Hesitant fuzzy WASPAS (Mishra, Rani, Pardasani and Mardani, 2019)

Three things change; the WASPAS logic of blending sum and product with a coefficient stays the same.

Cells. In crisp WASPAS every cell is a single number. Here every cell is a set. The set holds several plausible values for the same criterion together, for example {0.5; 0.7}. One expert might give a single value while another gives two or three. Weights are taken from outside as crisp numbers; where more than one expert is involved, DecisionMind first merges these experts' matrices into a single set, and where there is only one expert, this step changes nothing.

Complementation instead of scale equalisation. Crisp WASPAS equalises every column by dividing by its best value; this division is not defined for sets. Instead, on cost criteria, every element of every set is converted to its own complement (1 minus the element); benefit criteria are left as they are. This corresponds to crisp WASPAS's direction correction, but it is complementation, not division.

HFWA and HFWG instead of sum and product. Crisp WASPAS's weighted sum (WSM) is matched here by the Hesitant Fuzzy Weighted Average (HFWA). This aggregation matches every element of every criterion's set through a Cartesian product and builds a new, optimistic set; a high value on a single criterion can pull the overall result upward. The weighted product (WPM) is matched by the Hesitant Fuzzy Weighted Geometric (HFWG), where low values dominate. Both aggregations produce their own set; each is reduced to a single number by averaging the set's elements (the Xia-Xu 2011 score function).

Result and combination: λ is exposed to the user here. The two scores, one from HFWA and one from HFWG, are blended with a coefficient ϑ (or λ); DecisionMind assumes 0.5 if none is specified. Reading the DM3 manifest, this card's author found an important difference here. Unlike the other three WASPAS extensions, this coefficient (lambda_waspas) is defined as an explicit user input in the parameters list. The other three are the Complex fuzzy Z-number WASPAS, Cubic fuzzy WASPAS and Fermatean fuzzy WASPAS cards. The user can change this value between 0 and 1.

The number of set elements grows throughout the calculation. When two criteria's sets are matched, the resulting set carries as many elements as the product of the two sets' element counts; if all three of three criteria have two elements each, the resulting set grows to eight elements. This is a growth crisp WASPAS never encounters, and the set itself is not reported: only its average (the score) is used.

For this extension, DecisionMind fixes the complementation rule, the HFWA/HFWG aggregation, and the Xia-Xu score function. Weights come from outside; ϑ is a user-adjustable input.

The output is a combined score and a rank, as in crisp WASPAS, and it is read the same way: it is not a percentage or a probability, and the ranking can shift when the alternative set changes.

The difference is this: the score is no longer a single measurement but a blend of two different views, one optimistic (HFWA), the other cautious (HFWG). Because ϑ is a genuinely adjustable interface parameter here, whether the ranking changes when ϑ is varied on the same table can be tested directly inside the engine; in the other three WASPAS extensions, this test can only be performed outside the engine, by an independent calculation.

Thus instead of writing:

"According to hesitant WASPAS, the highest-scoring alternative is definitively the best"

the report should read:

"The HFWA and HFWG components have been blended with ϑ = 0.5; whether the ranking stays robust when ϑ is changed must be shown separately"

This extension is appropriate when more than one plausible, defensible degree exists for the same criterion-alternative pair, for example when several experts have scored independently and you want to keep these scores together without collapsing them into an average. Where a single measured value exists, a single number is written into the cell and no set is built; DecisionMind requires the table to hold a single data type. Crisp WASPAS's exit condition applies here too: the HFWA component is compensatory, and the method is unsuited to a criterion where no compromise is acceptable; where weights rather than a ranking are needed, methods such as AHP, BWM, CRITIC or Entropy should be considered.

Leaving ϑ at its default of 0.5 without ever testing it. This coefficient is genuinely adjustable here; reporting the result without looking at what the HFWA and HFWG components say separately is the same mistake found on the base WASPAS card, in its form for this extension.

Arbitrarily adding a rejection or a missing value to the set. Adding a value an expert never gave, on the grounds that "it would probably have been this," loses the set's genuine source; a set must carry only values that were actually given.

Skipping the complement on a cost criterion. The direction correction is an element-wise complement, not division; skipping this step rewards a high value on a lower-is-better criterion by mistake.

Interpreting set size without noticing its growth. Because of the Cartesian product, the resulting set grows quickly; this growth is not an error, but only the set's average (the score) should be reported, not the set itself.

Reporting only HFWA or only HFWG. The two have a different character; showing only one and skipping the other hides how sensitive the combined score is to ϑ.

The governing principle is this:

A set must genuinely come from more than one defensible source for the same criterion-alternative pair; because ϑ is adjustable here, the report must show how far the result depends on the choice of ϑ.