a Different mean, t-test (p<0.05);b Same variance, F-test (p>0.05)
The corresponding Shapley indices (Eq. 1) for each attribute computed from the fuzzy integral analysis are also presented in Table 4. The three higher values for each sample are marked in bold characters. From these results, it is possible to see that "freshness" is the most critical attribute for Sample 1 (1.65), followed by "ease of absorption" (1.57) and "residues" (1.22). The first two attributes were poorly graded in the test (0.31 and 0.35 in Table 4, respectively), which suggests that the heavy emollience of the product could influence the overall score. Indeed, Sample 1 contains mineral oil, an occlusive ingredient that hinders water evaporation from the skin, which is usually related to a low freshness sensation.56 In the case of Sample 2, "residues" has the highest index (i.e., 1.74) followed by "thickness" (i.e., 1.36) and "freshness" (i.e., 1.26). Among these attributes, "thickness" is also the lowest rated (0.26 in Table 4), which could indicate that Sample 2 is perceived as not being thick enough, thus affecting the overall performance score of the product. Similar results have been reported by other authors when the product has a low viscosity.67 Murofushi and Soneda or interaction indices (2) are listed in Table 5.