Geodesic
A study on the differential and sub-differential of fuzzy mapping and its application problem
Bao, Yu-E1 ; Li, Jin-Jun1
1 College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City 028043, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 1-17.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about the concept. At last, we study the relationships between sub-differential of fuzzy mapping and differential of convex fuzzy mappings. Moreover, a sufficient condition that a class of fuzzy mapping have convex extension is gained.
DOI : 10.22436/jnsa.010.01.01
DOI : 10.22436/jnsa.010.01.01
Classification : 03E72, 52A41, 58C20, 58C25
Keywords: Fuzzy number, fuzzy mapping, differential (sub-differential), convexification fuzzy mapping, convex extension.

Bao, Yu-E 1 ; Li, Jin-Jun 1

1 College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City 028043, China 
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Bao, Yu-E; Li, Jin-Jun. A study on the differential and sub-differential of fuzzy mapping and its application problem. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 1-17. doi : 10.22436/jnsa.010.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.01/

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