Neutrosophic WISP (Stanujkić et al., 2022)

Three things change. The four comparison logics and the decision logic stay the same.

Cells. In crisp WISP every cell is a single number. Here every cell consists of a degree of truth (T), indeterminacy (I) and falsity (F); all three lie between 0 and 1, and their sum cannot exceed 3. The founding source (Stanujkić et al., 2022) proposes deriving these triples from a nine-term linguistic scale (from "very poor" to "very good"). DecisionMind does not perform this scale mapping itself; the user enters the T, I, F degrees directly, the same input form as the rest of the family (such as Neutrosophic WPM). Criterion weights are taken from outside as crisp numbers.

Keeping the benefit and cost groups separate. Crisp WISP normalises cost cells the same way as benefit cells, dividing the column by its own largest value; it handles direction only at the fourth step, by keeping the benefit and cost sums separate, and never reverses any single cell on its own. Neutrosophic WISP preserves the same logic: a cost criterion's T, I, F values are not complemented, and stay as they are, the truth-indeterminacy-falsity degree of the judgement "this alternative has a high value on this criterion" for the criterion it belongs to. This is where it departs from Neutrosophic WPM within the same family, which complements the cost cell immediately (writing F, I, T instead of T, I, F). Because crisp WPM reverses the cost column in a single step, the WPM extension also complements the cell; because crisp WISP performs no such reversal, the WISP extension does not complement it either. Instead, DecisionMind gathers benefit criteria into one group and cost criteria into a separate group; each group's weights are renormalised to sum to 1 within that group.

Aggregation and defuzzification. For every alternative, the benefit group is reduced to two separate triples: one by a neutrosophic weighted ARITHMETIC mean (SVNWA, the neutrosophic counterpart of additive logic), and one by a neutrosophic weighted GEOMETRIC mean (SVNWG, the counterpart of multiplicative logic). The same operation is carried out for the cost group. This yields four neutrosophic triples: S^max, S^min (additive) and P^max, P^min (multiplicative). These four are reduced to single numbers by Stanujkić's own formula (s = (2 + T − I − F) / 3). This score function differs from the s = (1 + T − 2I − F) / 2 function seen elsewhere in the family (such as Neutrosophic WPM and Neutrosophic ARAS): it penalises indeterminacy once rather than twice, and its constant is 2/3 rather than 1/2. Four crisp numbers result (s_max, s_min, p_max, p_min). From these, crisp WISP's four measures are built: the additive difference (s_max − s_min), the multiplicative difference (p_max − p_min), the additive ratio (s_max / s_min), and the multiplicative ratio (p_max / p_min). All four are scaled against their own best alternative and then averaged.

For this extension, DecisionMind fixes Stanujkić's s = (2 + T − I − F) / 3 function as the defuzzification rule, along with the equally weighted average of the four measures. Weights are taken from outside; the method does not generate weights and does not support group decision-making.

The output is a score, as in crisp WISP. A value of 1 does not mean "perfect" but "the alternative all four logics find best in this set." The score is not a percentage and cannot be compared with the score of a different analysis.

The difference is this: each logic (additive, multiplicative) here passes first through the neutrosophic combination of the benefit and cost groups on their own, and then through the defuzzification of this combined triple. When two alternatives' scores are very close, this closeness may stem from genuine similarity in performance, or from the indeterminacy degrees (I) largely cancelling one another out within the score function. This distinction cannot be made without inspecting the T, I and F components separately.

Thus instead of writing:

"Neutrosophic WISP found the best alternative decisively"

the report should read:

"With these triple inputs, the average of the four comparison logics favours A1; the gap to A3 is very small, and the order between these two alternatives could change with a small shift in a criterion weight or a single cell"

Consider this extension when criteria come not from a measurement but from a judgement whose truth is contested, incomplete or contradictory. Which situations can be carried into the neutrosophic structure is covered on the Neutrosophic data-type card. Crisp WISP's exit condition applies here too: this extension is unsuitable when no compromise is acceptable on one criterion.

Forcing the sum of T + I + F to equal 1, or deriving I as 1 − T − F, zeroes out this extension's contribution; the general warning on the neutrosophic data-type card applies here too. Crisp WISP's sensitivity to a near-zero cell also carries over: if a group's aggregated T is very close to zero, the multiplicative measures (P^max, P^min) give an unreliable result.

Wrongly complementing the cost cell. In this extension, a cost criterion's (T, I, F) triple is not reversed into (F, I, T), unlike some other members of the family (such as Neutrosophic WPM). It enters the cost group as it is; the penalty happens in the difference/ratio operation at the fourth step. Computing it with the cell complemented rewards cost in the wrong direction.

Confusing the score function. This extension's defuzzification rule is s = (2 + T − I − F) / 3. The s = (1 + T − 2I − F) / 2 function used elsewhere in the family (Neutrosophic WPM, Neutrosophic ARAS) does not apply here. The two formulas carry different constants and a different weight on indeterminacy (once versus twice); confusing one with the other can produce a different ranking.

Forcing T + I + F to sum to 1. The neutrosophic components are independent; forcing their sum to equal 1 removes the structure's one contribution, carrying contradictory or incomplete evidence separately.

Never checking the four measures separately. Reporting only the final average, without checking whether the additive difference, multiplicative difference, additive ratio and multiplicative ratio favour the same alternative; when they disagree, the average conceals this disagreement.

The governing principle is this:

In Neutrosophic WISP, cost criteria are not complemented; they are gathered into a separate group and subtracted from, or set in ratio to, the benefit group. This extension's defuzzification rule differs from the rest of the family and must not be confused with it.