A Gröbner basis approach for finding positive solution of fully fuzzy polynomial equations systems

Article type: Research Article

Authors: Rahmany, Sajjad | Basiri, Abdolali | Farahani, Hamed | Borzabadi, Akbar Hashemi

Affiliations: School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran

Note: [] Corresponding author. Sajjad Rahmany, School of Mathematics and Computer Sciences, Damghan University, 3671641167, Damghan, Iran. E-mails: [email protected] (Sajjad Rahmany); [email protected] (Abdolali Basiri); [email protected] (Hamed Farahani); [email protected] (Akbar Hashemi Borzabadi).

Abstract: This paper presents a novel approach for finding positive solution of fully fuzzy polynomial equations systems employing Gröbner bases benefits. First, the system of fully fuzzy polynomial equations is converted to an equivalent crisp polynomial equations system. Then, using Gröbner basis properties a criteria for determining existence and finding positive fuzzy solutions of original system is introduced. The big advantage of the proposed method lies in the fact that it attains all positive fuzzy solutions of problem at a time. Finally, some applied numerical examples are illustrated to demonstrate the proficiency of the given approach.

Keywords: Fuzzy numbers, fully fuzzy polynomial equations systems, Gröbner bases, affine varieties

DOI: 10.3233/IFS-2012-0646

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 2, pp. 395-402, 2013