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Pablo D. Slemenson“Lógica de lo preconciente”33. Fuzzy Logic for the Management of Uncertainty, L.A. Zadeh and J. Kacprzyk(Eds.), John Wiley & Sons, New York, 1992.34. Fuzzy Logic, Neural Networks and Soft Computing, Communications of the ACM,37(3):77-84, 1994.35. The Role of Fuzzy Logic in Modeling, Identification and Control, ModelingIdentification and Control, 15(3):191-203, 1994.36. Why the Success of Fuzzy Logic is not Paradoxical, IEEE Expert, 9(4):43-45,1994. Soft Computing and Fuzzy Logic, IEEE Software, 11(1-6):48-56, 1994.37. Probability Theory and Fuzzy Logic are Complementary rather than Competitive,Technometrics, 37, 271-276,1995.38. Fuzzy Logic = Computing with Words, IEEE Transactions on Fuzzy Systems, 2,103-111, 1996.39. Fuzzy Logic and the Calculi of Fuzzy Rules and Fuzzy Graphs, InternationalJournal of Multiple-Valued Logic, 1, 1-39, 199640. >From Computing with Numbers to Computing with Words -- From Manipulationof Measurements to Manipulation of Perceptions, IEEE Transactions on Circuits andSystems, 45, 105-119, 1999.41. Outline of Computational Theory of Perceptions Based on Computing with Words,Soft Computing & Intelligent Systems, N.K. Sinha, M.M. Gupta, and L.A. Zadeh (eds),3-22. New York; Academic Press, 2000.Some abstractsGranulation and its Centrality in Human and Machine IntelligenceInformation(Professor Lotfi A. Zadeh)(NASA) NAC2-1177, (ONR) N00014-96-1-0556, (LLNL) B-291525, (ARO) DAAH04-961-0341, Berkeley Initiative on Soft Computing, and British TelecomIn our quest for machines that are capable of performing non-trivial human tasks, weare developing a better understanding of the centrality of information granulation inhuman cognition, human reasoning, and human decision-making. In many contexts,information granulation is a reflection of the finiteness of human ability to resolvedetail and store information. In many other contexts, granulation is employed to solve acomplex problem by partitioning it into simpler sub-problems. This is the essence ofthe strategy of divide and conquer.Apendice 314
Pablo D. Slemenson“Lógica de lo preconciente”What is remarkable is that humans are capable of performing a wide variety of taskswithout any measurements and any computations. A familiar example is the task ofparking a car. For a human it is an easy task so long as the final position of the car isnot specified precisely. In performing this and similar tasks, humans employ theirability to exploit the tolerance for imprecision to achieve tractability, robustness, andlow solution cost. What is important to recognize is that this essential ability is closelylinked to the modality of granulation and, more particularly, to information granulation.In a very broad sense, granulation involves partitioning of whole into parts. In morespecific terms, granulation involves partitioning a physical or mental object into acollection of granules, with a granule being a clump of objects (points) drawn togetherby indistinguishability, similarity, proximity, or functionality. Granulation may bephysical or mental; dense or sparse; and crisp or fuzzy, depending on whether theboundaries of granules are or are not sharply defined. Modes of informationgranulation (IG) in which granules are crisp play important roles in a wide variety ofmethods, 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, semanticnetworks, analog-to-digital conversion, constraint programming, image segmentation,cluster analysis, and many others. Important though it is, crisp IG has a major blindspot. More specifically, it fails to reflect the fact that in much--perhaps most--of humanreasoning 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. Eachof 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 isassociated with a set of fuzzy values. For example, in the case of the fuzzy attributeLength (hair), the fuzzy values are long, short, not very long, etc. The fuzziness ofgranules, their attributes, and their values is characteristic of the ways in which humanconcepts are formed, organized, and manipulated. In effect, fuzzy informationgranulation (fuzzy IG) may be viewed as a human way of employing data compressionfor reasoning and, more particularly, making rational decisions in an environment ofimprecision, uncertainty, and partial truth. In fuzzy logic, the machinery of fuzzyinformation granulation--based on the concepts of a linguistic variable, fuzzy if-thenrule, 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 thatApendice 315
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