RIM (Reference Ideal Method)

RIM is a ranking method for when you hold a decision table filled with numbers and want the alternatives placed in a single order. Its output is a closeness score between 0 and 1 for every alternative, together with the rank that score produces. RIM does not generate weights, it takes them from outside. The method was proposed by Cables, Lamata and Verdegay in 2016 in Information Sciences, and it entered the literature as an alternative that relaxes TOPSIS's assumption that "the best is always at an extreme."

The idea behind RIM is that the assumption "the more the better" or "the less the better" is not always true for every criterion. For some criteria, the ideal is not an extreme but a band: a device's operating temperature should be neither too low nor too high, a product's moisture content must stay within a certain range. RIM defines a reference ideal range for every criterion and measures each alternative's position relative to that range by the distance it falls outside it. Every value inside the range is equally ideal; the score falls the further a value strays outside it.

This structure is the key point that separates RIM from TOPSIS. TOPSIS always looks for the ideal at one extreme (the highest or lowest value); RIM can define the ideal as a range, and that range may sit in the middle of the criterion's span. RIM is also compensatory: a deviation on one criterion can be offset by closeness to the target on another.

The method proceeds through three steps.

First, normalisation against a range. RIM defines two ranges for every criterion: the widest range the criterion can actually take, and the reference ideal range it is desired to fall within. If an alternative's value on a criterion lies inside the reference ideal range, it scores full marks (1). If the value lies outside this range, its score falls towards 0 according to its distance from the range. Every cell thus answers the question "how close to the target" with a value between 0 and 1.

Second, weighting and distance to the reference points. RIM multiplies every normalised column by the criterion's weight. On the weighted table, each alternative's Euclidean distance is measured to a hypothetical ideal point ("on target on every criterion") and to a hypothetical zero point ("on target on no criterion").

Third, the relative closeness index. RIM divides an alternative's distance to the zero point by the sum of its distances to the ideal point and the zero point. For an alternative that matches the target exactly, this ratio approaches 1. RIM ranks alternatives from the highest index to the lowest.

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

The relative closeness index states how well an alternative fits the defined target ranges, and nothing more. An index of 0.81 does not mean "81 per cent good"; it means "the alternative that best fits the target ranges within this particular alternative set." It cannot be compared with an index computed on a different alternative set or with different reference ranges, because both the ideal point and the zero point are built from this analysis's own ranges. An index close to 1 does not mean "perfect" but "fully matching the defined target band."

Thus instead of writing:

"RIM found the best alternative"

the report should read:

"With these target ranges, these weights and this alternative set, the alternative closest to the target is this one; the result is sensitive to the reference range as defined"

RIM works with crisp data: a single number in every cell. DecisionMind currently holds no other data-type extension of this method; the founding authors' fuzzy extension (Cables et al., 2018) has not yet been added to DecisionMind.

You need alternatives in rows, criteria in columns, a number in every cell with no gaps; the widest range each criterion can take; the desired reference ideal range for each criterion; and criterion weights that sum to 1. The reference ideal range may sit at one end of the criterion's range or in the middle. RIM does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; the sweet spot lies between three and twelve criteria.

RIM is especially suitable when at least one of your criteria does not follow the "more is better" or "less is better" logic — that is, when the ideal is a band, such as a target temperature, a target moisture level or a target stock level. Where all your criteria genuinely perform best at an extreme, RIM and TOPSIS give similar results; RIM's real strength emerges when the ideal band sits in the middle of the criterion's range.

It should not be used where decision-makers cannot agree on what the reference ideal range should be; RIM does not determine this range for you, it takes it from outside. If no compromise can be made on a criterion, screening out sub-threshold alternatives first and ranking only the remainder is safer.

At least one criterion has an ideal that is a band, not an extreme → RIM

Every criterion has an ideal at an extreme (highest or lowest) → TOPSIS

No agreement on the reference range → clarify the range first, then apply RIM

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

RIM's most important advantage is that the ideal band can be defined anywhere within a criterion's range; this is more realistic than TOPSIS's "best at the extreme" assumption for many real decision problems, such as engineering tolerances, health indicators and environmental thresholds. Defining a separate reference range for every criterion lets the decision-maker feed expert knowledge directly into the model. Because its computational logic is close to TOPSIS's, it is easy to explain and its result is easy to trace.

Its limitations stem from the reference-range definition. First, if the reference range is set incorrectly or without justification, the entire result carries this error; RIM does not itself check the range's correctness. Second, it carries a full-compensation assumption: a deviation on one criterion can be offset by closeness to the target on other criteria. Third, when the alternative set changes, the ideal and zero points remain fixed in RIM (because they are tied to the reference range), but an independent examination of rank reversal, as frequently discussed for TOPSIS, remains limited in the literature for RIM; general MCDM findings should be taken as cautious guidance (Wang and Luo, 2009). Fourth, if the criterion range (the widest bound) is chosen too wide or too narrow, the normalisation is distorted.

The most common mistake is confusing the reference ideal range with the criterion's actual attainable range; the two are distinct concepts and must be defined separately. A second mistake is setting the reference range on every criterion to one extreme (the highest or lowest point), effectively using RIM as if it were TOPSIS; this forgoes RIM's real strength. A third mistake is assigning weights equally without justification. A fourth mistake is reading the index as a percentage and comparing it across different analyses.

The governing principle is this:

A RIM result is a summary of the target ranges and weights you have defined; if the range is defined wrongly, the result points in the wrong direction too.