SIR (Superiority and Inferiority Ranking)

SIR is a method for ranking alternatives once you hold a decision table filled with numbers ("which supplier," "which process," "which route"). Its output is a net flow value for every alternative and a complete ranking based on it. Xu proposed it in 2001, combining the "superiority, inferiority" idea from the European PROMETHEE and ELECTRE tradition with SAW's (Simple Additive Weighting) summation logic.

SIR's underlying idea is to measure an alternative's strength from two separate angles rather than one: how much it outperforms the others (superiority) and how much the others outperform it (inferiority). These two values are not simply each other's mirror image; each is computed, as in PROMETHEE, through a criterion-level preference function, then combined across criteria with SAW's logic (a weighted sum).

This dual structure carries a philosophical consequence. SIR combines PROMETHEE's fine-grained, criterion-level preference functions, sensitive to thresholds rather than a bare "which is larger," with SAW's simple and transparent summation logic. Because it reports superiority and inferiority separately, the result offers a richer intermediate picture than TOPSIS's reduction to a single distance score; but the final ranking still rests on one net value (superiority minus inferiority) and is compensatory in the same way TOPSIS is.

The method proceeds through six steps.

First, the direction-adjusted difference. For every criterion, the difference between two alternatives is calculated; for "lower is better" criteria this difference's sign is reversed, so that on every criterion a positive difference means "better."

Second, the preference function. This difference is mapped onto the range 0 to 1 through one of six preference functions from the PROMETHEE family. If there is no difference, or it is very small, the preference is zero; if the difference is large enough, the preference is one; between the two, an intermediate value is taken according to the function (linear, stepped or curved). Which function to use and what the thresholds are comes from the user.

Third, the superiority and inferiority indices. For every criterion, an alternative's average superiority and average inferiority relative to the others are calculated.

Fourth, the SAW summation. These criterion-level superiority and inferiority values are weighted and summed using the criterion weights, giving each alternative a single superiority score and a single inferiority score.

Fifth, the net flow and the flow ratio. The net flow is found by subtracting the inferiority score from the superiority score; in addition, the ratio of the superiority score to the sum of superiority and inferiority is calculated. If both superiority and inferiority are zero (the alternative neither stands out nor falls behind on any criterion), this ratio is recorded as the neutral value of 0.5.

Sixth, the complete ranking. In the SIR-SAW net-flow form DecisionMind implements, alternatives are ranked from the highest net flow to the lowest. SIR is a family of methods; Xu's own work also offers other ways of combining the indices, such as partial-intersection ranking, and DecisionMind does not silently replace these with SAW net flow.

The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.

The net flow shows, on average, how far ahead an alternative sits relative to the others; it is not a percentage or a degree of certainty. The flow ratio, meanwhile, is a value between 0 and 1: above 0.5 means "superiority exceeds inferiority," below it means "inferiority exceeds superiority," and this too is not a probability. The two values confirm one another without saying the same thing: net flow shows the size of the gap, and flow ratio shows the gap's direction and relative weight.

Thus instead of writing:

"SIR found the best alternative"

the report should read:

"With these weights, these preference functions and these thresholds, the alternative with the highest net flow is this one; the ranking may change if the preference function or threshold changes"

SIR works with crisp data: one number per cell. DecisionMind carries no separate data-type extension of this method; it stands alone in its base form.

You need alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; criterion weights summing to 1; and, for every criterion, which preference function to use and, where needed, indifference, preference and Gaussian thresholds. If a function requiring a threshold is chosen but no threshold is supplied, DecisionMind does not silently fall back to the simplest function; it rejects the missing input. SIR produces no weights of its own; it takes them from outside.

SIR is a suitable choice if your criteria are numerical, you want to tune preference functions at the criterion level (not just "which is larger" but "how much larger"), and it is useful to you to see superiority and inferiority separately.

It should not be used in the following situations: if you cannot justify the preference functions and thresholds, the method produces an arbitrary result. If no compromise is acceptable on one criterion, SIR is unsuitable, because it is compensatory and has no veto mechanism; and if a simple ranking is all that is needed, a method with fewer parameters should be preferred.

A fine-grained, criterion-level preference function is needed, and the superiority/inferiority split is useful → SIR

A simple, low-parameter ranking is enough → TOPSIS, SAW

No compromise on one criterion, sub-threshold alternatives must be screened out → PAMSSEM I, the ELECTRE family

Weights are needed rather than thresholds → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

SIR's greatest strength is that it combines PROMETHEE's flexible preference functions with a simple, explainable SAW summation. Reporting superiority and inferiority separately gives the decision-maker a more detailed answer than PROMETHEE does to the question "why did this alternative come out ahead, and where is it weak?" Its six alternative preference functions allow the tuning to be matched to a criterion's nature, whether threshold-sensitive or linear.

Its limitations concern the parameter burden. First, it requires a preference function and threshold choice for every criterion; if these choices are not justified, the result becomes arbitrary. Second, SIR is a family of methods, and the SAW net-flow form DecisionMind implements is not the only route in the literature; a different piece of software or paper using a different combination rule may not reproduce the same results exactly. Third, the method is fully compensatory, in the same way TOPSIS is; a weakness on one criterion can be papered over by others, and there is no veto mechanism. Fourth, the limitation shared by the PROMETHEE and ELECTRE families also applies here: the result is sensitive to the choice of preference function and threshold (Zhao, Xu and Ren, 2019, discuss this sensitivity separately while proposing a hesitant fuzzy extension of SIR).

The most common mistake is applying the same preference function, usually the simplest "usual" one, to every criterion without thinking it through; this ignores the threshold or gradual transition that the criterion's true nature may involve.

A second mistake is choosing a function that requires a threshold and hoping to leave the threshold blank; DecisionMind does not accept this and returns a missing-input error. A third is reading net flow as a percentage or a probability. A fourth is interpreting a flow ratio near 0.5 as "undecided" rather than "superiority and inferiority are nearly equal"; these are different statements. A fifth is presenting SIR as though it were a single universal formula without reporting which SIR variant (SAW plus net flow) DecisionMind applies.

The governing principle is this:

A SIR result is a summary of the chosen preference functions, thresholds and weights; if these choices change, the balance of superiority and inferiority changes with them.