Strongly Generalized Convex Fuzzy-Valued Function and Its Application in Fuzzy Optimization

BAI Yu-juan, LIU Kun, ZHANG Chen

doi:10.13371/j.cnki.chin.q.j.m.2020.04.005

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 4: 370 - 387

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.04.005

Strongly Generalized Convex Fuzzy-Valued Function and Its Application in Fuzzy Optimization

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College of Mathematics and Statistics, Longdong University, Qingyang 745000, China

BAI Yu-juan(1979-), female, native of Qingyang, Gansu, lecturer, master’s degree, engages in fuzzy analysis and its application; LIU Kun(1978-), male, native of Qingyang, Gansu, assistant professor, doctorate, engages in fuzzy matrix and its application; ZHANG Chen(1983-), female, native of Qingyang, Gansu, lecturer, master’s degree, engages in fuzzy graph theory.

Received date: 2020-07-30

Online published: 2021-01-06

Supported by

Supported by Natural Science Foundation of Gansu Province of China (Grant No. 18JR3RM238);

Research Foundation of Higher Education of Gansu Province of China (Grant No. 2018A-101);

Innovation Ability promotion Project of Higher Education of Gansu Province of China (Grant No. 2019A-117).

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Abstract

Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman, the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.

Key words： Fuzzy-number-valued functions; Strongly generalized convexity; Fuzzy optimization

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BAI Yu-juan, LIU Kun, ZHANG Chen . Strongly Generalized Convex Fuzzy-Valued Function and Its Application in Fuzzy Optimization[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(4) : 370 -387 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.005

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