Z-number EDAS

Three alternatives are scored as Z-numbers on three criteria. Every cell gives the A (value) triangle; reliability B is the same across all three criteria and all three alternatives: (0.70; 0.80; 0.90).

The method reduces every cell's Z-number to a crisp number by the Kang transformation. C1's average comes out at 0.70, C2's at 0.60, C3's (cost) at 0.50. It then weighs the parts of each alternative that sit above and below these averages and combines them into a single assessment score.

The result reads as follows. A2 sits markedly above the average (0.70) on C1, the most heavily weighted criterion, at 0.80, and below the average (0.50) on C3 (cost), that is, in its favour, at 0.40. On C2, however, A2's value (0.60) is exactly equal to that criterion's own average; this criterion contributes nothing to A2's score. A2's advantage comes entirely from C1 and C3.

The decision's hesitation is this. If the weights are changed to C1=0.10, C2=0.65, C3=0.25, the ranking reverses: A3 comes first at 0.955, A2 second at 0.797. A2's advantage depends on the weight given to C1 and C3. Once C2's weight is raised, A3 moves ahead, because A3 sits markedly above the average on C2.

Reliability B has no effect at all on these results. Even if B is lowered, say, to (0.01; 0.02; 0.03), the assessment scores come out exactly the same under both weighting scenarios. This has been verified by running the kernel.

In the report: "With weights C1=0.40, C2=0.35, C3=0.25, A2 sits in the most advantageous position relative to the set's average (1.000). If the weight of C2 is raised enough to overtake C1 (C2=0.65, C1=0.10), A3 moves ahead. The degree of reliability is not reflected in this result by the current engine."

Source: DecisionMind's Z-EDAS validation example; built as synthetic 3x3 fixed data, following the Z-number framework of Zadeh (2011) and Kang et al. (2012). The assessment scores and the sensitivity scenario have been independently recomputed by this card's author using the same algorithm, and match the manifest's expected values exactly (tolerance 1e-9).

An agricultural cooperative will choose among three feed suppliers for its member farms. The criteria are the feed's nutritional value, unit cost and the supplier's delivery regularity. All but cost are "higher is better," cost is "lower is better." Nutritional value is entered as a Z-number because it rests on the supplier's own laboratory report. A is the value stated in the report; B is whether that report was issued by an independent laboratory or by the supplier's own laboratory.

The method reduces the three suppliers' Z-numbers to crisp numbers by the Kang transformation and applies classical EDAS. Suppose the result places first the supplier whose nutritional value appears highest, where that value is reported only by its own laboratory.

The cooperative's hesitation is this. If this supplier's nutritional-value declaration has not passed an independent audit, it should be known that the current engine does not reflect this gap in the ranking at all. The cooperative should require an independent sample analysis before the selection.

In the report: "With the weights given, the supplier whose nutritional value appears highest is ahead relative to the set's average. This supplier's nutritional-value declaration has not passed an independent laboratory, and the current calculation does not reflect this gap; an independent sample analysis is recommended before the selection."

In the illustrative example, sharply lowering A2's reliability on the C1 criterion and expecting "A2's score should now fall" is wrong: the score does not change at all, because the current engine does not read B. The second error is failing to notice that A2 sits exactly at the average on C2 and interpreting this criterion as "also supporting A2"; its contribution is zero. The third error is reading the value of 1.000 as "a flawless supplier"; the score only compares these three alternatives against the set's own average.