Plithogenic MARCOS

Four things change; the decision logic does not.

Cells. In crisp MARCOS 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. Crisp MARCOS first takes the complement for a cost criterion, then builds the ideal (AI) and anti-ideal (AAI) rows from the observed best and worst values. This family follows the same order. First, the SVN complement (F, I, T) is taken for a cost criterion. Every cell is then adjusted by its own criterion's contradiction degree. The AAI (worst) and AI (best) rows are then built, component by component, from these adjusted cells.

Normalisation and combination. Every cell is divided by its own criterion's ideal (AI) value and weighted exponentially (the same power-weighting formula as in neutrosophic and plithogenic TOPSIS). These weighted cells are combined within a row so that each alternative, and the AAI and AI, arrives at a single T-I-F triple; this combination is a multiplicative aggregation (the complements of one component are multiplied together and subtracted from one). This combined triple is then reduced to a single score.

Utility ratios and result. Every alternative's score is divided separately by the AAI's score and the AI's score to give K⁻ and K⁺; these two are then combined in a utility function, exactly as in crisp MARCOS, to obtain the final utility degree f(K). Indeterminacy (I) and falsity (F) are not defuzzified in a separate step; they dissolve inside the multiplicative combination and the score function.

DecisionMind holds the cost complement, the contradiction adjustment, the power weighting and the multiplicative combination fixed in this family. Criterion weights and contradiction degrees are taken from outside, separately.

The output is a final utility degree, as in crisp MARCOS, and it is read the same way: a high value means "well positioned on this set's ideal-anti-ideal axis," not an absolute measure of quality.

The illustrative example below shows a notable feature: A2 and A3 receive exactly the same final utility degree (0.6221). This tie is specific to this table alone; it does not break when the weights are changed, and it does not break when the contradiction degrees between criteria are changed (this has been tested). This means the method cannot distinguish between these two alternatives; a further criterion, or a further preference principle, is needed to settle second place. Also, in this table, the alternative P-MARCOS ranks first (A1) differs from the one P-TOPSIS, P-EDAS and P-COPRAS rank first (A2) using the same data; this is not an error, it follows from MARCOS reading the ideal-anti-ideal ratio differently from TOPSIS's distance and EDAS's average.

Thus instead of writing:

"Plithogenic MARCOS found the best supplier"

the report should read:

"With these weights and these contradiction degrees, this is the alternative with the most balanced utility ratio against the ideal and anti-ideal references; if two alternatives come out equal, the method does not distinguish between them"

This extension is appropriate when your criterion scores are given as truth-indeterminacy-falsity triples and you want both "how much of the ideal has been reached" and "how far the anti-ideal has been left behind" to appear together. 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 MARCOS 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 your alternative set is very small, the ideal and anti-ideal references, being built from the alternatives themselves, can be fragile; this is the same warning as in crisp MARCOS.

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

Quietly separating alternatives that come out tied. In the illustrative example, A2 and A3 come out exactly equal; placing one ahead of the other and writing an unjustified ranking claims more than the method actually delivers. The report should show the tie as it is and propose a further criterion for distinguishing between them.

Assigning the contradiction degree without justification. The degree must rest on a justification for the criterion's independence relative to the dominant criterion; a degree chosen "to widen the gap" can make A1's superiority look larger, or smaller, than it is.

Running a cost criterion without taking its complement. Processing a cost criterion without taking the complement of (T, I, F) draws the highest-cost alternative towards the ideal.

The governing principle is this:

The plithogenic MARCOS result is a proportional summary of the T-I-F scores relative to this set's own ideal and anti-ideal points; when two alternatives come out equal, the answer is to look for a further distinguishing criterion, not to conceal the tie.