Mathematical Analysis of Uncertainty

Abstract

Classical Logic showed early its insufficiencies for solving AI problems. The introduction of Fuzzy Logic aims at this problem. There have been research in the conventional Rough direction alone or in the Fuzzy direction alone, and more recently, attempts to combine both into Fuzzy Rough Sets or Rough Fuzzy Sets. We analyse some new and powerful tools in the study of Uncertainty, as the Probabilistic Graphical Models, Chain Graphs, Bayesian Networks, and Markov Networks, integrating our knowledge of graphs and probability.