Neutrosophic RAWEC

Two things change. RAWEC's two-way deviation logic stays exactly as it is.

Cells. In crisp RAWEC every cell is a single number. Here every cell consists of three degrees: truth (T), indeterminacy (I) and falsity (F). Criterion weights come from outside as crisp numbers. Neutrosophic RAWEC does not generate its own weights.

Score function and normalisation. All of RAWEC's remaining steps operate on crisp numbers. The method therefore first reduces every triple to a single score. DecisionMind applies a formula here that uses all three of T, I and F together. In this formula indeterminacy is penalised at double weight. Once the score is produced, the same double normalisation as in crisp RAWEC, against both the best and the worst value, is applied.

This shows an important point. Indeterminacy is not carried as three separate numbers all the way to the end of the calculation, as it is in Fuzzy RAWEC. Truth, indeterminacy and falsity are already merged into a single score in the very first step. The rest of the method is identical to crisp RAWEC, operating on this single score.

Result. The Q index is, as in crisp RAWEC, a single number between −1 and 1.

DecisionMind holds the score formula and the double normalisation that follows it fixed in this extension. Weights come from outside as crisp numbers.

The Q index is read in the same way as in crisp RAWEC. A positive value shows that the alternative is on the good side. See the RAWEC card.

The difference lies here: Q is now built on a score that comes from three separate sources of evidence (favourable, adverse, unknown). Two alternatives can have the same score even though the favourable-adverse-unknown distribution beneath it is very different. The report should not hide this difference.

Thus instead of writing:

"The neutrosophic RAWEC index placed alternative A first"

the report should read:

"Alternative A has obtained the highest Q index with a score derived from its degrees of truth, indeterminacy and falsity. This score does not on its own show how much of the evidence beneath it is favourable, how much adverse and how much unknown"

Neutrosophic RAWEC is preferred when information about a criterion is missing, inconsistent or contradictory, and this matters for the decision. Opening a measured value into a truth-indeterminacy-falsity triple without justification adds no information. The neutrosophic data-type card explains this distinction in detail.

DecisionMind requires a single data type. If the table contains both measured and neutrosophic criteria, the measured criterion is also written as a triple, but its indeterminacy and falsity shares are kept close to zero. Crisp RAWEC's exit condition applies here too: if no compromise is acceptable on one criterion, this extension is not suitable either, since it too is compensatory.

Forcing the sum of the three components to equal 1. Truth, indeterminacy and falsity come from independent sources. Their sum exceeding 1 is natural, and not a mistake.

Deriving indeterminacy from truth and falsity. Indeterminacy should come from its own source of evidence; it should not be computed as 1 minus truth minus falsity.

Changing the score function without noticing it. Some sources propose a simpler score formula that uses only truth and falsity. DecisionMind uses a formula that also includes indeterminacy here, and this choice affects the result. Which formula was used must be stated in the report.

Extending a measured criterion without justification. A measured value should stay as a triple with indeterminacy and falsity shares close to zero. Fabricating a triple without justification produces an impression, not data.

The governing principle is this:

Every triple in neutrosophic RAWEC must rest on its own separate source of evidence for the same evaluation. If one component is derived from the other two, the method's sole contribution, keeping contradiction visible, is lost.