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

Authors

Gul Sana^1, , Muhammad Bilal Khan¹, Muhammad Aslam Noor¹, Pshtiwan Othman Mohammed², Yu-Ming Chu^{3, *}

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

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/).

Download article (PDF)
View full text (HTML)

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  -