# AG 555 The assignation of an environmental sustainability index begins

The assignation of an environmental sustainability index begins with the on-site actions in the building, according to each of the defined indicators, which are valued through a value function. This score is obtained with the mathematical AG 555 defined by Alarcón et al. [55]. The value functions (Vi) vary from 0 to 1 (respectively, the minimum and the maximum score of each indicator) and depend on several parameters related with the function shape and the way in which that indicator value corresponds to an a dimensional scale (“value”). The selected value function (mathematical expression) is as follows.equation(1)Vi=A+1B×1-e-ki×xalt-xminCiPiwhere Ci: abscissa value at the inflection point on curves with Pi > 1, xmin: the minimum reference point on the indicator scale. Indicator response generated = 0, xmax: maximum reference point on the bark indicator scale. Indicator response generated = 1, xalt: response to the assessed alternative regarding the respective indicator, value between xmin and xmax. Indicator response generated = Vi (xalt), Pi: form factor defining whether the curve is: concave, convex, straight or “S” shaped. Concave curves imply Pi < 1. Convex or “S” shaped curves imply Pi > 1. Straight lines Pi ≈ 1, Di: abscissa value at the inflection point (curves Pi > 1), Ki: ordinate value of point Ci, A: value of response “xmin”, A = 0 or A = 1 (usually A = 0), B: factor for maintaining value function in range [0–1] and the best response equal to 1 (see factor B below).equation(2)B=11-e-ki×xmax-xminCiPi