Extension card · Hesitant
Hesitant Fuzzy EDAS (Kutlu Gündoğdu, Kahraman and Civan, 2018)
The form of EDAS in which every cell is given as a triangular fuzzy number and DecisionMind reduces this number to a single value at the very start of the calculation, comparing it against the set's average.
Base method
EDAS →
Philosophy, mechanics, strengths and weaknesses are on the base method card; this card describes only the difference.
Data type (family)
Hesitant →
What this data type is, when to use it, how to write it in a cell: the family's full account is here.
What Changes from the Base Method?
Three things change. The decision logic stays the same.
Cells. In crisp EDAS every cell is a single number. Here every cell is a triangular fuzzy number made of three values: lowest, most likely and highest. The founding paper actually also defines holding more than one triangle together in the same cell; that is the genuinely hesitant version. But DecisionMind's running engine currently accepts only a single triangle per cell. More than one triangle cannot be carried in the same cell. Weights are given from outside, as crisp numbers.
Scale equalisation. HF-EDAS preserves classical EDAS's positive- and negative-deviation logic against the column average. But the comparison is not made on the triangles themselves; it is made on the weighted centroid of each triangle. DecisionMind converts every triangle into a single number by adding the lowest value plus four times the most-likely value plus the highest value, then dividing the sum by six. It reduces the column average to a single number the same way. The positive and negative deviation are computed from these two crisp numbers. This is a design that deliberately departs from the general principle described at the top of this card. In most extensions defuzzification is left for the very end. In HF-EDAS, by contrast, defuzzification comes right at the start, as soon as the matrix is built.
Distance, score and aggregation. Once defuzzification is complete, the rest of the calculation is crisp EDAS itself. Each alternative's defuzzified value is measured against whether, and by how much, it sits above or below the column average. These values are summed with the weights, normalised, and merged into a single assessment score.
Result and defuzzification. The output is, as in classical EDAS, an assessment score between 0 and 1. But because defuzzification is done at the very start of the calculation, the resulting score has been computed with crisp numbers from beginning to end. The width of the triangle, that is, the gap between its lowest and highest value, never shows up in the result.
DecisionMind holds this defuzzification formula and the early-defuzzification order fixed in classical HF-EDAS.
How to Read the Output
The assessment score is read exactly as in crisp EDAS. It shows a position relative to the set's own average and cannot be compared with a different analysis. What differs is this: there is no longer any fuzziness behind the score. Even though the input was collected in triangular form, the calculation runs entirely on crisp numbers. The gap between two alternatives is read with exactly the same precision as in classical EDAS. The width of the triangle never shows up in the result.
Thus instead of writing:
"HF-EDAS carries fuzziness all the way through, so the result is more reliable"
the report should read:
"The triangles were reduced to their weighted centroids at the very first step; the resulting score has been computed entirely on these single numbers, and the width of the triangle does not show up in the score"
When to Prefer This over the Base Method
Use this extension when criterion assessments have been collected as triangular fuzzy numbers, for instance when expert opinion is given as "worst, most likely, best", and what the organisation actually wants is classical EDAS's logic of position relative to the average. If genuinely hesitant data exists, that is, more than one triangle in the same cell, DecisionMind's HF-EDAS engine does not currently support this. The user must first reduce the triangles to a single representative triangle, for instance by averaging the experts' triangles. This is a DecisionMind limitation, and it goes beyond the genuine-hesitancy principle recommended on the data-type card.
Mistakes Specific to This Extension
Mistaking HF-EDAS for a method that carries uncertainty through to the end. Defuzzification is done at the very start. The width of the triangle never affects the score at any step; it affects only the centre value.
Trying to write more than one triangle into the same cell. The engine expects a single triangle. If more than one exists, they must first be aggregated, for example by averaging. This aggregation must be stated explicitly in the report.
Marking the cost and benefit direction wrongly. Because the calculation after defuzzification is identical to crisp EDAS, a direction error disrupts the ranking in exactly the same way.
The "more advanced" fallacy. A triangular input does not automatically mean a more accurate result than classical EDAS. Because defuzzification happens early, its contribution is limited to how the input was collected.
The governing principle is this:
In HF-EDAS, uncertainty is reduced to a single centre value at the very first step, before it ever enters the calculation, when the matrix is built. The report must not conceal this early defuzzification, and must state that the triangle's width does not reach the result.
Cases
The first case is a genuine literature case. It is the hospital-selection example from Kutlu Gündoğdu, Kahraman and Civan's (2018) paper, and the figures are taken from that paper. The second case is an illustrative fiction.
1. Healthcare: Choosing a hospital for organ transplantation (Kutlu Gündoğdu, Kahraman and Civan, 2018)
A health board in Istanbul will choose among three hospitals for organ-transplant services. There are twelve sub-criteria, gathered under the headings of tangibles, reliability, responsiveness and empathy. Three assessment groups' triangular fuzzy scores were aggregated to obtain them. Only the "value for money" criterion is "less is better"; the other eleven are all "more is better". Weights come from the board's own assessment.
