2.3.2. Modified Fuzzy DEMATEL: Improvements and Advantages

After the above preliminaries, this subsection presents the novel modified fuzzy DEMATEL,

which will be applied to solve a simple case by example, and then to address a real-world case study. As already stressed throughout the paper, we apply the method to the specific OSP problem. However, the application can be extended to use cases of other nature.

The modification proposed regards the first two steps of the procedure sketched in the previous section, while keeping invariant the remaining last three steps, which are actually shared also by the crisp version of the method. Specifically, we propose to bond the linguistic variable "influence" with a measurable parameter, quantitatively expressing the degree of interconnection among the network elements. In other terms, once defining and numerically calculating this parameter for each pair of elements, we propose to fix five numerical intervals, corresponding to the linguistic assessments and related TFNs of Table 1.

The flowchart of Figure 1 provides a detailed description of the steps of the new procedure. We summarise next the main advantages derived from our modified fuzzy DEMATEL.

First of all, the first step of the traditional procedure requires one to undertake a long process of feedback exchange with as many experts as possible, in order to accomplish a reliable acquisition of data. Each expert is asked to fill in a non-negative input matrix, providing subjective evaluations about the degree of influence between pairs of elements. It is evident as this stage may be highly time-consuming and scarcely precise. Moreover, experts can pairwise compare just a limited number of elements because they may doubt some evaluations. Obviously, it is nonsense to ask someone to pairwise compare hundreds of elements. This is the case with many real, complex problems involving a plethora of factors, which cannot be reduced if effective decisions have to be made. The traditional DEMATEL-based approach cannot be applied in such cases. Instead, our modified fuzzy DEMATEL may take into account very large sets of elements, since linguistic assessments are directly correlated to the numerical values taken by the chosen parameter of interest, according to which the input matrix can be easily compiled.

**Figure 1.** Flowchart of the modified fuzzy DEMATEL procedure.

Moreover, our solution permits one to better manage vagueness, since the collected data refer to a measurable parameter, not to personal opinions of experts, and the consequent use of fuzzy numbers further reduces uncertainty due to measurement errors.

Lastly, our proposal gives back directly a single fuzzy DRM, which will require just a simple operation of defuzzification, without aggregating data coming from many matrices of input issued by many experts.

Once this single matrix is defuzzified and normalised, the application continues through the same steps of the traditional method (from the TRM till the final ranking of elements and their graphical representation).
