From Undirected Structures to Directed Graphical Lasso Fuzzy Cognitive Maps using Ranking-based Approaches

Abstract

Fuzzy cognitive maps (FCMs) have gained popularity within the scientific community due to their capabilities in modelling and decision making for complex problems. However, learning FCM models automatically from data without any expert knowledge and/or historical data remains a considerable challenge. For our research, we use the estimated weight matrix from the graphical lasso (glasso) method with the EBIC regulation technique. Particularly, the glasso is a technique originated from machine learning which is used to model a problem by learning the weight matrix directly from a dataset. Moreover, the relationships are expressed by conditional independence among two nodes after conditioning on all the other nodes of the graph. However, the challenging task in this study is the investigation of the suitable transformation of the weight matrix from a symmetric matrix to asymmetric in order to determine the directions of the edges among the concepts and construct the glassoFCM model. For this reason, statistical comparisons are applied to examine if there are significant differences in the value of the output concept when the input concepts are rearranged according to four different cases. The whole approach was implemented in a business intelligence problem of evaluating the willingness of the employees to work in Belgian companies.