Theory of Fuzzy Information Granulation: Contributions to Interpretability Issues

Granular Computing is an emerging conceptual and computational paradigm for information processing, which concerns representation and processing of complex information entities called “information granules” arising from processes of data abstraction and knowledge derivation. Within Granular Computing, a prominent position is assumed by the “Theory of Fuzzy Information Granulation” (TFIG) whose centrality is motivated by the ability of representing and processing perception-based granular information. A key aspect of TFIG is the process of data granulation in a form that is interpretable by human users, which is achieved by tagging granules with linguistically meaningful (i.e. metaphorical) labels belonging to natural language. However, the process of interpretable information granulation is not trivial and poses a number of theoretical and computational issues that are subject of study in this thesis. In the first part of the thesis, interpretability is motivated from severa points of view, thus endowing with a robust basis for justifying its study within the TFIG. On the basis of this analysis, the constraintbased approach is recognized as an effective means for characterizing the intuitive notion of interpretability. Interpretability constraints known in literature are hence deeply surveyed with a homogeneous mathematical formalization and critically reviewed from several perspectives encompassing computational, psychological, and linguistic considerations. In the second part of the thesis some specific issues on interpretability constraints are addressed and novel theoretical contributions are proposed. More specifically, two main results are achieved: the first concerns the quantification of the distinguishability constraint through the possibility measure, while the second regards the formalization of a new measure to quantify information loss when information granules are used to design fuzzy models. The third part of the thesis is concerned with the development of new algorithms for interpretable information granulation. Such algorithms enable the generation of fuzzy information granules that accurately describe available data and are properly represented both in terms of quantitative and qualitative linguistic labels. These information granules can be used as building blocks for designing neuro-fuzzy models through neural learning. To avoid interpretability loss due to the adaptation process, a new architecture for neuro-fuzzy networks and its learning algorithm are proposed with the specific aim of interpretability protection.