Giancarlo Ciotoli , I recommend this paper: Spatial sensitivity analysis of multi-criteria weights in GIS-based land suitability evaluation. By Y. Chena, J. Yua, and S. Khana.
With growing interest in extending GIS to support multi-criteria decision-making (MCDM) methods, enhancing GIS-based MCDM with sensitivity analysis (SA) procedures is crucial to understand the model behavior and its limitations. This paper presents a novel approach of examining multi-criteria weight sensitivity of a GIS-based MCDM model. It explores the dependency of model output on the weights of input parameters, identifying criteria that are especially sensitive to weight changes and to show the impacts of changing criteria weights on the model outcomes in spatial dimension. A methodology was developed to perform simulations where the weights associated with all criteria used for suitability modelling were varied one-at-a-time (OAT) to investigate their relative impacts on the final evaluation results. A tool which incorporates the OAT method with the Analytical Hierarchy Process (AHP) within the ArcGIS environment was implemented. It permits a range of user defined simulations to be per- formed to quantitatively evaluate model dynamic changes, measures the stability of results with respect to the variation of different parameter weights, and displays spatial change dynamics. A case study of irrigated cropland suitability assessment addressing the application of the new GIS-based AHP-SA tool is described. It demonstrates that the tool is spatial, simple and flexible.
You are absolutely right about the need to perform sensitivity analysis.
However, you talk about a novel approach that consists in varying the weight of a selected criterion keeping the other constant or the OAT method, by using simulation. In reality, this is not new.
In the opinion of several researchers and in mine also, that procedure is incorrect, because that is not what happens in real life. If you vary the weight of one criterion even using simulation, it produces a simultaneous variation of the weight of others, as well as changes in the range of allowable variations in all of them.
It is not realistic to modify one criterion and keeping the others constant!
In reality, you have to consider SIMULTANEOUSLY the variations of all the criteria that determine the solution. This is called AAT, that is, 'All At a Time'. It is not my opinion only, if you want, I can give you literature about it.
In addition, you are using trade-off values, from AHP, not weights. The trade-offs values do not have the capacity to evaluate alternatives. I know that this is the standard procedure, but IT IS WRONG. I have asserted this many times in RG and in my books, and nobody said a word.
In addition, following the AHP procedure those trade-off are ARBITRARY.
In using GIS together with a MCDM method of course you have to assign a weight to the different levels, or themes, but not at random. You can use entropy weights which DO HAVE the capacity to evaluate alternatives.
In addition do you truly believe that the different levels on themes in GIS are independent?
For instance, do you think that the theme 'Populations' is independent of the the theme 'Rural homesteads'' or from 'Rivers crossing"?
Normally criteria in GIS hey are dependent then you CAN'T USE AHP. It is not me who says that, is SAATY, the AHP's creator.
I also have a question: How do you identify criteria that are sensitive to weight changes? It is not that criteria are sensitive, its is the alternatives that are sensitive to criteria changes. However, I agree with you that the less allowable range a criterion has, the more sensible it is to the alternatives.
If you need more detailed explanation, I suggest reading a recent article of mine, about GIS and MCDM entitled 'GIS and Processing Data with SIMUS' in the journal 'Current Trends in Civil & Structural Engineer', Open Access, published in August 2020