Plithogenic

A plithogenic data structure treats a criterion not as a single question but as a question with several sub-options: the values of a "colour" criterion might be red, green and blue; a "supply region" criterion, domestic, neighbouring country and distant country; a "treatment route" criterion, medication, surgery and observation. An alternative is rated separately on each of these sub-options, and in DM3 those ratings are written as a triple of truth, indeterminacy and falsity (T, I, F).

The distinctive part of the structure is the degree of contradiction between the sub-options. For each criterion, a dominant sub-option is fixed, and how contradictory each other sub-option is to that dominant one is given as a number between 0 and 1. If "domestic" is dominant, "neighbouring country" is only mildly contradictory to it, while "distant country" is highly contradictory. This contradiction enters the calculation when the degrees are aggregated: the degrees of sub-options that contradict one another combine with a different weighting than those of sub-options that are close to one another.

In short, an ordinary triple says "how far does this alternative meet the criterion"; the plithogenic structure says "which sub-option of the criterion does this alternative meet, by how much, and how far apart are those sub-options from one another."

Use it where a criterion naturally splits into sub-options and those sub-options are not equally distant from one another. Where the contradiction between a criterion's sub-options matters to the decision itself — for instance, where "two suppliers from the same region can stand in for each other, but one from a distant region cannot" is genuine information — the plithogenic structure carries it.

By contrast, where the criterion is a single question ("is the price acceptable?"), or the sub-options are equally distant from one another, the contradiction degree adds nothing; a neutrosophic structure, or something simpler, then suffices. There is no need to pick the plithogenic structure merely as "the most general one."

Yes, but three separate pieces of information are needed, and all three must be justified. The steps are as follows.

First, split the criterion into sub-options and write a judgement for each one: "the alternative meets this criterion via this sub-option." A measurement on its own does not become plithogenic; what is needed is a judgement about which sub-option the measurement falls under, and how far that sub-option is met.

Second, derive the three degrees for each sub-option from their own sources: truth from evidence in favour, falsity from evidence against, indeterminacy from information that is missing or conflicting. This step is the same as for the neutrosophic card.

Third, fix each sub-option's degree of contradiction relative to the dominant one. These degrees must not be a personal preference; they must come from the nature of the sub-options themselves, resting on a measurable basis such as distance, cost difference, or incompatibility.

What must not be done is dividing a single figure across the sub-options "by feel," and assigning contradiction degrees without justification; if the contradiction degree is invented, the aggregated result is invented too.

The contradiction degree measures how far a sub-option is opposed to the dominant sub-option, not how important it is. A high contradiction degree for the "distant country" sub-option does not mean that sourcing from a distant country is bad; it means only that it cannot be put in the same basket as domestic sourcing, that one cannot substitute for the other.

For that reason:

"This sub-option matters less, so let us set its contradiction degree high"

is better replaced by:

"This sub-option is contradictory to the dominant one to such an extent; importance weight is given separately, at the criterion level"

If the two are conflated, the same piece of information enters the calculation twice.

The chief advantage of the plithogenic structure is that it does not erase a criterion's internal structure. Structures that reduce sub-options to a single degree lose the information of "which sub-option" and the distance between sub-options; the plithogenic structure carries both through to the aggregation step.

Furthermore, in group decisions where several experts assess the same criterion through different sub-options, how far apart the experts' chosen sub-options are remains visible, so how hard consensus will be to reach can be measured.

The structure's weakest point is the contradiction degrees themselves. In the literature these are mostly assigned by the analyst, and the justification is often not shown; different contradiction degrees give different results. A contradiction degree with no measurable basis leaves the result dependent on the analyst's preference.

The data-collection burden is heavy: for every alternative, every sub-option of every criterion needs three degrees, plus one contradiction degree per sub-option. Even in a small problem, the cell count grows quickly. The literature is relatively young; there is no single settled practice for aggregation rules and score functions. Also, for criteria without sub-options, this structure collapses into the neutrosophic structure and adds nothing extra.

The most frequent mistake is forcing a criterion with no sub-options into the plithogenic structure; if "price" has no sub-options, its contradiction degree is meaningless, and the structure is no different from neutrosophic.

The second mistake is using the contradiction degree as if it were an importance weight, or giving every sub-option the same contradiction degree, which reduces the structure's contribution to zero. A third is generating the sub-options' triples by splitting a single figure; each sub-option's degrees must rest on its own evidence.

The governing principle is this:

The plithogenic structure is used only where the criterion has genuine sub-options; each sub-option's degrees must come from its own evidence, and the contradiction degrees from the sub-options' own nature.