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By Bilal M. Ayyub

Uncertainty has been a priority to engineers, managers, and scientists for a few years in engineering and sciences. Uncertainty has for a very long time been thought of synonymous with random, stochastic, statistic, or probabilistic. because the early sixties perspectives on uncertainty became extra heterogeneous and extra instruments that version uncertainty than facts were proposed via numerous engineers and scientists. The software/ solution to version uncertainty in a particular context may still relatively be offerings by means of contemplating the good points of the phenomenon into consideration no longer independently of what's recognized in regards to the procedure and what explanations uncertainty. utilized learn in Uncertainty Modeling research concentrates on common facets of uncertainty, modeling, and strategies, and includes huge numbers of examples on engineering and sciences.

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Ayyub 17 Bilal M. Ayyub REFERENCES Ayyub, B. , 2001, Elicitation of Expert Opinions for Uncertainty and Risks: Theory, Applications and Guidance, CRC Press, FL. Ayyub, B. , 2004. Uncertainty Modeling and Analysis in Engineering and the Sciences, Draft Book Manuscript, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742. Bouissac, P. 1992. “The Construction of Ignorance and the Evolution of Knowledge,” University of Toronto, Quarterly, Vol. 61, No. 4, Summer.

If is a fuzzy set, then is the membership function for evaluated a real number An of written is defined as for is separately defined as the closure of the union of all the A fuzzy number is a fuzzy subset of the real numbers satisfying: (1) for some (normalized); and (2) is a closed, bounded interval for A triangular fuzzy number is defined by three numbers where the graph of is a triangle with base on the interval and vertex at We write for triangular fuzzy numbers. A triangular shaped fuzzy number has curves, not straight line segments, for the sides of the triangle.

Fuzzy Measure Theory, Plenum Press, New York. , and Weinstein, M. , 1978. ” In R. A. ) Research in the Sociology of Knowledge, Science and Art, Volume 1, JAI Press, NY. Zadeh, L. , 1965, “Fuzzy Sets,” Information and Control, 8, 338-353. Zadeh, L. , 1987, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, 1, 3-28. Chapter 2 A SELF-ORGANIZING NEURAL NETWORK BY DYNAMIC AND SPATIAL CHANGING WEIGHTS† Noriyasu Homma, Madan M. Gupta, Masao Sakai, Makoto Yoshizawa, and Kenichi Abe 1.

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