Application of the Analytic Hierarchy Process to the Sociological Analysis

In this research the Analytic Hierarchy Process is applied to analyze the complex problems related to the social field, as, for example, the phenomenon of foreign students’ school integration, a phenomenon that is simultaneously considered complex and multidimensional by all the most recent literature. For this purpose a case study is presented, in which we have interviewed twelve teachers of a primary school. The opinions of each of these teachers are represented with three pairwise comparisons matrices: the matrix of paired comparisons of the sub-objectives with respect to the general objective, and the two matrices of paired comparisons of a set of variables with respect to every sub-objective. Precisely, starting from the definition of the general objective “foreign students’ school integration”, two sub-objectives have been single out: “the interpersonal communication” and “the degree of scholastic profit”. Furthermore nine variables B1, B2, ..., B9, have been introduced, in order to give an implicit definition of the general objective and of the sub-objectives. Furthermore, with Saaty’s AHP method, for every interviewed teacher, pairwise comparisons matrices are compiled. In order to give a group evaluation of opinions of teachers, for every set of homogeneous matrices, two summarizing matrices are introduced, the geometric mean G, and the uncertainty multiplicative index U. Matrices G and U are utilized to assign fuzzy triangular scores to sub-objectives, and to variables with respect to every sub-objective. In order to obtain the cores of such fuzzy scores, two criteria are considered and compared, the first one based on a weighted arithmetic mean of the columns of G, the second one based on eigenvalues and eigenvectors. As a significant social meaning, it has emerged from the results obtained that the interpersonal communication is resulted far more important than the degree of scholastic profit. Moreover, variables concerning relation and interaction capacity are dominant with respect to variables concerning school, sport or manual abilities.