Linguistic

A linguistic data structure expresses an alternative's standing on a criterion as a word chosen from an ordered term set, such as "very low, low, medium, high, very high". Each term occupies a position: in a five-term set, "medium" is third. The calculation works on these positions; the word is never converted into a triangular fuzzy number or any other figure, and the result is read back as a term: "on quality, this alternative sits between high and very high, closer to high".

What distinguishes this structure is that it preserves natural evaluative language exactly as given. When an expert says "good", nobody assumes which number that corresponds to; it is enough that "good" sits one place above "medium" and one below "very good", and the calculation uses only this ordering.

Linguistic data suits criteria whose natural measure is a word: service quality, user satisfaction, design aesthetics, institutional reputation, degree of fit. Experts struggle to give a number for such criteria but not to say "high" or "medium". It is valuable in group decisions where several experts share one term set, wherever the result should reach the decision-maker as a word, and wherever the scale assumption behind converting a word into a number is unwanted.

Conversely, if a criterion is genuinely measurable (price, duration, count), converting it into a word discards information; writing a measured value as "high" throws away the detail the figure carried.

Yes, but it takes two steps, and the second one costs information.

The first is declaring the term set and each term's boundaries before the analysis: how many terms, in what order, and which range of the measured value falls into which term. These boundaries must come from thresholds already accepted within the criterion's domain, not from arbitrary choice.

The second is assigning the measured value to a term against those boundaries. A price of 2,450 TL might fall, against declared budget thresholds, into "affordable". But this assignment erases the difference between 2,450 and 2,550; both become "affordable". A measurable criterion should therefore stay measured, and the linguistic structure should be reserved for criteria that cannot be.

What must not be done is defining the term set during or after the analysis by looking at the result. The number and order of terms must be identical for every expert and alternative, and this must be stated in the report.

Words also appear in the fuzzy data structure: "good" is converted, via a declared scale, into a triangular number such as (7, 9, 10), and the calculation then works with triangles. In the linguistic structure, by contrast, "good" is never converted into any number; the calculation runs on its position in the set and its ordinal relation to neighbouring terms.

The difference is which assumption is made. Converting to a triangle assumes "this is the numerical equivalent of 'good'", and the result depends on that assumption. The linguistic approach says only "good sits above medium and below very good"; it makes fewer assumptions but, in return, treats the distances between terms as equal.

For this reason:

"The experts assessed with words, so the words should be converted into numbers and a fuzzy method applied"

should give way to:

"The experts assessed with words; the words stay within the term set, and the result is read back as a term"

This is the correct use of the linguistic structure. Both approaches are legitimate; the distinction is whether one wishes to make a scale assumption at all.

The chief advantage of the linguistic structure is that it places no translation layer between what the expert says and what the calculation uses. Converting a word into a number requires a scale, and a scale is itself an assumption; different scales give different results, and the linguistic structure removes that assumption altogether.

Its second advantage is readability. Rather than "alternative A scored 0.73 on quality", the decision-maker sees "alternative A sits between high and very high on quality, closer to high" — the very language in which the assessment was made.

The linguistic structure treats the distance between terms as equal: the gap between "low" and "medium" is taken to equal that between "high" and "very high". This does not hold for every criterion; the gap between the extreme terms may in reality be larger or smaller.

How many terms are used affects the result. A five-term set is coarse, a nine-term set fine-grained, and whether experts can consistently distinguish nine terms is a separate question. Where different experts use different term sets, those sets must be mapped onto one another, and that mapping is itself an assumption.

In practice, the term set is inseparable from the analysis. The uploaded file must carry a scale sheet stating which terms exist in which order; without it, the cells cannot be read. This is not a shortcoming but a consequence of the fact that a label such as "s3" cannot be understood, outside the file, as a position in some particular set.

When a calculation runs over terms, the result often falls between two of them: somewhere between "medium" and "high". The classical structure rounds this to the nearest term and loses information. The 2-tuple linguistic structure instead preserves the result as a term plus a symbolic shift: ("high", −0.3) means "a little below high", so aggregation and ranking proceed without loss. A 2-tuple cell holds a term position and a shift value.

Where an expert gives several terms, each with a probability ("60 per cent high, 40 per cent very high"), the probabilistic linguistic structure is used. It preserves the expert's opinion as distributed across terms with their probabilities, which suits aggregating different experts' distributions in group decisions.

Where an expert uses an expression such as "at least medium" or "between medium and high" without a probability, that is the domain of the hesitant linguistic structure, covered under the hesitant data type.

The most frequent mistake is converting a measurable criterion into a word. Price, duration and count should stay as numbers; writing "affordable / not affordable" instead discards the detail.

The second is failing to declare the term set in advance, or letting it vary from expert to expert. If one expert's "good" is fourth in a five-term set and another's is fifth in a seven-term set, the two cannot be compared directly.

The third is treating term positions as plain numbers: saying "medium = 3, high = 4" and averaging smuggles back, through the rear door, the very scale assumption the linguistic structure was built to avoid. Discarding the shift when rounding to a single term, rather than keeping it as a 2-tuple, likewise destroys the discriminating power a group decision needs.

The governing principle is this:

The term set is declared before the analysis and held identical across every expert and alternative; a word is never converted into a number, and the result is read back as a word.

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