GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 2.2 GNGTS 2023 , expressed in percentage, whereas the AHP method determines weight using matrix ( , ) computation. = + · 1 − ⅇ − · , − | | ( ) ⎛ ⎝ ⎞ ⎠ = 1 (2) Where xmin is the minimum value; xi,A is the value of the alternative; A and B are parameters that allow the function to be between 0 and 1 in the y-axis and in the x-axis; P is a form factor that defines whether the curve is concave, convex, linear or S-shaped; C approximates the x-axis of the inflection point; K approximates the ordinate of the inflection point. A is usually equal to zero. Therefore, a summation that moves up the decision tree and combines the values of the MIVES functions with the weights produced by the AHP methodology is employed to arrive at the final result, known as the Sustainability Index (SI). It is feasible to determine which alternative best reflects the decision maker's preferences by comparing these indexes. = =1 ∑ α • β • γ • , ( ) = 1 (3) Where: i = last level criterion index; = number of last level criterion of considered second level criterion; α i = first level criterion weight; = second level criterion weight; = last level criterion β γ weight; = satisfaction value expressed in percentage by examining a Value Function ( , ) calculated in the assessed x with respect to last level criterion i for each Alternative (A) The TOPSIS was created in 1981 by Hwang and Yoon and is based on the geometric theory that the ideal solution should be the furthest away from a negative ideal solution (A-) and the closest to a positive ideal solution (A+). This distance is called relative closeness and it is obtained as follows: = − + + − (4) Where is the distance with the negative ideal solution and with the positive one. − + In an effort to get around the drawbacks of current methods, the proposed methodology combines the three techniques. The following criteria, clustered in a decision tree (Fig. 3) has been used for the sustainability evaluation of the four alternatives.