International Journal of Computational Intelligence Systems

Volume 14, Issue 1, 2021, Pages 1809 - 1822

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Authors
Gul Sana1, ORCID, Muhammad Bilal Khan1, Muhammad Aslam Noor1, Pshtiwan Othman Mohammed2, Yu-Ming Chu3, *
1Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
2Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Iraq
3Department of Mathematics, Huzhou University, Huzhou, P. R. China
*Corresponding author. Email: chuyuming@zjhu.edu.cn
Corresponding Author
Yu-Ming Chu
Received 5 April 2021, Accepted 14 June 2021, Available Online 28 June 2021.
DOI
10.2991/ijcis.d.210620.001How to use a DOI?
Keywords
Harmonically convex fuzzy interval-valued function; Fuzzy interval fractional integral operator; Hermite–Hadamard inequality; Hermite–Hadamard–Fejér inequality
Abstract

It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann–Liouville fractional operator. With the help of fuzzy order relation and fuzzy-interval Riemann–Liouville fractional, we derive some integrals inequalities of Hermite–Hadamard (H-H) type and Hermite–Hadamard–Fejér (H-H Fejér) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.

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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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
14 - 1
Pages
1809 - 1822
Publication Date
2021/06/28
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.210620.001How 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

TY  - JOUR
AU  - Gul Sana
AU  - Muhammad Bilal Khan
AU  - Muhammad Aslam Noor
AU  - Pshtiwan Othman Mohammed
AU  - Yu-Ming Chu
PY  - 2021
DA  - 2021/06/28
TI  - Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities
JO  - International Journal of Computational Intelligence Systems
SP  - 1809
EP  - 1822
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210620.001
DO  - 10.2991/ijcis.d.210620.001
ID  - Sana2021
ER  -