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A new fuzzy system based on rectangular pyramid.

Jiang M, Yuan X, Li H, Wang J - ScientificWorldJournal (2015)

Bottom Line: The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm.It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain.Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A new fuzzy system is proposed in this paper. The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm. It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain. Moreover, this paper provides one sufficient condition of approximating function so that the new fuzzy system can approximate any continuous function of two variables with bounded partial derivatives. Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation.

No MeSH data available.


Related in: MedlinePlus

The division of small rectangular area [xi, xi+1]×[yj, yj+1] of S(x, y).
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4383317&req=5

fig3: The division of small rectangular area [xi, xi+1]×[yj, yj+1] of S(x, y).

Mentions: when xi ≤ x ≤ xi+1, yj + ((yj+1 − yj)/(xi+1 − xi))(x − xi) ≤ y ≤ yj+1, yj+1 + ((yj − yj+1)/(xi+1 − xi))(x − xi)≤y ≤ yj+1,(24)Sx,y=y−yj+1−2y+3yj+1−yjzij+yj+1−yjxi+1−x−2y+3yj+1−yjxi+1−xizi,j+1+yj+1−yjx−xi−2y+3yj+1−yjxi+1−xizi+1,j+1+yj+1−y−2y+3yj+1−yjzi+1,j;


A new fuzzy system based on rectangular pyramid.

Jiang M, Yuan X, Li H, Wang J - ScientificWorldJournal (2015)

The division of small rectangular area [xi, xi+1]×[yj, yj+1] of S(x, y).
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4383317&req=5

fig3: The division of small rectangular area [xi, xi+1]×[yj, yj+1] of S(x, y).
Mentions: when xi ≤ x ≤ xi+1, yj + ((yj+1 − yj)/(xi+1 − xi))(x − xi) ≤ y ≤ yj+1, yj+1 + ((yj − yj+1)/(xi+1 − xi))(x − xi)≤y ≤ yj+1,(24)Sx,y=y−yj+1−2y+3yj+1−yjzij+yj+1−yjxi+1−x−2y+3yj+1−yjxi+1−xizi,j+1+yj+1−yjx−xi−2y+3yj+1−yjxi+1−xizi+1,j+1+yj+1−y−2y+3yj+1−yjzi+1,j;

Bottom Line: The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm.It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain.Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A new fuzzy system is proposed in this paper. The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm. It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain. Moreover, this paper provides one sufficient condition of approximating function so that the new fuzzy system can approximate any continuous function of two variables with bounded partial derivatives. Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation.

No MeSH data available.


Related in: MedlinePlus