Dimensionality in fuzzy systems
Wallace E. Kelly, John H. Painter · 1997
Chair of Advisory Committee: Dr. John H. Painter This dissertation explores the theoretical and practical aspects of dimensionality in fuzzy systems. First, the author shows that fuzzy logic can be formulated from first principles of Bayesian probability theory. Such a formulation helps focus theoretical development of fuzzy logic techniques. For example, the effect of anomalous inputs on various forms of fuzzy inference can be understood and considered during the design process. The Bayesian interpretation of fuzzy logic has also guided a fundamental improvement in the state-of-the-art of fuzzy system engineering. Known as hypertrapezoidal fuzzy membership functions (HFMF), this new method of defining multidimensional fuzzy relationships is motivated by an on-going research project in smart-cockpit technologies. The Automated Safety and Training Avionics project of Texas A&M seeks to improve the safety of the general aviation industry by utilizing artificial intelligence techniques in on-board avionics systems. Efforts to enhance on-board situational awareness revealed a fundamental weakness in fuzzy logic systems. HFMFs address this weakness by enabling the design of correlated fuzzy models with relatively few parameters. HFMFs can be successfully used for automatic flight mode interpretation and hold promise for many other applications. Finally, the