Plithogenic SPOTIS

Cells. In crisp SPOTIS every cell is a single number. Here every cell is a truth (T), indeterminacy (I) and falsity (F) triple. One criterion is taken as dominant, with a contradiction degree of zero; the other criteria's opposition to the dominant one is given as a contradiction degree between 0 and 1. Criterion weights are supplied from outside as crisp numbers.

Contradiction adjustment and score. For a cost criterion, the triple is complemented first. Each cell is then adjusted by its own criterion's contradiction degree and reduced to a single number with the neutrosophic score function ((1 + T − 2I − F)/2).

The most critical difference: fixed bounds are never taken from outside here. The founding principle that makes SPOTIS what it is, is that the ideal point and the scaling bounds are built BEFORE the analysis, from the decision-maker's answer to "what is the best and worst value that can realistically be expected on this criterion." In the Fuzzy SPOTIS and Neutrosophic SPOTIS extensions, if these bounds are not given explicitly in the analysis input, DecisionMind silently falls back to the data set's own observed bounds; this is at least a "default" behaviour, and supplying a fixed bound as input is theoretically possible. In P-SPOTIS the situation runs deeper: nowhere in the kernel code is there an input path (an extras scan) that reads fixed bounds. The ideal (s*) and the scaling range are ALWAYS, unconditionally, built from the observed minimum and maximum of that analysis's own alternative scores; there is nowhere for the engine to accept a fixed bound even if the user wants to enter one. This is the strongest "silent default" case in the family: what is at issue here is not "falling back to a default" but "no other way is possible."

It can be shown that the contradiction degree never changes the result. The contradiction adjustment transforms every cell's score linearly, as s' = (1 − c)·s + c/2. The scaled distance, |s − s*|/(smax − smin), is a pure difference ratio; this ratio is UNCHANGED when every value in the column, score, ideal and bounds alike, undergoes the same linear transformation. An independent Python test showed that, when the contradiction degrees were varied over a wide range, the distance values remained IDENTICAL to the decimal place (see the verification notes). This belongs to the same family as the ineffectiveness seen in P-CoCoSo, P-RAFSI and P-ROV.

DecisionMind fixes this score function. The weighted sum and the ascending order (a small distance is good) follow crisp SPOTIS.

As in crisp SPOTIS, a small distance value is good, a large one is bad. But crisp SPOTIS's most important promise is that this distance is measured against a ruler fixed before the analysis began; this promise holds under no circumstances in P-SPOTIS. The ideal and the scaling bounds are always built from that analysis's own alternatives, which effectively turns the method into a plithogenic TOPSIS, a closeness measure whose ideal point is built from the data. When a new alternative is added, the existing alternatives' distances also change; the "rank reversal free" property that gives SPOTIS its name is never provided here.

The contradiction degree, for its part, has no measurable effect in this engine; two analyses do not give different results merely because their contradiction degrees differ.

Thus instead of writing:

"According to P-SPOTIS, A2's distance is 0.14, and because this rests on a fixed ruler, it is a reliable and repeatable result"

the report should read:

"A2's distance has been computed with an ideal built from these three alternatives' own data; because this engine has no path for entering a fixed bound, the result will change when a new alternative is added. The contradiction-degree parameter also has no measurable effect"

This extension can be considered when information about a criterion is incomplete, inconsistent or contradictory. But in today's engine, P-SPOTIS does NOT provide, in any analysis, the "stable comparison against a fixed ruler" that defines SPOTIS; the situation in which SPOTIS is actually needed, an alternative set that will change over time, a ranking that must stay stable, and bounds that are known and defensible in advance, is not met by this engine. If that need genuinely exists, another route should be followed today, for example fixing the bounds separately and by hand in the report and verifying the distances manually; the detail is in the verification notes.

Turning a measured criterion into a T-I-F triple is not modelling uncertainty but producing it. If no compromise is acceptable on one criterion, the exit condition on the base SPOTIS card applies unchanged.

Assuming P-SPOTIS is a fixed-bound method. As proven above, this is wrong; the engine has no input path for a fixed bound, and the bounds are always built from the data.

Thinking "if I supply a fixed bound, SPOTIS's promise will hold." This is possible in Fuzzy and Neutrosophic SPOTIS (falling back to the default if no bound is given); in P-SPOTIS, supplying a bound has no effect at all, since the kernel does not read it under any circumstances.

Assuming the contradiction degree is effective, as in P-PSI. In P-SPOTIS the contradiction degree does not change the result algebraically.

Reading the distance value the wrong way round. In the SPOTIS family a small distance is good; reading a large distance as "best" reverses the ranking.

The governing principle is this:

P-SPOTIS takes its name from SPOTIS but, in today's engine, never applies the fixed-ruler principle that defines SPOTIS; the ideal and the bounds are built, in every analysis, from that analysis's own data, which means the method in effect works like a plithogenic TOPSIS.