Details:
Title  Resolution of a system of fuzzy polynomial equations using the Gröbner basis  Author(s)  Abdolali Basiri, Ali Abbasi Molai, Rahmany Sajjad  Type  Article in Journal  Abstract  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 Gröbner basis. In this approach, first, the hcut 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 Gröbner basis is computed for the ideal generated by the hcuts of the system with respect to the lexicographical order using Faugère’s algorithm, i.e., F4 algorithm. The Gröbner 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.  Keywords  Fuzzy number, System of fuzzy polynomial equation, Gröbner basis, Lexicographical order, Faugère’s algorithm, F4 algorithm  ISSN  00200255 
URL 
http://www.sciencedirect.com/science/article/pii/S0020025512005014 
Language  English  Journal  Information Sciences  Volume  220  Pages  541  558  Year  2013  Note  Online Fuzzy Machine Learning and Data Mining  Edition  0  Translation 
No  Refereed 
No 
