caa a22 4500 605470642 CHVBK 20210128100329.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00500-014-1249-1 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1249-1 Resolution of a system of fuzzy polynomial equations using eigenvalue method [Elektronische Daten] [Hamed Farahani, Sajjad Rahmany, Abdolali Basiri, Ali Abbasi Molai] In this paper, a system of fuzzy polynomial equations is studied. Two solution types are defined for this system, called solution and $$r$$ r -cut solution. Then sufficient and necessary conditions are proposed for existence of solution and $$r$$ r -cut solution of the system, respectively. The solution set of the system is also determined. Moreover, a new algorithm is designed to find all the solutions and all the $$r$$ r -cut solutions of the system based on the eigenvalue method. Finally, some examples are given to illustrate the concepts and the algorithm. Springer-Verlag Berlin Heidelberg, 2014 Fuzzy numbers nationallicence System of fuzzy polynomial equations nationallicence Gröbner basis nationallicence Real solution nationallicence Eigenvalue method nationallicence Farahani Hamed School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut Rahmany Sajjad School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut Basiri Abdolali School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut Abbasi Molai Ali School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 283-291 1432-7643 19:2<283 2015 19 500 https://doi.org/10.1007/s00500-014-1249-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1249-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farahani Hamed School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut NATIONALLICENCE 700 1- Rahmany Sajjad School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut NATIONALLICENCE 700 1- Basiri Abdolali School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut NATIONALLICENCE 700 1- Abbasi Molai Ali School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 283-291 1432-7643 19:2<283 2015 19 500