Generalized derivatives and optimization problems for n-dimensional fuzzy-number-valued functions-Reference-Cited by-同舟云学术

Generalized derivatives and optimization problems for n-dimensional fuzzy-number-valued functions

Published:2020-01-01 Issue:1 Volume:18 Page:1451-1477
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Xie Ting¹,Gong Zengtai²,Li Dapeng³

Affiliation:

1. College of Social Development and Public Administration, Northwest Normal University, Lanzhou 730070, China and Institute of Modern Physics, Chinese Academy of Sciences , Lanzhou , 730000 , China

2. College of Mathematics and Statistics, Northwest Normal University , Lanzhou , 730070 , China

3. Institute of Modern Physics, Chinese Academy of Sciences , Lanzhou , 730000 , China

Abstract

Abstract In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping. Furthermore, the relations among generalized derivative, directional generalized derivative, subdifferential and convexity for n-dimensional fuzzy-number-valued functions are investigated. Finally, under two kinds of partial orderings defined on the set of all n-dimensional fuzzy numbers, the duality theorems and saddle point optimality criteria in fuzzy optimization problems with constraints are discussed.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0081/pdf

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