A new approach using Mixed Graphical Model for automatic design of Fuzzy Cognitive Maps from ordinal data

Abstract

This research study proposes a new method for automatic design of Fuzzy Cognitive Maps (FCM) using ordinal data based on the efficient capabilities of mixed graphical models. The approach is able to model all variables on the proper domain of ordinal data by combining a new class of Mixed Graphical Models (MGMs) with a structure estimation approach based on generalized covariance matrices. It can work with a large amount of categorical data. It represents its structure as a sparser graph, while maintaining a high likelihood, by producing an adjacent weight matrix, where relationships are expressed by conditional independences. By maximizing the likelihood indicates that the model fits better to the data under the assumption that the observed data are the most likely data. The whole approach was implemented in a business intelligence problem of evaluating the attractiveness of Belgian companies. Through the analysis of results and conducted scenarios, the usefulness of the proposed MGM method for designing FCM capable to make decisions, is demonstrated. Comparisons with the previous known methodology for automatic construction of FCMs based on distance-based algorithm, showed that the proposed approach provides more understandable/useful relationships among nodes, through a less complex structure for making decisions.