A study on the differential and sub-differential of fuzzy mapping and its application problem

Volume 10, Issue 1, pp 1--17 http://dx.doi.org/10.22436/jnsa.010.01.01

Publication Date: January 26, 2017 Submission Date: July 04, 2016

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Authors

Yu-E Bao - College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City 028043, China. Jin-Jun Li - College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City 028043, China.

Abstract

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.

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Keywords

• Fuzzy number
• fuzzy mapping
• differential (sub-differential)
• convexification fuzzy mapping
• convex extension.

MSC

•  03E72
•  52A41
•  58C20
•  58C25

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