An analysis of fuzzy integral decision: A novel approach to EEG source localization

The human brain is one of the most complex structures known to exist. The dynamics of the brain can be observed either through the electroencephalography (EEG) or the magnetoencephalography (MEG). One useful method for understanding brain dynamics and for clinical diagnosis of brain abnormalities is EEG-based source localization. The importance of the problem lies in the direct association between the underlying neuronal activities inside the brain and their neurophysiological functions. The difficulty lies in the lack of suitable methodologies for inverse mapping from EEG to its underlying neuronal activities. In this thesis, a novel approach to this problem is given within the framework of decision making. This approach is called the Hierarchical Decision Module (HDM). The approach extends the degree of freedom in model space and employs multiple neural networks, information theory, decision theory, and digital signal processing tools and algorithms in an interdisciplinary fashion.; Fuzzy integral is considered as a utility function in the framework of decision making and used as an aggregation tool in the HDM. Fuzzy measure is considered as belief function (belief measure). The sensitivity of the fuzzy integral to the changes in its domain, formed by a fuzzy measure and an attribute function, is analyzed and the fuzzy integral decision is linked to the belief function decision. In the most general case, it is observed that the fuzzy integral is less sensitive to the fluctuations in its domain. When the domain is heavily influenced by fuzzy measure, it is shown that the fuzzy integral decision is bounded by the belief function decision, yielding the most cautious decision strategy. It is further shown that the fuzzy integral yields a decision with an absolute (unity) confidence when its domain is heavily influenced by the attribute function. After these analysis, the HDM was explicitly designed for the source localization problem to make a decision about the best model for both simulated and real EEGs. Three different source models are used for the same head model: the single dipole, the disc, and the line source models. The performance of the HDM was verified by using spindle signals, and the HDM suggested a model from its model space which best satisfies its decision criteria.