Intuitionistic fuzzy variational inequalities and their applications
In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterizat...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241634 |
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| author | Tareq Saeed |
| author_facet | Tareq Saeed |
| author_sort | Tareq Saeed |
| collection | DOAJ |
| description | In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally, some variational inequalities, known as intuitionistic fuzzy variational inequality and intuitionistic fuzzy variational mixed inequalities, are introduced. The results obtained in this paper can be regarded as refinements and extensions of previously established results. |
| format | Article |
| id | doaj-art-4cd9a7fe982645d68b1ab7944cfc445c |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-4cd9a7fe982645d68b1ab7944cfc445c2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912342893431010.3934/math.20241634Intuitionistic fuzzy variational inequalities and their applicationsTareq Saeed0Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaIn this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally, some variational inequalities, known as intuitionistic fuzzy variational inequality and intuitionistic fuzzy variational mixed inequalities, are introduced. The results obtained in this paper can be regarded as refinements and extensions of previously established results.https://www.aimspress.com/article/doi/10.3934/math.20241634intuitionistic fuzzy numbersintuitionistic convex fuzzy mappingsintuitionistic quasi-convex fuzzy mappingsglobal minimumintuitionistic fuzzy variational inequalities |
| spellingShingle | Tareq Saeed Intuitionistic fuzzy variational inequalities and their applications AIMS Mathematics intuitionistic fuzzy numbers intuitionistic convex fuzzy mappings intuitionistic quasi-convex fuzzy mappings global minimum intuitionistic fuzzy variational inequalities |
| title | Intuitionistic fuzzy variational inequalities and their applications |
| title_full | Intuitionistic fuzzy variational inequalities and their applications |
| title_fullStr | Intuitionistic fuzzy variational inequalities and their applications |
| title_full_unstemmed | Intuitionistic fuzzy variational inequalities and their applications |
| title_short | Intuitionistic fuzzy variational inequalities and their applications |
| title_sort | intuitionistic fuzzy variational inequalities and their applications |
| topic | intuitionistic fuzzy numbers intuitionistic convex fuzzy mappings intuitionistic quasi-convex fuzzy mappings global minimum intuitionistic fuzzy variational inequalities |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241634 |
| work_keys_str_mv | AT tareqsaeed intuitionisticfuzzyvariationalinequalitiesandtheirapplications |