Hesitant

A hesitant data structure expresses an alternative's assessment on a criterion not through a single value but through several possible values at once. The aim of this approach is to preserve the different assessments or plausible states within a decision process, rather than collapsing them into a single figure too early.

A hesitant structure does not only capture a single expert's indecision. Differing expert opinions, different scenarios, repeated measurements, or decision-relevant distinct states within a data distribution can equally be the source of hesitant information.

Use it wherever a single value falls short for a criterion and more than one value is accepted as plausible at once. It is particularly useful in expert assessments, group decisions, scenario-based analyses, and problems where performance varies across different conditions.

By contrast, where a single value has been measured reliably and exactly, converting the data into a hesitant structure merely to use a more elaborate model is not necessary.

Yes. But turning classical data into hesitant data requires a genuine source of information or a justification for the variability.

Adding new values around a single exact figure arbitrarily is not correct. By contrast, where repeated observations, different periods, market scenarios, or decision-relevant points of a distribution represent more than one plausible state, a hesitant structure can be built.

Two steps are required. First, the raw measurement is moved onto the criterion's scale: the values in a hesitant set are degrees between 0 and 1, so a measurement such as "2,450 Turkish lira" or "140 mmHg" is first converted into a normalised degree of success on that criterion. Second, each plausible state is derived from its own source: each scenario, each period, each expert contributes one value to the set.

What matters here is that a reason can be given for why each chosen value is meaningful for the decision problem.

A standard deviation on its own is not hesitant data. It is a statistical measure of how spread out the data is.

Where a hesitant structure is to be built from a distribution, it is not the standard deviation itself but the decision-relevant distinct states within the distribution that should be used. Low, typical and high performance levels, or particular percentile values, might be assessed for this purpose.

For that reason:

"The distribution is wide, so a hesitant structure is used"

is better replaced by:

"The distribution contains more than one decision-relevant state, so these states are kept together"

The chief advantage of the hesitant data structure is that it does not collapse information into a single value too early. Differences between experts, scenarios, or meaningful variability in performance can thereby be preserved throughout the analysis.

This structure provides richer information particularly in problems where uncertainty or variability matters to the decision. It prevents differing assessments from vanishing into an average and allows a more detailed comparison of alternatives.

Carrying more information means the model needs more decision rules. How hesitant values are compared, how sets of differing lengths are handled, and which score or distance function is used can all affect the results.

Not every kind of uncertainty should be represented with a hesitant structure. Measurement error, randomness, probability, interval uncertainty and expert hesitation are different concepts, and the data structure should be chosen according to the true source of the uncertainty.

In a classical hesitant structure there is more than one possible value, but the probability of each one occurring is not expressed separately.

Where the probability or weight of each state is known, the Probabilistic Hesitant structure is more suitable. This brings not only which values are possible but also how likely each one is into the model.

This distinction is particularly valuable in fields such as finance, risk analysis and health, where how often different states occur matters.

The most frequent mistake is assuming that hesitant methods, being more elaborate, will always give a better result. Generating extra values for an exact figure with no justification adds no information; it manufactures artificial uncertainty instead.

Likewise, using a standard deviation directly as a hesitant value, interpreting hesitant values as though they were probabilities, or adding different states to the same set with no selection rule at all also lead to methodological problems.

The governing principle is this:

Every value in a hesitant set must represent a defensible and meaningful plausible state for the same decision assessment.

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