Fuzzy Bayesian Nets and Influence Diagrams with Cognitive Numerical Judgment of Imprecise Probabilities

Abstract

The chapter will explain a connection between subjective uncertainty during the probability assessment and mental number representation of different probabilities expressed by approximate numbers. Subjective probabilities are represented as information granules described by linguistic terms and modeled as triangular fuzzy numbers. The proposed optimization functions proved to be efficient in determination of feasible probability bounds, yet corresponding to the human cognitive process. The usage of optimized fuzzy probabilities is illustrated on simple Influence diagram solving the e-commerce transaction. The quadratic programming model is proposed that can be easily solved, and simulation results are concurrent with the experimental findings of subjective probability assessment.