Determining of Level Sets for a Fuzzy Surface Using Gröbner Basis

Hamed Farahani, Sajjad Rahmany and Abdolali Basiri
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Hamed Farahani: Chabahar Maritime University, Sistan Va Baluchestan Iran, Iran
Sajjad Rahmany: School of Mathematics and Computer Sciences Damghan University, Damghan, Iran
Abdolali Basiri: School of Mathematics and Computer Sciences Damghan University, Damghan, Iran

International Journal of Fuzzy System Applications (IJFSA), 2015, vol. 4, issue 2, 1-14

Abstract: In this paper, a manner to determine the level sets of a fuzzy surface using the benefits of Gröbner basis is presented. Fuzzy surfaces are constructed from incomplete datasets or from data that contain uncertainty which has not statistical nature. The authors firstly define the concept of level sets for the fuzzy surfaces. Then, employing Gröbner bases benefits a criterion is proposed for when the level sets of the fuzzy surface are nonempty sets. Moreover, a new algorithm is designed to determine the level sets. The big advantage of the proposed method lies in the fact that it attains all members of the level sets of the fuzzy surface at a time. Finally, some applied numerical examples are illustrated to demonstrate the proficiency of the given approach.

Date: 2015
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