Some New Classes of Preinvex Fuzzy-Interval-Valued Functions and Inequalities

Authors

Muhammad Bilal Khan¹, Muhammad Aslam Noor¹, Lazim Abdullah^2, , Yu-Ming Chu^3,

¹Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

²Management Science Research Group, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kuala Terengganu, Malaysia

³Department of Mathematics, Huzhou University, Huzhou, P. R. China

^*Corresponding author. Email: chuyuming@zjhu.edu.cn

DOI

10.2991/ijcis.d.210409.001How to use a DOI?

Keywords

Fuzzy-interval-valued functions; Fuzzy Riemann integrals; h1,h2-preinvex fuzzy-interval-valued functions; Hermite–Hadamard inequalities

Abstract

It is well known that convexity and nonconvexity develop a strong relationship with different types of integral inequalities. Due to the importance of the concept of nonconvexity and integral inequality, in this paper, we present some new classes of preinvex fuzzy-interval-valued functions involving two arbitrary auxiliary functions is known as h1,h2-preinvex fuzzy-interval-valued functions (h1,h2-preinvex fuzzy-IVFs). With the help of these classes, we derive some new Hermite–Hadamard inequalities (HH-inequalities) by means of fuzzy order relation on fuzzy-interval space and verify with the support of some nontrivial examples. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on fuzzy-interval space. Moreover, several new and previously known results are also discussed which can be deducted from our main results. These results and different approaches may open new directions for fuzzy optimization problems, modeling, and interval-valued functions.

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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TY  - JOUR
AU  - Muhammad Bilal Khan
AU  - Muhammad Aslam Noor
AU  - Lazim Abdullah
AU  - Yu-Ming Chu
PY  - 2021
DA  - 2021/04/19
TI  - Some New Classes of Preinvex Fuzzy-Interval-Valued Functions and Inequalities
JO  - International Journal of Computational Intelligence Systems
SP  - 1403
EP  - 1418
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210409.001
DO  - 10.2991/ijcis.d.210409.001
ID  - Khan2021
ER  -