Dual hesitant fuzzy TODIM (Liu, Tariq, Khan and Abdullah, 2023)

An international body wants to compare the resilience of five regions (Australia, Europe, North America, South America, Asia) against the impact of the Russia-Ukraine war on global supply chains. There are five criteria, all higher-is-better: energy supply, transport, supply-chain integrity, edible-oil supply, and food supply. An expert panel evaluated every region-criterion pair with a verbal term (very high, high, medium, low, very low), and these terms were converted to support-rejection pairs using a pre-declared dictionary. Weights were given as 0.25 to energy and transport, 0.20 to supply-chain integrity and edible-oil supply, and 0.10 to food supply (energy is the reference criterion; the lowest-numbered criterion is chosen when weights tie).

The method finds each cell's support-rejection score, builds the criteria's relative weights, compares each pair of regions two at a time, collecting a positive contribution on the winning side and a negative contribution magnified by Φ = 1 on the losing side, and scales the global value to the 0-1 range.

The result reads as follows. Australia has the highest support set on the energy and edible-oil criteria; these are the reference criterion and the second most heavily weighted criterion. This advantage more than offsets its middling performance on the other criteria. Europe has the highest support on transport, but stays low on energy and finishes last.

This result is entirely different from the paper's published ranking (Europe first, North America second, Australia third, Asia fourth, South America fifth); it is almost the reverse. The board's hesitation is this: does this difference come from the choice of the attention coefficient Φ? When Φ is tried from 0.5 up to 5 (rerunning the same engine independently in Python), the ranking stays unchanged as Australia-Asia-South America-North America-Europe. So the difference does not come from Φ. It comes from the complex-number component carried by the paper's own method, and DecisionMind does not account for this component in this extension.

In the report: "DecisionMind's dual hesitant TODIM engine finds Australia first on this data set; this ranking does not change between Φ = 0.5 and Φ = 5. However, this result does not match the ranking published by the paper that is the source of the same data (Liu et al., 2023), whose full model with the complex component finds Europe first; DecisionMind runs only the complex-component-free special case of the model, and this difference must be stated in the report without fail."

Source: The input table is taken from Tables 3 and 4 of Liu, Tariq, Khan and Abdullah's (2023) paper (the verbal-term dictionary and the regional scores). The global values were computed by this card's author by independently running DecisionMind's dual hesitant TODIM engine (without the complex component), and they match the manifest's own validation record exactly (±0.001 tolerance). The figures for the Φ-sensitivity scenario were also computed separately with the same engine.

A public authority will choose among three providers for a network-security monitoring service. There are three criteria, all higher-is-better: threat-detection speed, low false-alarm rate, and incident-response team experience. Drawing on past penetration tests and reference interviews, the security team reported for each provider both how much they trust it and, from a separate rationale, how much reservation they hold. Trust and reservation come from different sources (test results and reference interviews) and are not derived from one another. The highest weight is given to threat-detection speed.

The method compares the three providers two at a time: it determines the winning-losing direction from the support-rejection score difference on each criterion, computes the distance between the sets, and builds the global value. Suppose the provider with the fastest detection time also has the widest rejection set on incident-response experience; it still comes out first, because the weight on detection speed is highest.

The team's hesitation is this: the rejection set concerning this provider's response experience is wide, meaning some references gave a negative view and others a positive one. This disagreement is represented in the global value with a small weight and can stay invisible. The team should investigate the source of this disagreement separately before signing the contract.

In the report: "With the highest weight given to threat-detection speed, the fastest provider stands out. There is a disagreement among references about this provider's incident-response experience; the source of this disagreement should be investigated separately before signing the contract."

In the illustrative table, deriving every cell's rejection set from its support set (for example, adding a rejection set of {0.4;0.6;0.6} for Australia's energy criterion opposite a support set of {0.4;0.4;0.6}) effectively collapses the dual structure into plain hesitant TODIM; the independent contribution of the rejection side becomes invisible. The second error is reporting DecisionMind's result on this table (Australia first) as if it were the paper's (Liu et al., 2023) own result; the paper's full model with the complex component finds Europe first on the same data, and these two results are not the same thing. The third error is turning Australia's global value of 1.000 into an absolute judgement, "the most resilient region"; this value only scales these five regions relative to one another.