| Hospital | C11 | C12 | C13 | C14 (less is better) | C21 | C22 |
|---|---|---|---|---|---|---|
| A | (0; 0.43; 0.63) | (0; 0.41; 0.6) | (0.54; 0.71; 0.8) | (0.31; 0.45; 0.55) | (0.27; 0.45; 0.58) | (0; 0; 0.74) |
| B | (0.6; 0.77; 0.86) | (0; 0.33; 0.57) | (0; 0.38; 0.59) | (0; 0.71; 0.87) | (0.25; 0.38; 0.47) | (0.55; 0.78; 0.9) |
| C | (0.25; 0.38; 0.47) | (0; 0.63; 0.81) | (0.77; 0.94; 1) | (0; 0.49; 0.67) | (0.22; 0.38; 0.5) | (0.16; 0.37; 0.58) |
| Hospital | C31 | C32 | C33 | C41 | C42 | C43 |
|---|---|---|---|---|---|---|
| A | (0; 0; 0.75) | (0.27; 0.45; 0.58) | (0; 0; 0.75) | (0; 0.76; 0.88) | (0; 0; 0.3) | (0.31; 0.45; 0.55) |
| B | (0.74; 0.92; 1) | (0.25; 0.38; 0.47) | (0.74; 0.92; 1) | (0.6; 0.77; 0.86) | (0.74; 0.92; 1) | (0; 0.31; 0.53) |
| C | (0.75; 0.93; 1) | (0; 0.34; 0.49) | (0; 0.49; 0.7) | (0.43; 0.59; 0.69) | (0; 0; 0.44) | (0.44; 0.6; 0.69) |
| Weight | C11 | C12 | C13 | C14 | C21 | C22 | C31 | C32 | C33 | C41 | C42 | C43 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.11 | 0.16 | 0.01 | 0.16 | 0.13 | 0.10 | 0.10 | 0.08 | 0.01 | 0.02 | 0.11 | 0.01 |
The method reduces every triangle to a single number with the weighted-centroid formula. It defuzzifies the column average the same way. It then sums, as in classical EDAS, how far above or below this average each hospital falls, weighted by the criteria.
| Hospital | Assessment score | Rank |
|---|---|---|
| B | 0.844 | 1 |
| C | 0.408 | 2 |
| A | 0.065 | 3 |
The result reads as follows. B has defuzzified values clearly above average on heavily weighted criteria, in particular C31, C33 and C42. A falls below average on the same criteria and comes last.
The board's hesitation is this. C13 is hospital C's strongest criterion, but its weight is only 0.01. C42 is hospital B's strongest criterion, and its weight is 0.11. If these two weights swap, that is, if C13 rises to 0.11 and C42 falls to 0.01, the ranking changes: C moves to first with 0.723, and B drops to second with 0.668. B's first place rests essentially on the relative size of these two weights.
In the report: "According to the assessment score, Hospital B is in the most advantageous position relative to the average (0.844). This result rests on the responsiveness criterion's weight being kept higher than the tangibles criterion's. When the weights swap, Hospital C moves ahead."
Source: Kutlu Gündoğdu, Kahraman and Civan (2018), Table 5, Table 13 and Table 10, pp. 7-11. The assessment scores and the weight-swap scenario were obtained by independently re-running DecisionMind's HF-EDAS engine. The result matches the paper's Table 10 ranking (B, then C, then A).
2. Food safety: Choosing a cold-chain monitoring system
A food-safety authority will choose among three technology providers for cold-chain temperature monitoring in the meat and dairy supply chain. There are four criteria: unit sensor cost, temperature-measurement precision, data-transmission latency, and a score for how easily field technicians can install the system. Cost and latency are "less is better". The authority has gathered each provider's performance from laboratory tests as a triangular fuzzy number in "worst, most likely, best" form. For instance, one provider's precision score came out at 0.5 in the worst case, 0.7 as most likely, and 0.85 in the best case. The weights come from the authority's technical unit.
The method reduces every triangle to its weighted centroid, then computes the positive and negative deviation against the column average. Suppose the lowest-cost provider also has the lowest precision. It still comes second relative to the average, because the weight on cost has been kept lower than the weight on precision.
The authority's hesitation is this. The width of the triangle on the precision criterion may reflect the gap between laboratory and field conditions. But DecisionMind's early-defuzzification step never takes this width into account, using only the centre value. The authority should not decide on score alone for criteria with wide triangles, without backing them up with a separate field-validation test.
In the report: "According to the assessment score, the provider with the highest precision comes out ahead. This criterion's triangle width reflects the gap between laboratory and field conditions and does not show up in the score. A separate field test is recommended to confirm it."
3. What Not to Do
Had the value-for-money criterion in the hospital table been marked "more is better", the most expensive hospital would have been rewarded, and the ranking would become meaningless. The second error is, when a hospital genuinely has more than one independent triangular score on a criterion, for instance from two separate audit rounds, forcing them directly into a single cell without averaging them first; the engine expects a single triangle, and the aggregation step must be shown in the report. The third error is reading Hospital B's score of 0.844 as "84 per cent quality"; this score only compares these three hospitals against the set's own average.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/hf-edas
Kutlu Gündoğdu, F., Kahraman, C., & Civan, H. N. (2018). A novel hesitant fuzzy EDAS method and its application to hospital selection. Journal of Intelligent & Fuzzy Systems, 35(6), 6353–6365. DOI: 10.3233/JIFS-181172
Keshavarz Ghorabaee, M., Zavadskas, E. K., Olfat, L., & Turskis, Z. (2015). Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica, 26(3), 435–451. DOI: 10.15388/Informatica.2015.57
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. DOI: 10.1002/int.20418
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. DOI: 10.1016/S0019-9958(65)90241-X