Extension card · Linguistic
2-tuple linguistic neutrosophic EDAS (Wang, Wang & Wei, 2019)
2-tuple linguistic neutrosophic EDAS is the form of EDAS for situations where criterion assessment is made in words chosen from a term set, with a degree of truth, indeterminacy and falsity attached to those words. The combined result is not rounded to a term; it is carried together with its term and translation value.
Base method
EDAS →
Philosophy, mechanics, strengths and weaknesses are on the base method card; this card describes only the difference.
Data type (family)
Linguistic →
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?
Five things change; the distance-from-average logic does not.
Cells. In crisp EDAS every cell is a single number. In 2-tuple linguistic TOPSIS every cell is a single 2-tuple made of a term and a translation value. Here, by contrast, every cell consists of three separate 2-tuples: a term and translation value for truth, a term and translation value for indeterminacy, and a term and translation value for falsity. This means that each component of the neutrosophic triple (truth, indeterminacy, falsity) is itself chosen from a term set and held together with a translation value. In a plain 2-tuple linguistic method, a single word's degree of "highness" is asked; here, for the same judgement, "how true," "how indeterminate" and "how false" are each asked separately, from separate term sets.
Cost direction. Direction reversal on a cost criterion is done by swapping the truth 2-tuple with the falsity 2-tuple; the indeterminacy component does not change.
Group combination. If there is more than one decision-maker, each expert's triple 2-tuple is reduced to a single triple using a weighted combination rule (2TLNNHWA). With a single decision-maker this step changes nothing.
Average solution and scoring. The average solution is built on the same logic as in crisp EDAS, by combining every criterion across all alternatives; but here the combination is not a numerical average, it is done with the triple 2-tuples' own combination rule. The positive and negative deviation are computed not on the raw triples but on the single number each triple is reduced to by a score function.
Result and defuzzification. The reduction to a score happens immediately before the average and deviation calculation, not before. The weighted sums, normalisation and assessment score then proceed in exactly the same form as crisp EDAS.
DecisionMind fixes, in this extension, the triple 2-tuple's score function and the group-combination rule. Weights are taken from outside as crisp numbers; the method does not generate weights.
How to Read the Output
The assessment score is read as in crisp EDAS: it is a position relative to the set's own average, not a percentage or a probability. The difference lies here: beneath the score sit three separate 2-tuples, that is, three separate terms and translation values. Two alternatives can reach the same score through different combinations of truth, indeterminacy and falsity; one might arrive at it through high truth and low indeterminacy, another through medium truth and high indeterminacy. A single score hides this difference.
Thus instead of writing:
"2-tuple linguistic neutrosophic EDAS carries uncertainty in a separate component, so the result is more reliable"
the report should read:
"Assessments were given as truth, indeterminacy and falsity terms, reduced to a single score, and ranked relative to the average; the three terms beneath the score should be reported separately"
When to Prefer This over the Base Method
This extension suits situations where experts can assess a judgement not merely as "how high" but as three separate terms, "how true, how indeterminate, how false," and where these three terms need to be carried without rounding to a single term. If the expert speaks in only a single term, the 2-tuple linguistic TOPSIS family suffices; adding the truth-indeterminacy-falsity distinction would build an artificial layer. For a measured criterion, crisp EDAS suffices; expanding a measured value into three terms adds no information.
The same exit condition as crisp EDAS applies: if no compromise is acceptable on one criterion, this extension too is compensatory and will not screen out anything below a threshold.
Mistakes Specific to This Extension
Discarding the translation value and using only the term. Discarding each component's translation value and rounding to the nearest term voids the 2-tuple structure's purpose of preventing information loss.
Compressing the truth-indeterminacy-falsity triple into a single 2-tuple. The three components come from separate term sets and are carried separately; averaging one against another reduces the method to plain 2-tuple linguistic EDAS.
Converting indeterminacy as well as truth and falsity on a cost criterion. In the direction change, only truth and falsity swap places; the indeterminacy component stays as it is.
Citing the retracted source as the sole basis. Because the founding paper has been retracted, the report should state which independent source (the 2-tuple linguistic representation, the neutrosophic set) separately validates the formula chain.
The governing principle is this:
In 2-tuple linguistic neutrosophic EDAS, uncertainty is carried in three separate terms and falls to a single score only immediately before the average-deviation calculation. Any application that discards the translation value, conflates the three components, or cites the retracted paper as the sole source damages either the extension's contribution or its credibility.
Cases
The founding paper's (Wang, Wang & Wei, 2019) numerical example did not publish the matrix combined across decision-makers; only one decision-maker's raw scores and the final ranking are available. When DecisionMind's engine is run with this incomplete data, the cells collapse to zero and the ranking becomes meaningless; this behaviour is documented explicitly in the engine's own documentation. For this reason the first case is a three-alternative validation example faithful to the formula chain, rather than the paper's table. The second case is an illustrative construction.
