In decision analysis,sometimes several parameters are not clearly defined,and in this case to handle such models , one of the possible ways is to use fuzzy analysis.

As noticed by Zadeh the human decision making includes a range of possibilities between Yes and No such as certainly yes, possibly yes, cannot say, possibly n,o certainly no, etc. Also, there is a lack of quantitative data. For instance, consider the following:

Fuzzy Linguistic Variables for Temperature: {Freezing, Cool, Warm, Hot}

Question: How you feel about the temperature?

Answer: I feel warm.

Question: How warm do you feel?

The Fuzzification and the Defuzzification process enables us to derive scalar values, i.e. the desired quantitative data so as to draw conclusions and make a decision.

"In recent years, the number and variety of applications of fuzzy logic have increased significantly. The applications range from consumer products such as cameras, camcorders, washing machines, and microwave ovens to industrial process control, medical instrumentation, decision-support systems, and portfolio selection."

Source: https://www.mathworks.com/help/fuzzy/what-is-fuzzy-logic.html

Zadeh, L. A. (1965). "Fuzzy sets". Information and Control. 8 (3): 338–353.

Zadeh, L. A. (1968). "Fuzzy algorithms". Information and Control. 12 (2): 94–102.

Zimmermann, H.-J. (1996) . "Fuzzy logic on the frontiers of decision analysis and expert systems ". Proceedings of North American Fuzzy Information Processing, Berkeley, CA, USA, 65-69. doi: 10.1109/NAFIPS.1996.534705 . https://ieeexplore.ieee.org/abstract/document/534705/

Because data uncertainty

Why not !?

Objective values and subjective judgements have some (big, not very big, small,...etc..) uncertainties/imprecisions ....

To use probabilistic meth..??

For this, we should have: {probabilistic space, [sigma -algebra of...] measurable sets, probabilistic measure}, or some statistics...

Do we have ...!??

As a rule, no...!

Fuzzy sets, fuzzy numbers are suitable... In addition, we can use linguistic approaches (eg, as I wrote above, or: very bad, bad, ..., good, very good...).

There are elaborated fuzzy logic, fuzzy rules and inferences...

And then..., in our life: fuzzy controllers, fuzzy machines, engines/cars... etc..., fuzzy intelligent system, fuzzy neural nets, etc..

And..., Fuzzy Decision Analysis, Fuzzy MCDA... though, it's not so easy and....,

not so justified...- in general case. However, problems can be overcome ..!-)

So, why not to use Fizzy Methodology....!-))

Because of the following three reasons

1. Information about criteria or attribute values in the virtually growing intricate network of socio-economic environment is uncertain or known with accuracy.

2. The presence of vagueness in psychological perspective of human .

3. Decision makers have to make decision within limited time, knowledge and data or they have very little attention for analysing and processing the available information.

Go through the following papers

1. Article Decision Maker Priority Index and Degree of Vagueness Couple...

The subjectivity generally is involved in decision analysis problem, in this sense fuzzy has potential to manipulate subjective (fuzzy) information.

I recomend to you the next paper

MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

Volume 2018, Article ID 2602376, 10 pages

https://doi.org/10.1155/2018/2602376

It's due to the uncertainties of the quantities assigned to measurable or incommensurable alternatives as well as the diversity of input data (Material Properties).