Abstract
A new concept of interval and fuzzy equations solving based on the generalized procedure of interval extension called ”interval extended zero” method is proposed. The central for this approach is the treatment of ”interval zero” as an interval centered around 0. It is shown that such proposition is not of heuristic nature, but is a direct consequence of interval subtraction operation. It is shown that the resulting solution of interval linear equations based on the elaborated method may be naturally treated as a fuzzy number. An important advantage of new method is that it substantially decreases the excess width effect.
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References
Abbasbandy, S., Asady, B.: Newton’s method for solving fuzzy nonlinear equations. Applied Mathematics and Computation 159, 349–356 (2004)
Abbasbandy, S.: Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method. Applied Mathematics and Computation 170, 648–656 (2005)
Buckley, J.J., Qu, Y.: Solving linear and quadratic fuzzy equations. Fuzzy S e t s and Systems 38, 43–59 (1990)
Buckley, J.J., Eslami, E.: Neural net solutions to fuzzy problems: The quadratic equation. Fuzzy Sets and Systems 86, 289–298 (1997)
Buckley, J.J., Eslami, E., Hayashi, Y.: Solving fuzzy equations using neural nets. Fuzzy Sets and Systems 86, 271–278 (1997)
Cleary, J.C.: Logical Arithmetic. Future Computing Systems 2, 125–149 (1987)
Dymova, L., Gonera, M., Sevastianov, P., Wyrzykowski, R.: New method for interval extension of Leontiefs input-output model with use of parallel programming. In: Dymova, L., Gonera, M., Sevastianov, P., Wyrzykowski, R. (eds.) Proceedings of the International Conf. on Fuzzy Sets and Soft Computing in Economics and Finance(FSSCEF), St.Petersburg, Russian, pp. 549–556 (2004)
Gardnes, E., Mielgo, H., Trepat, A.: Modal intervals: Reasons and ground semantics. In: Nickel, K. (ed.) Interval mathematics 212. LNCS, pp. 27–35. Springer, Berlin (1985)
Hanss, M., Klimke, A.: On the reliability of the influence measure in the transformation method of fuzzy arithmetic. Fuzzy Sets and Systems 143, 371–390 (2004)
Jaulin, L., Kieffir, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)
Moore, R.E.: Interval analysis, Englewood Cliffs, N. Prentice-Hall, Englewood Cliffs (1966)
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Sevastjanov, P., Dymova, L. (2008). Fuzzy Solution of Interval Linear Equations. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_147
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DOI: https://doi.org/10.1007/978-3-540-68111-3_147
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68105-2
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