How can I convert linguistic variables to fuzzy numbers. i.e
Intensity level Definition Explanation
1 Equal preference Two factors equally preferred.
3 Somewhat more preference One is slightly favored over other on the basis of judgment and experience
5 Much more preference one is strongly favored over other
7 Very much more preference Very strongly preference
9 Absolutely more preference Extreme preference
It depends. For example, we can use a triangular fuzzy numbers. Then, much more preference (5) can be written as (4, 5, 6), but it depends what kind of uncertainty we have.
(5) -> (4, 5, 6)
(5) -> (4.5, 5, 6)
(5) -> (4, 5, 6.5)
(5) -> (4.75, 5, 6.25)
The most difficult task is found a way to properly identification of a fuzzy number.
I think you must read Fuzzy Inference and you will know how can you do it. The phase of "fuzzification" will help u understanding
Unless you have done proper scaling and operationalization (e.g., mapping "preference" onto some quantifiable behavioral or physiological variable, assessed and validated independently), any such scheme you use, fuzzified or not, will be arbitrary. People do this not infrequently, but that doesn't make it right. To illustrate: let's make up a scheme:
Married = 3; Separated = 2; Divorced = 1; Never married = 0
By this scheme, perhaps we would extrapolate that someone married 4 times should get a 7. Or perhaps they should stay at 3. Or revert to 1? Or get a negative score? Hmmm.... See, now we have exited the borders of science and good measurement theory, and entered the realm of social-pseudoscience. But this fundamental methods-measurement fallacy is found not only in the social sciences: it's also in psychology, medicine, etc. For example, pain scales, or any other psychophysical judgements that rely on arbitrarily chosen, equal-interval Likert rating schemes, will distort perceptual judgments into a mathematically convenient but phenomenologically arbitrary coding scheme. Now, in psychophysics there are alternative ways to quantify perceptions and judgments (see any good sensation and perception text). But for linguistic judgments, there are not such well-established methods. The preferred scientific approach is to forego conscious judgments completely, and use physiological or behavioral effects (e.g., priming) to detect and even scale processing-differences between items.
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