Logic Constructs with Information Granules: Data Analytics

Witold Pedrycz


In data analytics, system modeling, and decision-making models, the aspects of interpretability and explainability are of paramount relevance, just to refer to explainable Artificial Intelligence (XAI). They are especially timely in light of the increasing complexity of systems one has to cope with. We advocate that there are two factors that immensely contribute to the realization of the above important features, namely, a suitable level of abstraction in describing the problem and a logic fabric (topology) of the resultant construct. It is advocated that their conceptualization and the consecutive realization can be conveniently carried out with the use of information granules (for example, fuzzy sets, sets, rough sets, and alike).

Concepts are building blocks forming the interpretable environment capturing the essence of data and key relationships existing there. The emergence of concepts is supported by a systematic and focused analysis of data. At the same time, their initialization is specified by stakeholders or/and the owners and users of data.   We present a comprehensive discussion of information granules-directed design of concepts and their description by engaging an innovative mechanism of conditional (concept)-driven clustering. It is shown that the initial phase of the process is guided by the formulation of some generic (say, low profit) or some complex multidimensional concepts (say, poor quality of environment or high stability of network traffic) all of which are described by means of some information granules. In the sequel is explained by other variables through clustering focuses by the context. The description of concepts is delivered by a logic expression whose calibration is completed by a detailed learning of the associated logic neural network. The constructed network helps quantify contributions of individual information granules to the description of the underlying concept and facilitate a more qualitative characterization achieved with the aid of linguistic approximation. This form of approximation delivers a concise and interpretable abstract description through linguistic quantifiers. A detailed case study of systematic interpretability concerns functional rule-based models with the rules in the form “if x is A then y=f(x)”. The layers at which interpretability is positioned are structured hierarchically by starting with the initial fuzzy set level (originating from the design of the rules), moving to information granules of finite support (where interval calculus is engaged) and finally ending up with symbols built at the higher level. The rules emerging at the level of symbols are further interpreted by engaging linguistic approximation. For high-dimensional problems, dimensionality reduction is realized with the aid of relational matrix factorization which transforms original fuzzy set-based encoded variables and results in a logic-oriented level of activation of individual rules.