Balanced SPOTIS (Shekhovtsov, Dezert and Sałabun, 2025)

What changes here is not the data type but the number of reference points. Cells are identical to crisp SPOTIS: a single number.

Input. Crisp SPOTIS asks for a single fixed pair of bounds (the "best/worst conceivable" for every criterion) and builds its ideal (ISP) from them. Balanced SPOTIS asks for the same fixed bounds, but additionally takes, as input, an "expected target point" (ESP, Expectation Solution Point) set by the decision-maker. The ESP is not "the theoretical best" but a target that "counts as realistically sufficient under these conditions"; it must stay inside the fixed bounds. An α (alpha) coefficient is also entered; this sets the weight between the two reference points.

Reference point. Crisp SPOTIS has a single reference (the ISP), and every alternative's distance is measured to it alone. Balanced SPOTIS builds two references: the ISP from the fixed bounds (the upper bound for a benefit criterion, the lower bound for a cost criterion), and the ESP taken directly from the decision-maker's input. Both are scaled against the same fixed bound range.

Distance and combination. Crisp SPOTIS computes a single scaled distance. Here, two separate scaled distances are computed for every alternative: D_isp (distance to the ideal) and D_esp (distance to the target). The two distances are blended with the α coefficient: P_i = (1−α)·D_isp,i + α·D_esp,i. At α = 0 the method reduces to crisp SPOTIS itself (only the ideal is considered); at α = 1 the method looks only at distance to the target. An intermediate α value takes both references into account together.

Result and defuzzification. As in crisp SPOTIS, a small P value is good, and the ranking runs by increasing distance. This direction does not change.

DecisionMind fixes, for Balanced SPOTIS, the rule that builds the ISP from the fixed bounds and the formula that blends the two distances. Weights are taken from outside as crisp numbers; the method does not generate weights.

The distance value is read as in crisp SPOTIS: a small value is good, a large value is bad, and as long as the fixed bounds do not change, one alternative's distance does not change when the alternative set changes.

The difference is here. Because this distance is now a blend of two references, "how close to the ideal" and "how close to the realistic target" are merged into a single number. At α = 0.5, if an alternative's value on a criterion falls between the ESP and the ISP, that criterion's contribution becomes independent of the alternative's exact position. This is a theorem the source paper proves itself (Equations 7–8), not a computational error; it is a natural consequence of the region between the two references being treated as balanced-out "indifferent" territory.

Thus instead of writing:

"According to Balanced SPOTIS, A2 scores 0.425, and this is a single, final result"

the report should read:

"A2's distance at this α value is 0.425; as α changes (for instance between α = 0, which looks only at the ideal, and α = 1, which looks only at the target), this distance can change, and the α range over which the ranking stays stable must be shown separately"

This extension is used when the decision-maker wants to evaluate not only against the theoretical ideal but also against a target that is "realistically sufficient under these conditions." It suits, for example, recurring decisions compared over time, where an institution wants to carry both a minimum acceptable standard and a desired best standard together. Crisp SPOTIS's exit condition applies here too: if the fixed bounds are unknown or contested, or if no compromise is acceptable on one criterion, this extension should likewise not be used.

If evaluation against a single reference (the ideal) alone is sufficient, base SPOTIS is used; the extra burden of defining a second reference point (justifying the ESP and α) is not needed.

Entering the ESP outside the fixed bounds. The source paper explicitly requires that the ESP stay inside the fixed bound range for every criterion. An ESP outside that range makes the distance calculation meaningless.

Choosing the fixed bounds narrower than the real value range. This is also a known error in crisp SPOTIS, but it matters particularly here. If an alternative's real value goes beyond the fixed bound (and hence the ISP), that alternative is treated not as having "reached" the ideal but as having "exceeded" it. Its distance can then come out worse than an alternative that stays within the bound. If an alternative sitting exactly on the fixed upper bound could in fact score even higher, that is a sign the bound does not cover the realistic upper value and should be widened.

Assuming the region between the two references is "discriminating" at α = 0.5. If an alternative's value on a criterion falls between the ESP and the ISP, that criterion's contribution at α = 0.5 is independent of the alternative's position. This is a theorem the source paper proves itself. If fine differences in this region are being sought, α should be moved away from 0.5, or the analysis should be repeated with several α values (for instance 0.1, 0.5 and 0.9).

Reading the distance value the wrong way round. In the SPOTIS family a small distance is good; reading a large distance as "the best" reverses the ranking.

The governing principle is this:

Balanced SPOTIS's promise is to place a realistic target alongside the ideal and balance the two; this balance is trustworthy only when the ESP is set inside the fixed bounds with justification, and when the report explains what the chosen value of α means.