Towards A neural-based understanding of the cauchy deviate method for processing interval and fuzzy uncertainty

2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings

Volumn , Issue , 2009, Pages 1264-1269

  Kreinovich, Vladik ^a   Nguyen, Hung T ^b  

^a UNIVERSITY OF TEXAS AT EL PASO   (United States)

^b NEW MEXICO STATE UNIVERSITY   (United States)

Author keywords

Cauchy deviate method; Fuzzy uncertainty; Interval uncertainty; Monte Carlo simulations; Neural networks

Indexed keywords

CAUCHY DEVIATE METHOD; CAUCHY DISTRIBUTION; FUZZY DATA; FUZZY UNCERTAINTIES; INTERVAL UNCERTAINTY; MONTE CARLO; MONTE CARLO SIMULATION;

FUZZY SYSTEMS; INTELLIGENT SYSTEMS; NEURAL NETWORKS;

FUZZY LOGIC;

EID: 84871884051     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. J. Aczel, Lectures on functional equations and their applications, Dover, New York, 2006.
2. C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, 2006.
3. D. Dubois and H. Prade, Operations on fuzzy numbers, International Journal of Systems Science, 1978, Vol. 9, pp. 613-626.
4. Interval computations website http://www.cs.utep.edu/interval-comp
5. L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics, Springer-Verlag, London, 2001.
6. G. Klir and B. Yuan, Fuzzy sets and fuzzy logic, Prentice Hall, New Jersey, 1995.
7. V. Kreinovich, J. Beck, C. Ferregut, A. Sanchez, G. R. Keller, M. Averill, and S. A. Starks, "Monte-Carlo-type techniques for processing interval uncertainty, and their potential engineering applications", Reliable Computing, 2007, Vol. 13, No. 1, pp. 25-69.
8. V. Kreinovich and S. Ferson, "A New Cauchy-Based Black-Box Technique for Uncertainty in Risk Analysis", Reliability Engineering and Systems Safety, 2004, Vol. 85, No. 1-3, pp. 267-279.
9. V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, Computational complexity and feasibility of data processing and interval computations, Kluwer, Dordrecht, 1998.
10. V. Kreinovich and C. Quintana. "Neural networks: what non-linearity to choose?," Proceedings of the 4th University of New Brunswick Artificial Intelligence Workshop, Fredericton, N.B., Canada, 1991, pp. 627-637.
11. J. Lawrence, Introduction to Neural Networks, California Scientific Software Press, 1994.
12. R. E. Moore and W. Lodwick, Interval Analysis and Fuzzy Set Theory, Fuzzy Sets and Systems, 2003, Vol. 135, No. 1, pp. 5-9.
13. H. T. Nguyen and V. Kreinovich, Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications, In: R. B. Kearfott and V. Kreinovich, eds., Applications of Interval Computations, Kluwer, Dordrecht, 1996, pp. 245-290.
14. H. T. Nguyen and V. Kreinovich, Applications of Continuous Mathematics to Computer Science, Kluwer, Dordrecht, 1997.
15. H. T. Nguyen and E. A. Walker, A First Course in Fuzzy Logic, CRC Press, Boca Raton, Florida, 2006.
16. S. Rabinovich, Measurement Errors and Uncertainties: Theory and Practice, American Institute of Physics, New York, NY, 2005.
17. I. M. Singer and S. Sternberg, "Infinite groups of Lie and Cartan, Part 1", Journal d'Analyse Mathematique, 1965, Vol. XV, pp. 1-113.
18. P. J. Werbos, "Intelligence in the brain: A theory of how it works and how to build it", Neural Networks, 2009, to appear.
19. N. Wiener, Cybernetics, or Control and Communication in the animal and the machine, MIT Press, Cambridge, MA, 1962.