Plithogenic WISP

Three things change; the four comparison logics and the separate treatment of the benefit and cost groups do not.

Cells. In crisp WISP every cell is a single number. Here every cell is a truth (T), indeterminacy (I) and falsity (F) triple. As on the plithogenic data-type card, every criterion is given a dominant value, with a contradiction degree of zero; how far the other criteria oppose the dominant one is given as a contradiction degree between 0 and 1. This degree belongs to the criterion and does not vary from one alternative to another. Criterion weights are a separate input from the contradiction degree, supplied from outside.

The contradiction adjustment is applied without complementing, even on the cost criterion. DecisionMind first adjusts every cell by its criterion's contradiction degree: truth is enlarged towards the dominant criterion (T + c·(1 − T)), while indeterminacy and falsity shrink by the same proportion (I·(1 − c), F·(1 − c)). This adjustment is applied DIRECTLY to the raw (T, I, F), including on a cost criterion; a cost criterion's triple is not complemented into (F, I, T). This is a point on which this extension differs, within the same family, from Plithogenic WPM. WPM's crisp form reverses the cost column in a single multiplicative step, so the WPM extension also complements the cell. WISP's crisp form reverses no column at all; it handles direction only at the grouping step (sum of benefits over sum of costs), and so the WISP extension does not complement either.

Scoring and scale equalisation. Each contradiction-adjusted cell is first reduced to a single number with the neutrosophic score function (s = (1 + T − 2I − F)/2). This number is then scaled onto 0-to-1 differently according to the criterion's direction: for a benefit criterion it is divided by the column's largest value, and for a cost criterion the column's smallest value is divided by the cell. This differs from crisp WISP's rule of "divide all columns by the largest, and separate direction only at the fourth step"; here direction enters earlier, at the scaling step. The reason is that DecisionMind uses one shared pre-processing step (score plus direction-sensitive ratio) for every extension in the plithogenic family.

The four measures and defuzzification. Crisp WISP's four measures, benefit sum, cost sum, benefit product, cost product, are built over the scaled crisp values (here direct sums and products take the place of crisp WISP's differences and ratios). The final Q score is found by averaging the four.

DecisionMind fixes, in this extension, the score function (s = (1 + T − 2I − F)/2) and the equal-weighted average of the four measures. Weights and contradiction degrees are supplied from outside; the method generates neither weights nor contradiction degrees itself.

As in crisp WISP, the Q score is a score that shows a ranking within this alternative set; it is not a percentage or a probability, and it cannot be compared with a score from a different analysis.

The difference is here: beneath this score lie both the T-I-F triple and the contradiction degree. As shown on the Plithogenic CoCoSo card, in some DecisionMind engines the contradiction degree can end up with NO effect at all on the final score; this happens because that engine's column-wise (min-max) scaling absorbs the linear transformation the contradiction produces. In Plithogenic WISP the situation is DIFFERENT: the direction-sensitive RATIO normalisation (dividing by the column's largest or smallest value) does not behave like min-max scaling and does not absorb the transformation the contradiction produces. For this card the kernel was run directly in Python, and it was found that the Q scores GENUINELY change when the contradiction degree is changed, and that within certain ranges the ranking itself changes (see Case 1 and the verification notes).

Thus instead of writing:

"The contradiction degree also has no effect on the result in Plithogenic WISP, because this was proven for another member of the family"

the report should read:

"In this engine the contradiction degree genuinely changes the result; which engine is sensitive to this parameter must be tested separately for every member of the family, and ineffectiveness proven for one member cannot be generalised to another"

This extension is considered when your criterion scores are given as a truth-indeterminacy-falsity triple and some criteria are a more independent or more contradictory source of information than others; the detail is on the Plithogenic data-type card. The exit condition on crisp WISP applies here too: if no compromise is acceptable on one criterion, this extension is not suitable. No cell should be allowed to fall to a score very close to zero, or the multiplicative measures break down.

Complementing the cost cell by mistake. In this extension, the cost criterion's (T, I, F) triple is not complemented; the contradiction adjustment is applied to the raw triple, and direction is handled only at the scaling step (dividing by the column's smallest value). Complementing the cell first and then scaling carries over a step that belongs to a different family member (Plithogenic WPM) and produces a different result.

Assuming the contradiction degree is ineffective in this engine too. The ineffectiveness proven for Plithogenic CoCoSo is a property arising from that engine's min-max scaling. Plithogenic WISP uses a different scaling, and the contradiction degree genuinely changes the result here; writing the report on that assumption gives a false assurance.

Choosing the dominant criterion at random. Because the contradiction degree's effect is real in this engine, the decision as to which criterion is taken as dominant (zero contradiction) is particularly important here and must be justified in the report.

Never checking the four measures separately. Reporting only the final Q average without checking whether the benefit/cost sums and the benefit/cost products point to the same alternative.

The governing principle is this:

In Plithogenic WISP the contradiction degree is applied to the raw cell, and the cost criterion is not complemented; the contradiction degree also has a genuine, measurable effect on the result in this engine. Ineffectiveness proven for another family member must not be generalised here.