Fuzzy Modeling through Granular Computing

Abstract

In this thesis, we introduce a concept of feature reduction, in which the reduction is guided by a criterion of structure retention. In other words, the features forming the reduced space are selected in such a way that the original structure present in the highly dimensional space is retained in the reduced space to the highest possible extent. Then, we provide a new method for complexity reduction in fuzzy modeling through the feature and data reduction approach. Data and feature reduction activities are advantageous to fuzzy models in terms of both the effectiveness of their construction and the interpretation of the resulting models. The formation of a subset of meaningful features and a subset of essential instances is discussed in the context of fuzzy rule-based models. The reduction problem is combinatorial in its nature and, as such, calls for the use of advanced optimization techniques. Here, we use the technique of Particle Swarm Optimization as an optimization vehicle for forming a subset of features and data to design a fuzzy model. Next, we develop a comprehensive design process of granular fuzzy rule-based systems. These constructs arise as a result of a structural compression of fuzzy rule-based systems in which a subset of originally existing rules is retained. Because of the reduced subset of the originally existing rules, the remaining rules are made more abstract (general) by expressing their conditions in the form of granular fuzzy sets, hence the name of granular fuzzy rule-based systems emerging during the compression of the rule bases. The design of these systems dwells upon an important mechanism of allocation of information granularity using which the granular fuzzy rules are formed. Finally, we introduce a new framework of Takagi-Sugeno-Kang fuzzy systems via the concept of information granulation. In spite of the standard TSK model being used, the representation of the antecedent part is numeric (coming from structure identification process via fuzzy clustering). We consider a concept of granular antecedent and consequent parts that generalize the numeric representation of the firing strength for the predicted output, in this way; helps capture more details about the fuzzy system.