Bipolar fuzzy EDAS (Jana & Pal, 2021)

Cells. In crisp EDAS every cell is a single number. Here every cell is two numbers: a positive pole and a negative pole. The positive pole states, on a scale of 0 to 1, how strongly the alternative performs in the desired direction on this criterion. The negative pole states the effect in the opposite direction, on a scale of 0 to −1. Bipolar fuzzy EDAS can combine the scores of several experts; each expert carries their own weight, and the founding paper was already written for a group decision.

Scale equalisation. For a cost criterion, every cell is complemented: the positive pole is subtracted from 1, and the negative pole is rewritten as its absolute value minus 1. This is the bipolar counterpart of turning crisp EDAS's "lower is better" criterion into "higher is better."

Average solution and distance. Crisp EDAS takes the arithmetic mean of every column. Bipolar EDAS instead uses a geometric bipolar average: a bipolar fuzzy weighted average (BFWA) of all the cells in a column, a combination in which every cell enters with equal weight. This average is also a bipolar pair, not a single number. Both every cell and this average are then reduced to a single number with the score function (positive plus negative, plus 1, divided by 2). From this point, the positive and negative distances from the average (PDA, NDA) are computed exactly as in crisp EDAS: a cell whose score exceeds the average's score produces a positive distance, and one below it produces a negative distance.

Result and defuzzification. The weighted sums of positive and negative distance (SP, SN) are normalised by dividing by their own highest values, then averaged to give the appraisal score (AS). The score is a single number between 0 and 1, and the higher one is preferred.

DecisionMind fixes, for bipolar EDAS, the bipolar average solution and the score function that follows it. Weights are taken from outside as crisp numbers; where there is more than one expert, expert weights are likewise taken from outside.

The output is an appraisal score and a resulting ranking, as in crisp EDAS. The score states how well or poorly the alternative is positioned relative to the set's average; it cannot be compared with a different set, because the average is built, in every analysis, from that analysis's own alternatives.

The difference is here: the average solution itself is now a bipolar pair, not a single crisp number. Whether an alternative counts as "good" or "bad" relative to this average depends on how the average itself has been combined. With a small number of alternatives (three, four), a single extreme value can shift the average noticeably. This is a valid caution in crisp EDAS too; in a bipolar combination, the poles amplifying one another can increase this sensitivity.

Thus instead of writing:

"A high AS score in bipolar EDAS means the alternative is good in absolute terms"

the report should read:

"The AS score shows the alternative's position relative to this set's bipolar average solution; if the set changes, the average, and hence the scores, change with it"

Use this extension when an alternative has a measurable effect in both the desired and the opposite direction on a criterion, and several experts' two-directional judgements need to be combined without being reduced to an average first. Typical situations: a technology's efficiency contribution alongside its cost risk, or board decisions in which several experts assess the same criterion from opposite directions.

If a criterion is one-directional and already measured, there is no second pole, and crisp EDAS is sufficient. The exit condition is the same as for crisp EDAS: this extension is likewise suitable only where the logic of deviation from the average is acceptable.

Deriving the negative pole from the positive pole. The negative pole comes from its own body of evidence; it is not computed from the positive pole.

Reading the negative pole as a degree of rejection. In the bipolar structure there is no constraint that the two poles must sum to no more than 1.

Confusing the bipolar fuzzy set with the m-polar fuzzy set at m = 2. A bipolar set measures a single criterion's two-directional effect; an m-polar set at m = 2 measures two independent viewpoints. Where two independent viewpoints genuinely exist, a member of the m-polar family is used instead.

Building the average solution from a single expert's score. When several experts are involved, deriving the average solution from only one of them discards the evidence of the rest.

Changing the score function without declaring it. A different defuzzification form changes the PDA and NDA values, and with them the AS.

The governing principle is this:

The average solution must genuinely be built from the bipolar evidence of all experts and all alternatives; no pole or expert's share may be shortcut into a single number.

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