1. Illustrative example: Three alternatives assessed on three criteria (DecisionMind validation example)
Three alternatives are assessed on three criteria (C1, C2 higher-is-better; C3 lower-is-better) with the truth-indeterminacy-falsity triple. The term set has seven steps (s0 to s6); every component is given as a term from this set, with translation values of zero. Weights are C1 = 0.40, C2 = 0.35, C3 = 0.25.
| Alternative | C1 (truth, indeterminacy, falsity) | C2 | C3 (cost) |
|---|---|---|---|
| A1 | s5, s2, s1 | s3, s3, s3 | s4, s2, s2 |
| A2 | s6, s1, s1 | s5, s2, s1 | s2, s2, s4 |
| A3 | s4, s2, s2 | s4, s3, s2 | s3, s3, s3 |
The method swaps truth and falsity on C3, reduces every triple to a single score, builds the column average over these scores, and applies the remaining steps of crisp EDAS.
| Alternative | Assessment score | Rank |
|---|---|---|
| A2 | 0.745 | 1 |
| A1 | 0.291 | 2 |
| A3 | 0.000 | 3 |
The result reads as follows. A2's score is above average on C1 and C2, the two heaviest criteria. On the cost-direction C3, once reversed, it is also below average. Being advantaged on all three criteria, it comes first. A3 never rises above average on any criterion and remains last.
The decision's hesitation: if the cost criterion C3's weight is raised from 0.25 to 0.70, and C1's and C2's weights are lowered to 0.15 each, the ranking changes entirely. When DecisionMind's engine is independently rerun with these new weights, A1 comes first at 0.872, A3 second at 0.193, A2 third at 0.168. This shows how much A2's first place depends on C3's low weight.
In the report: "With the given weights (C1 = 0.40, C2 = 0.35, C3 = 0.25), A2 is in the most advantaged position relative to the set's average (0.745). If the cost criterion's weight is markedly raised (C3 = 0.70), the ranking reverses entirely and A1 comes first; the cost criterion's weight should therefore be separately justified."
Source: DecisionMind's validation example for the L2T-EDAS engine. Because the founding paper's (Wang, Wang & Wei, 2019) combined decision matrix was never published, and the paper was later retracted, the table was built synthetically, staying faithful to the formula chain (score, average, deviation, normalisation). The assessment scores and the weight scenario were validated by this card's author independently running DecisionMind's engine (scripts/method_runner.py L2T-EDAS).
2. Theatre: A municipal theatre's choice of next season's play
A municipal theatre will stage one of three play scripts next season. The criteria are: expected audience interest, staging cost, and cast-fit; staging cost is lower-is-better. The dramaturgy board has reported, for each play on each of the three criteria, how confident (truth), how undecided (indeterminacy) and how negative (falsity) it feels, choosing terms from a pre-declared term set.
The method reduces each play's triple on the three criteria to a single score, measures its favourable and unfavourable deviation from the column average, combines these with the weights, and gathers them into a single assessment score. Suppose the play with the highest expected audience interest also requires the most expensive staging, and still comes first, because the weight on audience interest has been set higher than the weight on cost.
The board's hesitation is this: choosing an expensive play on audience interest alone could strain the season budget. The board should not fold this risk into the assessment score but should limit it through a separate budget-ceiling pre-screening.
In the report: "The priority order has been shaped by the play that stays above average on this criterion, owing to the high weight given to expected audience interest. A separate budget ceiling is recommended for plays whose staging cost is above average."
3. What Not to Do
In the illustrative example, discarding the translation value on A2's C1 triple and using only the terms "s6, s1, s1" does not change the result here, because the translation values are already zero; but in a real group decision, if the translation value comes out non-zero and is discarded, the combination result gets rounded to the nearest term and information is lost. The second error is ignoring that C3 is a cost criterion and failing to apply the truth-falsity swap; this mistakenly rewards the most expensive alternative. The third error, in the theatre example, is citing the retracted founding paper as the sole source and saying "the method has been validated in the literature"; because the paper has been retracted, this claim must be separately flagged in the report.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/l2t-edas
Wang, P., Wang, J., Wei, G., & Zhang, J. (2019). EDAS method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment. Journal of Intelligent & Fuzzy Systems, 37(2), 1597–1608. DOI: 10.3233/JIFS-179223 (this article has been retracted by the publisher)
Wang, P., Wang, J., Wei, G., Wu, J., Wei, C., & Wei, Y. (2020). CODAS method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment. Informatica, 31(1), 161–184. DOI: 10.15388/20-INFOR399
Herrera, F., & Martínez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746–752. DOI: 10.1109/91.890332
Smarandache, F. (1998). Neutrosophy: Neutrosophic Probability, Set, and Logic. American Research Press, Rehoboth. (no DOI)
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