Fuzzy MEREC (Saidin, Lee, Marjugi, Ahmad & Seow, 2023)

Three things change. The removal-effect logic and the final weight calculation do not.

Cells. In crisp MEREC every cell is a single number. Here every cell carries three numbers: lowest, most likely, highest. If an expert gives a verbal score ("near excellent", "very good"), a pre-declared scale converts that word into a triangle. MEREC does not require weights; neither does this form — the only difference is that the input has three components.

Scale equalisation. There is a point worth noting here: the direction of normalisation is reversed between crisp MEREC and the fuzzy version. In crisp MEREC, a small value on a benefit criterion takes a large share, because the column's smallest value is divided into every value. In the fuzzy version it is the opposite for a benefit criterion: every triangle is divided by the largest upper value in the column, so a large value takes a large share. For a cost criterion, the fuzzy version reverses this by dividing the column's smallest lower value into every triangle. This difference comes not from DecisionMind's own design but from the founding paper's own definition, Saidin and colleagues (2023); DecisionMind applies that definition verbatim.

Defuzzification. Crisp MEREC has no defuzzification step, because it already works with crisp numbers. When the fuzzy version reduces a normalised triangle to a single number, it does not use the simple average (an equally weighted mean of the three components) that PSI and RAFSI use. Instead it applies a rule that gives the middle, most-likely value four times the weight; this rule is called the graded mean integration. It produces a number somewhat different from an equally weighted average of the three components, and it trusts the most-likely value more.

From this defuzzified number onward, everything else is identical to crisp MEREC. Each alternative's overall performance is computed by a logarithmic sum. Then each criterion is removed in turn and performance is recomputed; the resulting difference is summed and turned into a weight.

DecisionMind holds this normalisation direction and the graded mean integration fixed.

The output is not a ranking, as in crisp MEREC, but a weight vector that sums to 1. A criterion receiving a high weight means that removing that criterion disturbs the overall evaluation a great deal; it does not indicate that criterion's importance in the decision-maker's eyes. This reading is the same as for crisp MEREC. The difference is that, where the input is verbal or approximate, the direction of normalisation behind the weight has been reversed. This is why comparing a criterion's weight under fuzzy MEREC directly with the weight that crisp MEREC would give for the same data is misleading. The two methods normalise the same data in opposite directions.

So instead of:

"Because Fuzzy MEREC and crisp MEREC use the same logic, their weights can be compared directly"

the report should read:

"Fuzzy MEREC normalises in the opposite direction. Applying crisp MEREC to the same data would give different weights; before placing two results side by side, which method was used must be stated in the report"

Fuzzy MEREC is appropriate if you want the weights to be derived from the data and the criterion scores you have are also not measured, but come from expert judgement or approximate estimation. Opening a measured value into a triangle without justification is wrong here too; the rule on the fuzzy data-type card applies.

If the weights need to reflect a known priority held by the decision-maker, the exit condition on the base MEREC card applies just the same. In that case a subjective weighting method such as AHP, BWM or SWARA should be preferred.

Letting the defuzzified value reach or exceed 1. The next step takes the logarithm of 1 minus this value. If the defuzzified value reaches or passes 1, this operation becomes undefined, and the engine is expected to stop fail-closed.

Leaving a zero or negative lower value on a cost criterion. The cost criterion's normalisation divides by this value. A zero or negative lower value risks division by zero. On a benefit criterion, zero causes no problem as long as the column's largest value is positive.

Assuming the same normalisation direction as crisp MEREC. As explained above, the direction is reversed; ignoring this difference and comparing the two methods' weights directly produces a wrong result.

Taking expert scores from a single person who already reaches the same conclusion. The source article, Saidin and colleagues (2023), assumes that scores from multiple experts have already been aggregated beforehand. DecisionMind does not perform this aggregation itself; it expects a ready-made triangular matrix.

The governing principle is this:

In Fuzzy MEREC the direction of normalisation is the exact opposite of crisp MEREC's. This comes not from an error but from the founding paper's own definition. But if this difference is not reported, the weights of the two methods can mistakenly be taken to be on the same scale.