Linear Fuzzy Integers and Bezout's Identity
Abstract
Fuzzy arithmetic is a powerful tool to solve engineering problems with uncertain parameters. In doing so, the uncertain parameters in the model equations are expressed by fuzzy numbers, and the problem is solved by using fuzzy arithmetic to carry out the mathematical operations in a generalized form. Diophantine equations have played an important role in many applications of optimization and decision making problems. This work considers the solution of Diophantine equations and Bezout’s Identity with Linear Fuzzy Integer coefficients. Overestimation is also addressed.References
R.E. Bellman, L.A. Zadeh, Decision making in a fuzzy environment, Management Science,17 (1970), B141–B164.
D. Dubois, H. Prade, System of linear fuzzy constraints, Fuzzy Sets and Systems, 13 (1982), 1–10.
B. Monk, A Proposed Theory of Fuzzy Random Variables, Dissertation, University of Alabama, 2001.
J. Neggers, H. Kim, Fuzzy posets on sets, Fuzzy sets and systems, 17 (2001), 391–402.
J. Neggers, H. Kim, On Linear Fuzzy Real Numbers, Manuscript for book under development, 2007.
C.V. Negoita, Fuzziness in management, OPSA/TIMS, Miami, 1970.
R. Prevo, Entropies of families of fuzzy random variables: an introduction to an in-depth exploration of several classes of important examples, Dissertation, University of Alabama, 2002.
F. Rogers, J. Neggers, Y. Jun. Method for Optimizing Linear Problems with Fuzzy Constraints. International Mathematical Forum, 3 (2008), 1141-1155.
H. Tanaka, K. Asai, Fuzzy linear programming problems with fuzzy numbers, Fuzzy sets and Systems, 13 (1984), 1–10.
H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming, J. Cybernetics, 3 (1984), 37–46.
H.J. Zimmermann, Fuzzy mathematical programming, Comput. Ops. Res., 10 (1983), 291–298.
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