New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals
Numerous applications of the theory of convex and nonconvex mapping exist in the fields of applied mathematics and engineering. In this paper, we have defined a new class of nonconvex functions which is known as up and down pre-invex (pre-incave) fuzzy number valued mappings (<i>F-N-V∙M</i&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2322 |
| _version_ | 1797466380951355392 |
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| author | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | Numerous applications of the theory of convex and nonconvex mapping exist in the fields of applied mathematics and engineering. In this paper, we have defined a new class of nonconvex functions which is known as up and down pre-invex (pre-incave) fuzzy number valued mappings (<i>F-N-V∙M</i>s). The well-known fuzzy Hermite–Hadamard (𝐻𝐻)-type and related inequalities are taken into account in this work. We extend this mileage further using fuzzy Riemann integrals and the fuzzy number up and down pre-invexity. Additionally, by imposing some light restrictions on pre-invex (pre-incave) fuzzy number valued mappings, we have introduced two new significant classes of fuzzy number valued up and down pre-invexity (pre-incavity), which are referred to as lower up and down pre-invex (pre-incave) and upper up and down pre-invex (pre-incave) fuzzy number valued mappings. By using these definitions, we have amassed a large number of both established and novel exceptional situations that serve as implementations of the key findings. To support the validity of the fuzzy inclusion relations put out in this research, we also provide a few examples of fuzzy numbers valued up and down pre-invexity. |
| first_indexed | 2024-03-09T18:36:08Z |
| format | Article |
| id | doaj.art-5bfb3641e63348b1acb69597865ac79f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:36:08Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5bfb3641e63348b1acb69597865ac79f2023-11-24T07:08:28ZengMDPI AGSymmetry2073-89942022-11-011411232210.3390/sym14112322New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann IntegralsMuhammad Bilal Khan0Gustavo Santos-García1Savin Treanțǎ2Mohamed S. Soliman3Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanFacultad de Economíay Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, SpainDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaNumerous applications of the theory of convex and nonconvex mapping exist in the fields of applied mathematics and engineering. In this paper, we have defined a new class of nonconvex functions which is known as up and down pre-invex (pre-incave) fuzzy number valued mappings (<i>F-N-V∙M</i>s). The well-known fuzzy Hermite–Hadamard (𝐻𝐻)-type and related inequalities are taken into account in this work. We extend this mileage further using fuzzy Riemann integrals and the fuzzy number up and down pre-invexity. Additionally, by imposing some light restrictions on pre-invex (pre-incave) fuzzy number valued mappings, we have introduced two new significant classes of fuzzy number valued up and down pre-invexity (pre-incavity), which are referred to as lower up and down pre-invex (pre-incave) and upper up and down pre-invex (pre-incave) fuzzy number valued mappings. By using these definitions, we have amassed a large number of both established and novel exceptional situations that serve as implementations of the key findings. To support the validity of the fuzzy inclusion relations put out in this research, we also provide a few examples of fuzzy numbers valued up and down pre-invexity.https://www.mdpi.com/2073-8994/14/11/2322fuzzy-number valued mappingfuzzy Riemann integralup and down pre-invex fuzzy number valued mappingHermite–Hadamard inequalityHermite–Hadamard–Fejér inequality |
| spellingShingle | Muhammad Bilal Khan Gustavo Santos-García Savin Treanțǎ Mohamed S. Soliman New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals Symmetry fuzzy-number valued mapping fuzzy Riemann integral up and down pre-invex fuzzy number valued mapping Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| title | New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals |
| title_full | New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals |
| title_fullStr | New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals |
| title_full_unstemmed | New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals |
| title_short | New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals |
| title_sort | new class up and down pre invex fuzzy number valued mappings and related inequalities via fuzzy riemann integrals |
| topic | fuzzy-number valued mapping fuzzy Riemann integral up and down pre-invex fuzzy number valued mapping Hermite–Hadamard inequality Hermite–Hadamard–Fejér inequality |
| url | https://www.mdpi.com/2073-8994/14/11/2322 |
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