Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems
Abstract The fuzzy set theory enables us to represent our knowledge under multiple interpretations and axiomatic foundations from linguistic to computational representations. While the intuitionistic fuzzy set, as a generalization of the fuzzy set, cannot only represent the tolerance levels, but als...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02777-1 |
| _version_ | 1828734185892741120 |
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| author | Ting Xie Dapeng Li |
| author_facet | Ting Xie Dapeng Li |
| author_sort | Ting Xie |
| collection | DOAJ |
| description | Abstract The fuzzy set theory enables us to represent our knowledge under multiple interpretations and axiomatic foundations from linguistic to computational representations. While the intuitionistic fuzzy set, as a generalization of the fuzzy set, cannot only represent the tolerance levels, but also the intolerance levels which a decision maker can tolerate and cannot tolerate in the accomplishment of a linguistic interpretation, in this paper, we introduce the generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations. It is shown that such problems can be transformed into the classical (nonfuzzy) generalized variational inequalities by means of level sets of the intuitionistic fuzzy relation. Furthermore, the equivalence between the generalized variational inequalities with intuitionistic fuzzy relations and the fuzzy fixed point problems is established. Finally, based on the projection method, we propose an iterative algorithm and a projected neural network model for the generalized variational inequalities with intuitionistic fuzzy relations, and the stability of the proposed projected dynamical system is also investigated. |
| first_indexed | 2024-04-12T22:43:49Z |
| format | Article |
| id | doaj.art-7834671e4de843d4b411c2f8fa160238 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T22:43:49Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-7834671e4de843d4b411c2f8fa1602382022-12-22T03:13:38ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-04-012022111610.1186/s13660-022-02777-1Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systemsTing Xie0Dapeng Li1College of Social Development and Public Administration, Northwest Normal UniversityInstitute of Modern Physics, Chinese Academy of SciencesAbstract The fuzzy set theory enables us to represent our knowledge under multiple interpretations and axiomatic foundations from linguistic to computational representations. While the intuitionistic fuzzy set, as a generalization of the fuzzy set, cannot only represent the tolerance levels, but also the intolerance levels which a decision maker can tolerate and cannot tolerate in the accomplishment of a linguistic interpretation, in this paper, we introduce the generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations. It is shown that such problems can be transformed into the classical (nonfuzzy) generalized variational inequalities by means of level sets of the intuitionistic fuzzy relation. Furthermore, the equivalence between the generalized variational inequalities with intuitionistic fuzzy relations and the fuzzy fixed point problems is established. Finally, based on the projection method, we propose an iterative algorithm and a projected neural network model for the generalized variational inequalities with intuitionistic fuzzy relations, and the stability of the proposed projected dynamical system is also investigated.https://doi.org/10.1186/s13660-022-02777-1Variational inequalityIntuitionistic fuzzy relationLevel setProjection methodLyapunov stability |
| spellingShingle | Ting Xie Dapeng Li Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems Journal of Inequalities and Applications Variational inequality Intuitionistic fuzzy relation Level set Projection method Lyapunov stability |
| title | Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| title_full | Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| title_fullStr | Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| title_full_unstemmed | Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| title_short | Generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| title_sort | generalized variational inequalities for linguistic interpretations using intuitionistic fuzzy relations and projected dynamical systems |
| topic | Variational inequality Intuitionistic fuzzy relation Level set Projection method Lyapunov stability |
| url | https://doi.org/10.1186/s13660-022-02777-1 |
| work_keys_str_mv | AT tingxie generalizedvariationalinequalitiesforlinguisticinterpretationsusingintuitionisticfuzzyrelationsandprojecteddynamicalsystems AT dapengli generalizedvariationalinequalitiesforlinguisticinterpretationsusingintuitionisticfuzzyrelationsandprojecteddynamicalsystems |