Abstract
This paper presents a framework for reasoning using intervals. Two interpretations of intervals are examined, one treats intervals as bounds of a truth evaluation function, and the other treats end points of intervals as two truth evaluation functions. They lead to two different reasoning approaches, one is based on interval computations, and the other is based on interval structures. A number of interval based reasoning methods are reviewed and compared within the proposed framework.
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C. Brink, Power structures, Algebra Universalis, 30, 177–216, 1993.
P.P. Bonissone, Summarizing and propagating uncertain information with triangular norms, International Journal of Approximate Reasoning, 1, 71–101, 1987.
A. Bundy, Incidence calculus: a mechanism for probabilistic reasoning, Journal of Automated Reasoning, 1, 263–283, 1985.
D. Dubois, and P. Prade, Possibility Theory: an Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.
R. Fagin, and J.Y. Halpern, Uncertainty, belief, and probability, Computational Intelligence, 7, 160–173, 1991.
J.Y. Halpern, and R. Fagin, Two views of belief: belief as generalized probability and belief as evidence, Artificial Intelligence, 54: 275–317, 1992.
G.J. Klir, and B. Yuan, Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice Hall, New Jersey, 1995.
R.E. Moore, Interval Analysis, Englewood Cliffs, New Jersey, Prentice-Hall, 1966.
C.V. Negoiţa, and D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Basel, Birkhäuser Verlag, 1975.
Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11, 341–356, 1982.
J.R. Quinlan, Inferno: a cautious approach to uncertain inference, The Computer Journal, 26, 255–269, 1983.
G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, 1976.
P. Smets, Resolving misunderstandings about belief functions, International Journal of Approximate Reasoning, 6, 21–344.
S.K.M. Wong, L.S. Wang, and Y.Y. Yao, On modeling uncertainty with interval structures, Computational Intelligence, 11, 406–426, 1995.
Y.Y. Yao, Interval-set algebra for qualitative knowledge representation, Proceedings of the Fifth International Conference on Computing and Information, 370–374, 1993.
Y.Y. Yao, A comparison of two interval-valued probabilistic reasoning methods, Proceedings of the 6th International Conference on Computing and Information, May 26–28, 1994, Peterborough, Ontario, Canada. Special issue of Journal of Computing and Information, 1, 1090–1105 (paper number D6), 1995.
Y.Y. Yao, and X. Li, Comparison of rough-set and interval-set models for uncertain reasoning, Fundamenta Informaticae, 27, 289–298, 1996.
Y.Y. Yao, and N. Noroozi, A unified framework for set-based computations, Proceedings of the 3rd International Workshop on Rough Sets and Soft Computing, Lin, T.Y. (Ed.), San Jose State University, 236–243, 1994.
Y.Y. Yao, and J. Wang, Interval based uncertain reasoning using fuzzy and rough sets, Advances in Machine Intelligence & Soft-Computing, Volume IV, Wang, P.P. (Ed.), Department of Electrical Engineering, Duke University, Durham, North Carolina, USA, 196–215, 1997
Y.Y. Yao, S.K.M. Wong, and L.S. Wang, A non-numeric approach to uncertain reasoning, International Journal of General Systems, 23, 343–359, 1995.
L.A. Zadeh, Fuzzy sets, Information & Control, 8, 338–353, 1965.
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© 1997 Springer-Verlag Berlin Heidelberg
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Yao, Y.Y., Wong, S.K.M. (1997). Interval approaches for uncertain reasoning. In: Raś, Z.W., Skowron, A. (eds) Foundations of Intelligent Systems. ISMIS 1997. Lecture Notes in Computer Science, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63614-5_37
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DOI: https://doi.org/10.1007/3-540-63614-5_37
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