NEW ADVANCES OF THE COMPATIBILITY INDEX “G” IN WEIGHTED ENVIRONMENTS
This article addresses the problem of measuring closeness in weighted environments (decision-making environments). This article is relevant because of the importance of having a dependable cardinal measure of distance in weighted environments. A weighted environment is a non-isotropic structure where the different directions (axes) may have different importance (weight) hence, privileged directions exist. In this kind of a structure, it would be very important to have a cardinal reliable index that is able to show how close or compatible the set of measures of one individual is with respect to the group or to any other, or how close one pattern of behavior is to another. A few common examples of the application of this are the interaction between actors in a decision making process (system values interaction), matching profiles, pattern recognition, and any situation where a process of measurement with qualitative variables is involved.
Aldred, J. (2005). Intransitivity and vague preferences. Cambridge, UK: Emmanuel College. Doi:10.1007/s10892-005-7977-9
Garuti, C.A. (2007). Measuring compatibility in weighted environments: When close really means close? International Symposium on AHP, 9, Viña del Mar, Chile.
Garuti, C. (2012). Measuring in weighted environments: Moving from metric to order topology. Santiago, Chile: Universidad Federico Santa Maria. Doi: 10.5772/63670
Garuti, C.A. (2014). Compatibility of AHP/ANP vectors with known results. Presentation of a suggested new index of compatibility in weighted environments. International Symposium of the AHP.
Garuti, C. (2016). Consistency and compatibility (Two sides of the same coin). International Symposium of the AHP.
Hilbert, D. (1895). Ueber die gerade Linie als kürzeste Verbindung zweier Punkte. MathematischeAnnalen, 46, 91–96.Doi:10.1007/BF02096204
Jaccard P. (1901). Distribution de la flore alpine dans le bassin des Dranses et dans quelques regions voisines. Bulletin de la SociétéVaudoise des Sciences Naturelles, 37, 241-272.
Mahalanobis, P.C. (1936). On the generalized distance in statistics. Proceedings of the National Institute of Science of India, 12, 49-55.
Papadopoulos, A., Troyanov, M. (2014). Handbook of Hilbert Geometry. Zurich: European Mathematical Society. Doi: 10.4171/147
Saaty, T.L. (2001). The Analytic Network Process: Decision making with dependence and feedback. Pittsburgh, PA: RWS Publications. Doi: 10.4018/978-1-59140-702-7.ch018
Saaty, T.L. (2010). Group decision making: Drawing out and reconciling differences. Pittsburgh, PA: RWS Publications.
Whitaker, R. (2007). Validation examples of the Analytic Hierarchy Process and Analytic Network Process. Mathematical and Computer Modeling, 46, 840-859. Doi: http://dx.doi.org/10.1016/j.mcm.2007.03.018