Layered information granulation based on non-transitive, perceptual indistinguishability

Abstract

Fuzzy information granulation is key to many applications. Fuzzy Inference Systems (FIS) are an important technology in control systems and reasoning. ANFIS, FIS trained with Adaptive Networks, are a promising machine learning method to tackle the so-called data deluge. The heterogeneity and lack of quality control in big-data, however, lead to inhomogeneous, dynamically changing, non-partitioning granularities. Rough set theory is a powerful, widely used tool to model and represent information granulation in representations. Classical rough set theory is based on an indiscernibility relation that is an equivalence relation. As such it can describe well how information granulation at multiple layers of granularity gives rise to granularity phenomena, where partitions at a finer granularity group into partitions of a coarser granularity. This is usually given if classification is designed by an expert, e.g., using a classical taxonomy. However, information from different sources or untrained users, e.g. from social media or mobile phone sensors, may not be consistent in this manner. This paper investigates a generalization of rough set theory that assumes an indistinguishability relation, which behaves similar to indiscernibility but is not transitive, i.e. not an equivalence relation. In contrast to the even more general tolerance relations in rough set theory, indistinguishability retains an important property from perceptual indistinguishability in human cognition. The paper shows that many important properties of rough set theory do not depend on the transitivity property but can be achieved with this weaker cognitively motivated property, opening the way for new applications of the theory in domains such as volunteered geographic information.