Mathematics Colloquium #1

Prof. George J. Klir

Binghamton University - SUNY

will give a talk on

ABSTRACT:
A research program whose objective is to study uncertainty and uncertainty-based information in all their manifestations was introduced by the author in the early 1990’s under the name “generalized information theory.” This research program is based on a two-dimensional expansion of the framework of classical information theory based on probability theory. In one dimension, additive probability measures, which are inherent to classical information theory, are expanded to various types of nonadditive measures. In the other dimension, the formalized language of classical set theory, within which probability measures are formalized, is expanded to more expressive formalized languages that are based on fuzzy sets of various types. As in classical information theory, uncertainty is the primary concept in generalized information theory and information is defined in terms of uncertainty reduction. This restricted interpretation of the concept of information is usually described in the literature by the qualified term “uncertainty-based information.” Each possible uncertainty theory within the expanded framework is characterized by choosing a particular formalized language (a theory of fuzzy sets of some particular type) and expressing relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) involved in situations described in this language in terms of a measure of some particular type (additive or nonadditive). The number of possible uncertainty theories is thus equal to the product of the number of recognized types of fuzzy sets and the number of recognized types of measures. This number has been growing quite rapidly with the recent developments in both fuzzy set theory and the theory of generalized measures. In order to develop any of these theories of uncertainty operationally requires that issues at each of the following four levels must be adequately addressed: (i) the theory must be formalized in terms of appropriate axioms; (ii) a calculus of the theory must be developed by which the formalized uncertainty is manipulated within the theory; (iii) a meaningful way of measuring the amount of relevant uncertainty in any situation formalizable in the theory must be found; and (iv) various methodological aspects of the theory must be developed. The purpose of this seminar is to discuss motivations for developing GIT, to describe the conceptual framework within which GIT operates, and to present an overview of results that have been obtained in GIT.

BIOGRAPHICAL SKETCH : George J. Klir Distinguished Professor of Systems Science Dept. of Systems Science & Industrial Engineering Thomas J. Watson School of Engineering and Applied Science Binghamton University - SUNY Binghamton, New York 13902-6000 Tel.: 607/798-9202 or 607/777-6509; Fax: 607/777-4094; e-mail gklir@binghamton.edu GEORGE J. KLIR is currently a Distinguished Professor of Systems Science at the Department of Systems Science and Industrial Engineering, Thomas J. Watson School of Engineering and Applied Science, State University of New York at Binghamton. He was born on April 22, 1932, in Prague, Czechoslovakia, immigrated to the USA in 1966, and became naturalized in 1972. He received the M.S. Degree (Summa Cum Laude) in Electrical Engineering from the Czech Technical University in Prague in 1957, and the Ph.D. degree in Computer Science from the Czechoslovak Academy of Sciences in 1964. He is also a graduate of the IBM System Research Institute in New York. He began his professional career at the Computer Research Institute and Charles University in Prague. After immigrating to the United States in 1966, he held academic positions at UCLA (1966-68) and Fairleigh Dickinson University in New Jersey (1968-69). Since 1969, he has been with the State University of New York at Binghamton, where he served as Chairman of the Department of Systems Science (1978-94) and Director of the Center for Intelligent Systems (1994-2000). He has also worked part time for IBM, Sandia Laboratories, Bell Laboratories, and Canadian Government, and taught summer courses at the University of Colorado, Portland State University in Oregon, and Rutgers University in New Jersey. During the academic years 1975-1976 and 1982-1983, he was a Fellow at the Netherlands Institute for Advanced Studies, and in 1980 he was a Fellow of the Japan Society for the Promotion of Science. During the earlier stages of his professional career, Dr. Klir conducted research in the areas of systems modeling and simulation, logic design, computer architecture, and discrete mathematics. His current research interests include the areas of intelligent systems, generalized information theory, knowledge acquisition and discovery, fuzzy set theory and fuzzy logic, theory of monotone measures, various theories of imprecise probabilities, systems modeling and simulation, and soft computing, as well as some aspects of the philosophy of science and philosophy of mathematics. At SUNY-Binghamton, he supervised 28 completed doctoral dissertations, five of which received Outstanding Dissertation Awards, and has taught graduate courses on Fuzzy Systems, Generalized Information Theory, Systems Problem Solving, Discrete Mathematics, Logic Design and Computer Architecture, Fault-Tolerant Computing, Automata Theory, Introduction to Systems Science, and Combinatorial Analysis. He is the author of over three hundred articles, holds a number of patents, and is an author or co-author of 15 books, among them Cybernetic Modelling (Van Nostrand, 1967), Methodology of Switching Circuits (Van Nostrand, 1972), Architecture of Systems Problem Solving (Plenum Press, 1985), Fuzzy Sets, Uncertainty, and Information (Prentice Hall, 1988), Facets of Systems Science (Plenum Press, 1991), Fuzzy Measure Theory (Plenum Press, 1992), Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice Hall, 1995), Uncertainty-Based Information (Springer-Verlag, 1998), and Fuzzy Sets: An Overview of Fundamentals, Applications, and Personal Views (Beijing Normal Univ. Press, 2000). He is also an editor of 10 books. Some of the books and papers were translated into foreign languages: Spanish, German, Japanese, Chinese, Russian, Polish, and Czech. Dr. Klir has been Editor-in-Chief of the International Journal of General Systems since 1974 and Editor of the Book Series on Systems Science and Engineering, sponsored by the Intern. Federation for Systems Research (IFSR) since 1985. He is a member of Editorial Boards of 19 journals. He was President of the Society for General Systems Research in 1981-82, the first President of the IFSR in 1980-84, President of the North American Fuzzy Information Processing Society (NAFIPS) in 1988-1991, and President of the International Fuzzy Systems Association (IFSA) in 1993-1995. He has received numerous awards and honors, including 5 honorary doctoral degrees, the Gold Medal of Bernard Bolzano in mathematical sciences from the Czech Academy of Sciences, Lotfi A. Zadeh Best Paper Award, Distinguished Leadership Award from the International Society for the Systems Sciences, Award from the Netherlands Society for Systems Research for advancing general systems research, Award from the Austrian Society for Cybernetic Studies for outstanding contributions to cybernetics, Award for the Highest Achievement in Scholarship from the Simon Bolivar University in Caracas, Venezuela, the Kaufmann’s Gold Medal Prize for excellence in uncertainty research, Award from the Society for Computing Anticipatory Systems for outstanding scientific work on anticipatory and intelligent systems, and SUNY University Award for Excellence in Research. He is Life Fellow of IEEE, Life Fellow of the Netherlands Institute for Advanced Studies, and Fellow of IFSA. His biography is included in many biographical sources, including Who’s Who in America, Who’s Who in the World, American Men and Women of Science, Outstanding Educators of America, Contemporary Authors, etc. His research have been supported for more than 20 years by grants from NSF, ONR, Air Force, NASA, NATO, Canadian Government, Sandia Laboratories, and some industries.

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