International Journal of Computational Intelligence Systems

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Volume 14, Issue 1, 2021, Pages 1856 - 1870

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Authors
Muhammad Bilal Khan1, Muhammad Aslam Noor1, Khalida Inayat Noor1, Yu-Ming Chu2, *, ORCID
1Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
2Department of Mathematics, Huzhou University, Huzhou, P. R. China
*Corresponding author. Email: chuyuming@zjhu.edu.cn
Corresponding Author
Yu-Ming Chu
Received 14 February 2021, Accepted 31 May 2021, Available Online 28 June 2021.
DOI
10.2991/ijcis.d.210616.001How to use a DOI?
Keywords
Higher-order strongly preinvex fuzzy mapping; Invex fuzzy mappings; Fuzzy monotonicity; Fuzzy mixed variational-like inequalities
Abstract

A family of fuzzy mappings is called higher-order strongly preinvex fuzzy mappings (HOS-preinvex fuzzy mappings), which take the place of generalization of the notion of nonconvexity is introduced through the “fuzzy-max” order among fuzzy numbers. This family properly includes the family of preinvex fuzzy mappings and is included in the family of quasi preinvex fuzzy mappings. With the support of examples, we have discussed some special cases. Some properties are derived and relations among the HOS-preinvex fuzzy mappings, HOS-invex fuzzy mappings, and fuzzy HOS-monotonicity are obtained under some mild conditions. Then, we have shown that optimality conditions of generalized differentiable HOS-preinvex fuzzy mappings and for the sum of generalized differentiable (briefly, G-differentiable) preinvex fuzzy mappings and nongeneralized differentiable HOS-preinvex fuzzy mappings can be distinguished by HOS-fuzzy variational-like inequalities and HOS-fuzzy mixed variational-like inequalities, respectively which can be viewed as novel applications. These inequalities are very interesting outcome of our main results and appear to be new ones. Several exceptional cases are debated. Presented results in this paper can be considered and development of previously established results.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
14 - 1
Pages
1856 - 1870
Publication Date
2021/06/28
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.210616.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Muhammad Bilal Khan
AU  - Muhammad Aslam Noor
AU  - Khalida Inayat Noor
AU  - Yu-Ming Chu
PY  - 2021
DA  - 2021/06/28
TI  - Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities
JO  - International Journal of Computational Intelligence Systems
SP  - 1856
EP  - 1870
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210616.001
DO  - 10.2991/ijcis.d.210616.001
ID  - Khan2021
ER  -