Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities
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 introd...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer
2021-06-01
|
| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125958280/view |
| _version_ | 1811301351052804096 |
|---|---|
| author | Gul Sana Muhammad Bilal Khan Muhammad Aslam Noor Pshtiwan Othman Mohammed Yu-Ming Chu |
| author_facet | Gul Sana Muhammad Bilal Khan Muhammad Aslam Noor Pshtiwan Othman Mohammed Yu-Ming Chu |
| author_sort | Gul Sana |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T07:07:13Z |
| format | Article |
| id | doaj.art-e52a2032d2ff4f7d91d2733785c10796 |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T07:07:13Z |
| publishDate | 2021-06-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-e52a2032d2ff4f7d91d2733785c107962022-12-22T02:56:58ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832021-06-0114110.2991/ijcis.d.210620.001Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral InequalitiesGul SanaMuhammad Bilal KhanMuhammad Aslam NoorPshtiwan Othman MohammedYu-Ming ChuIt 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.https://www.atlantis-press.com/article/125958280/viewHarmonically convex fuzzy interval-valued functionFuzzy interval fractional integral operatorHermite–Hadamard inequalityHermite–Hadamard–Fejér inequality |
| spellingShingle | Gul Sana Muhammad Bilal Khan Muhammad Aslam Noor Pshtiwan Othman Mohammed Yu-Ming Chu Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities International Journal of Computational Intelligence Systems Harmonically convex fuzzy interval-valued function Fuzzy interval fractional integral operator Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| title | Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities |
| title_full | Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities |
| title_fullStr | Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities |
| title_full_unstemmed | Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities |
| title_short | Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities |
| title_sort | harmonically convex fuzzy interval valued functions and fuzzy interval riemann liouville fractional integral inequalities |
| topic | Harmonically convex fuzzy interval-valued function Fuzzy interval fractional integral operator Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| url | https://www.atlantis-press.com/article/125958280/view |
| work_keys_str_mv | AT gulsana harmonicallyconvexfuzzyintervalvaluedfunctionsandfuzzyintervalriemannliouvillefractionalintegralinequalities AT muhammadbilalkhan harmonicallyconvexfuzzyintervalvaluedfunctionsandfuzzyintervalriemannliouvillefractionalintegralinequalities AT muhammadaslamnoor harmonicallyconvexfuzzyintervalvaluedfunctionsandfuzzyintervalriemannliouvillefractionalintegralinequalities AT pshtiwanothmanmohammed harmonicallyconvexfuzzyintervalvaluedfunctionsandfuzzyintervalriemannliouvillefractionalintegralinequalities AT yumingchu harmonicallyconvexfuzzyintervalvaluedfunctionsandfuzzyintervalriemannliouvillefractionalintegralinequalities |