Information Granulation and Its Centrality in Human and Machine Intelligence

In our quest for machines which are capable of performing non-trivial human tasks, we are developing a better understanding of the centrality of information granulation in human cognition, human reasoning and human decision-making. In many contexts, information granulation is a reflection of the finiteness of human ability to resolve detail and store information. In many other contexts, granulation is employed to solve a complex problem by partitioning it into simpler subproblems. This is the essence of the strategy of divide and conquer. What is remarkable is that humans are capable of performing a wide variety of tasks without any measurements and any computations. A familiar example is the task of parking a car. For a human it is an easy task so long as the final position of the car is not specified precisely. In performing this and similar tasks, humans employ their ability to exploit the tolerance for imprecision to achieve tractability, robustness and low solution cost. What is important to recognize is that this essential ability is closely linked to the modality of granulation and, more particularly, to information granulation. In a very broad sense, granulation involves partitioning of whole into parts. In more specific terms, granulation involves partitioning a physical or mental object into a collection of granules, with a granule being a clump of objects (points) drawn together by indistinguishability, similarity, proximity or functionality. Granulation may be physical or mental; dense or sparse; and crisp or fuzzy, depending on whether the boundaries of granules are or are not sharply defined. Modes of information granulation (IG) in which granules are crisp play important roles in a wide variety of methods, approaches and techniques. Among them are: interval analysis, quantization, chunking, rough set theory, diakoptics, divide and conquer, Dempster-Shafer theory, machine learning from examples, qualitative process theory, decision trees, semantic networks, analog-to-digital conversion, constraint programming, image segmentation, cluster analysis and many others. Important though it is, crisp IG has a major blind spot. More specifically, it fails to reflect the fact that in much - perhaps most - of human reasoning and concept formation the granules are fuzzy rather than crisp. For example, the fuzzy granules of a human head are the nose, ears, forehead, hair, cheeks, etc. Each of the fuzzy granules is associated with a set of fuzzy attributes, e.g., in the case of hair, the fuzzy attributes are color, length, texture, etc. In turn, each of the fuzzy attributes is associated with a set of fuzzy values. For example, in the case of the fuzzy attribute Length(hair), the fuzzy values are long, short, not very long, etc. The fuzziness of granules, their attributes and their values is characteristic of the ways in which human concepts are formed, organized and manipulated. In effect, fuzzy information granulation (fuzzy IG) may be viewed as a human way of employing data compression for reasoning and, more particularly, making rational decisions in an environment of imprecision, uncertainty and partial truth. In fuzzy logic, the machinery of fuzzy information granulation - based on the concepts of a linguistic variable, fuzzy if-then rule and fuzzy graph has long played a key role in most of its applications. However, what is emerging now is a much more general theory of information granulation which goes considerably beyond its place in fuzzy logic. This more general theory leads to two linked methodologies - granular computing (GrC) and computing with words (CW). In CW, words play the role of labels of granules and the initial and terminal datasets are assumed to consist of propositions expressed in a natural language. The input interface serves to translate from a natural language (NL) to a generalized constraint language (GCL), while the output interface serves to re-translate from GLC to NL. Internally, granular computing is employed to propagate constraints from premises to conclusions. The importance of the methodologies of granular computing and computing with words derives from the fact that they make it possible to conceive and design systems which achieve high MIQ (Machine Intelligence Quotient) by mimicking the remarkable human ability to perform complex tasks without any measurements and any computations. Although GrC and CW are intended to deal with imprecision, uncertainty and partial truth, both are well-defined theories built on a mathematical foundation. In coming years, they are likely to play an increasingly important role in the conception, design, construction and utilization of information/intelligent systems.