The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications
In this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values −∞˜ and +∞˜ at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concept...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2024/8335864 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850215243318296576 |
|---|---|
| author | T. Allahviranloo M. R. Balooch Shahryari O. Sedaghatfar M. R. Shahriari R. Saadati S. Noeiaghdam U. Fernandez-Gamiz |
| author_facet | T. Allahviranloo M. R. Balooch Shahryari O. Sedaghatfar M. R. Shahriari R. Saadati S. Noeiaghdam U. Fernandez-Gamiz |
| author_sort | T. Allahviranloo |
| collection | DOAJ |
| description | In this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values −∞˜ and +∞˜ at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concepts such as fuzzy indicator function and fuzzy infimal convolution for extended fuzzy-valued functions. Finally, we introduce the concept of directional generalized derivative for extended above functions and its properties. Eventually, we give a practical example that will illustrate well the directional g-derivative for the extended fuzzy-valued convex function. |
| format | Article |
| id | doaj-art-84f4c4cbc8074ca8ad302eb57c4fbace |
| institution | OA Journals |
| issn | 1687-711X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-84f4c4cbc8074ca8ad302eb57c4fbace2025-08-20T02:08:40ZengWileyAdvances in Fuzzy Systems1687-711X2024-01-01202410.1155/2024/8335864The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their ApplicationsT. Allahviranloo0M. R. Balooch Shahryari1O. Sedaghatfar2M. R. Shahriari3R. Saadati4S. Noeiaghdam5U. Fernandez-Gamiz6Software Engineering DepartmentDepartment of MathematicsDepartment of MathematicsSoftware Engineering DepartmentSchool of MathematicsIndustrial Mathematics LaboratoryNuclear Engineering and Fluid Mechanics DepartmentIn this paper, we are thus motivated to define and introduce the extended fuzzy-valued convex functions that can take the singleton fuzzy values −∞˜ and +∞˜ at some points. Such functions can be characterized using the notions of effective domain and epigraph. In this way, we study important concepts such as fuzzy indicator function and fuzzy infimal convolution for extended fuzzy-valued functions. Finally, we introduce the concept of directional generalized derivative for extended above functions and its properties. Eventually, we give a practical example that will illustrate well the directional g-derivative for the extended fuzzy-valued convex function.http://dx.doi.org/10.1155/2024/8335864 |
| spellingShingle | T. Allahviranloo M. R. Balooch Shahryari O. Sedaghatfar M. R. Shahriari R. Saadati S. Noeiaghdam U. Fernandez-Gamiz The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications Advances in Fuzzy Systems |
| title | The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications |
| title_full | The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications |
| title_fullStr | The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications |
| title_full_unstemmed | The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications |
| title_short | The Investigation of Some Essential Concepts of Extended Fuzzy-Valued Convex Functions and Their Applications |
| title_sort | investigation of some essential concepts of extended fuzzy valued convex functions and their applications |
| url | http://dx.doi.org/10.1155/2024/8335864 |
| work_keys_str_mv | AT tallahviranloo theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT mrbaloochshahryari theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT osedaghatfar theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT mrshahriari theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT rsaadati theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT snoeiaghdam theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT ufernandezgamiz theinvestigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT tallahviranloo investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT mrbaloochshahryari investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT osedaghatfar investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT mrshahriari investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT rsaadati investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT snoeiaghdam investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications AT ufernandezgamiz investigationofsomeessentialconceptsofextendedfuzzyvaluedconvexfunctionsandtheirapplications |