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

Authors:
Sajjad Rahmany;Abdolali Basiri;Hamed Farahani;Akbar Hashemi Borzabadi
Affiliations:
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran;School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran;School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran;School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

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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.