of T, I and F to equal 1. This reduces the structure to a dependent triple of "yes/abstain/no" proportions and removes the rationale for using neutrosophic data at all; DecisionMind's manifest check only requires each component to lie in [0,1] and the sum to lie between 0 and 3, not that it equals 1.

Computing I as 1 − T − F. In this case indeterminacy carries no independent information; because N-MOORA's score formula penalises I at double weight, a derived I produces the same numerical effect as a genuine I while representing different information, namely an unsourced assumption.

Changing the score function while reporting it as unchanged. DecisionMind's score of (1 + T − 2I − F)/2 is one of several score functions proposed in the literature; another score function (using only T − F, for instance) can give a different ranking, and which one was used must be stated in the report.

Converting a verbal rating ("good", "average") into a T-I-F triple without a stated rule. Each component must be derived from its own source, favourable evidence, the unknown-record share, unfavourable evidence; opening a word into a triple by feel produces a fabricated input.

The governing principle is this:

In N-MOORA, defuzzification happens in the first step, through a score function that penalises indeterminacy at double weight; if this score function is changed, or the components are produced dependently, the method's neutrosophic contribution disappears.