Plithogenic EDAS

Four things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I), falsity (F). The sub-option idea from the plithogenic data-type card is carried, in this family, to the criteria themselves: one of the criteria is taken as dominant, with a contradiction degree of zero. How far each other criterion opposes this dominant criterion is given by a contradiction degree. This degree belongs to the criterion, not to the alternative; it does not vary from alternative to alternative.

Scale equalisation and scoring. In crisp EDAS the average is taken directly over the numbers. Here the triple is first reversed for a cost criterion, and every cell is then adjusted by its own criterion's contradiction degree. Each adjusted triple is then reduced to a single score: the score is built as truth plus twice indeterminacy and falsity minus, divided by two. This score function is the same as the one used on the neutrosophic cards. EDAS's own distinctive step, "the set's average," is computed over these single-number scores.

Deviation and weighted sums. Every alternative's score gives two separate deviations, according to whether it falls above or below the criterion's average score. One is the portion falling on the favourable side of the average (positive deviation), the other the portion falling on the unfavourable side (negative deviation). These are multiplied by the criterion weights and summed, giving each alternative a favourable sum and an unfavourable sum. This step is identical to crisp EDAS; the only difference is that the deviation is measured over a single score derived from T-I-F.

Result and defuzzification. The favourable and unfavourable sums are each normalised by dividing by the largest value among themselves, and the average of the two is taken to form a single assessment score. Indeterminacy (I) and falsity (F) are not defuzzified in a separate step; they dissolve inside the score function, and the remaining steps of EDAS proceed with crisp numbers.

DecisionMind holds the cost complement, the contradiction adjustment and the score function fixed in this family. Criterion weights and contradiction degrees are taken from outside, separately.

The output is an assessment score and ranking, as in crisp EDAS, and it is read the same way: it is not a percentage, it is not compared with a different analysis, and an alternative added to or removed from the set changes the average, and hence every score.

The difference lies here: the average across criteria is now the average of a score derived from T-I-F, and this score has itself already been adjusted according to the criterion's contradiction degree. In the illustrative example below, A2 leads clearly (1.0000); the gap between A3 (0.1883) and A1 (0.0702) is also noticeable, but once the weights shift towards C2 this distance narrows, and A3 can even overtake A2.

Thus instead of writing:

"This alternative was chosen because plithogenic EDAS found it best relative to the set's average"

the report should read:

"This is the alternative in the most favourable position relative to the set's average; this position is sensitive to the criterion weights and to the assumed contradiction degree between criteria"

This extension is appropriate when your criterion scores are given as truth-indeterminacy-falsity triples and the "position relative to the set's average" measure suits your decision. If some criteria are a more independent, or more contradictory, source of information than others, this strengthens the case for it. Where the T-I-F triple alone suffices and no such dominance-contradiction relationship exists between criteria, neutrosophic EDAS (n-edas) is already sufficient; the plithogenic form adds one further assumption, and if that assumption is supplied without justification it creates a spurious distinction.

Turning a measured criterion into a T-I-F triple is producing uncertainty, not modelling it. If all alternatives sit very close to the average on a criterion, that criterion's discriminating power falls in this family too; this is not a fault but a natural consequence of the method.

Violating the value space. Every cell must be a valid T, I, F triple, and every criterion's contradiction degree must be declared.

Assigning the contradiction degree without justification. When the weights are shifted from C1 to C2 (0.40→0.10, 0.35→0.65), A3 overtakes A2; the same kind of shift can also be produced through the contradiction degree. The contradiction degree should be set on a justification for how independent a criterion's information is relative to the dominant criterion, not to pull the ranking in a desired direction.

Changing the score function. The weighted score — truth plus, indeterminacy and falsity minus — is fixed; comparing results against a different defuzzification formula is a difference between definitions, not between methods.

Reading closeness to the average as "the criterion is unimportant." This mistake in crisp EDAS applies here too; scores clustering near the average on a criterion does not mean that criterion is actually unimportant.

The governing principle is this:

The plithogenic EDAS result is a summary of the T-I-F scores' position relative to the set's own average; this position is sensitive both to the weights and to the assumed contradiction degree between criteria, and the report must show both.