Since its inception in the early fifties, AI has scored a number of major successes, among them the defeat of Gary Kasparov by DEEP BLUE. However, what we also see is that alongside the brilliant achievements lie areas in which progress has been slow and difficult to realize. In such areas, problems do not lend themselves to precise formulation, and the underlying modes of reasoning are approximate rather than exact. A case in point is the problem of summarization--a problem that is orders of magnitude more complex than the problem of machine translation. Although substantial progress has been realized (Mani and Maybury 1999), we are still far from being able to construct programs that are capable of summarizing a nonstereotypical story or providing a synopsis of a book.
Why is it that major successes have been achieved in some areas but not in others? A thesis that I should like to put on the table is that progress has been, and continues to be, slow in those areas where a methodology is needed in which the objects of computation are perceptions--perceptions of time, distance, form, direction, color, shape, truth, likelihood, intent, and other attributes of physical and mental objects.
Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, for example, driving in city traffic, humans base whatever decisions have to be made on information that, for the most part, is perception, rather than measurement, based. The computational theory of perceptions (CTP), which is outlined in this article, is inspired by the remarkable human capability to operate on, and reason with, perception-based information.
An essential difference between measurements and perceptions is that in general, measurements are crisp, whereas perceptions are fuzzy (figure 1). Furthermore, the finite ability of sensory organs to resolve detail necessitates a partitioning of objects (points) into granules, with a granule being a clump of objects (points) drawn together by indistinguishability, similarity, proximity, or function. Thus, perceptions, in general, are both fuzzy and granular or, for short, f-granular. For example, a perception of age can be described as very young, young, middle aged, old, and very old, with very young, young, and so on, constituting the granules of the variable age (figure 2). In this perspective, natural languages can be viewed as systems whose primary function is to describe perceptions.
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Information granulation plays key roles in both human and machine intelligence. Modes of information granulation in which the granules are crisp, that is, c-granular (figure 3), play important roles in a wide variety of methods, approaches, and techniques. Among them are interval analysis, quantization, rough-set theory, diakoptics, divide and conquer, Dempster-Shafer theory, machine learning from examples, chunking, qualitative process theory, qualitative reasoning, decision trees, semantic networks, analog-to-digital conversion, constraint programming, Prolog, and cluster analysis.
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Important though it is, crisp information granulation 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 (f-granular) rather than crisp. In the case of a human body, for example, the granules are fuzzy in the sense that the boundaries of the head, neck, arms, legs, and so on, are not sharply defined. Furthermore, the granules are associated with fuzzy attributes, for example, length, color, and texture in the case of hair. In turn, fuzzy attributes can have fuzzy values; for example, in the case of the fuzzy attribute length (hair), the fuzzy values could be long, short, very long, and so on. …