On an installation of Buchberger's algorithm
Journal of Symbolic Computation
Solving fuzzy equations: a new solution concept
Fuzzy Sets and Systems
Solutions of algebraic equations involving generalized fuzzy numbers
Information Sciences: an International Journal
Gröbner bases computation using syzygies
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Solution of non-linear fuzzy systems by decomposition of incremental fuzzy numbers
Information Sciences: an International Journal
Numerical solution of a system of fuzzy polynomials by fuzzy neural network
Information Sciences: an International Journal
Toward a generalized theory of uncertainty (GTU)--an outline
Information Sciences: an International Journal
Perturbation analysis of fuzzy linear systems
Information Sciences: an International Journal
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on Bio-inspired Learning and Intelligent Systems
Solution of fuzzy polynomial equations by modified Adomian decomposition method
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on Bio-inspired Learning and Intelligent Systems
On fuzzy relational equations and the covering problem
Information Sciences: an International Journal
Information Sciences: an International Journal
Linear optimization with bipolar max-min constraints
Information Sciences: an International Journal
Resolution of fuzzy relational equations - Method, algorithm and software with applications
Information Sciences: an International Journal
Information Sciences: an International Journal
Resolution of a system of the max-product fuzzy relation equations using LºU-factorization
Information Sciences: an International Journal
Information Sciences: an International Journal
Hi-index | 0.07 |
The occurrence of imprecision in the real world is inevitable due to some unexpected situations. The imprecision is often involved in any engineering design process. The imprecision and uncertainty are often interpreted as fuzziness. Fuzzy systems have an essential role in the uncertainty modelling, which can formulate the uncertainty in the actual environment. In this paper, a new approach is proposed to solve a system of fuzzy polynomial equations based on the Grobner basis. In this approach, first, the h-cut of a system of fuzzy polynomial equations is computed, and a parametric form for the fuzzy system with respect to the parameter of h is obtained. Then, a Grobner basis is computed for the ideal generated by the h-cuts of the system with respect to the lexicographical order using Faugere's algorithm, i.e., F"4 algorithm. The Grobner basis of the system has an upper triangular structure. Therefore, the system can be solved using the forward substitution. Hence, all the solutions of the system of fuzzy polynomial equations can easily be obtained. Finally, the proposed approach is compared with the current numerical methods. Some theorems together with some numerical examples and applications are presented to show the efficiency of our method with respect to the other methods.