Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data
The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/3947261 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553669873106944 |
|---|---|
| author | Zhenghai Ai Xiaoqin Shu Zeshui Xu |
| author_facet | Zhenghai Ai Xiaoqin Shu Zeshui Xu |
| author_sort | Zhenghai Ai |
| collection | DOAJ |
| description | The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data. |
| format | Article |
| id | doaj-art-2b8844825a664841a504563b859d5dce |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2b8844825a664841a504563b859d5dce2025-02-03T05:53:30ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/39472613947261Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous DataZhenghai Ai0Xiaoqin Shu1Zeshui Xu2College of Mathematics and Information Science, Leshan Normal University, Leshan, Sichuan 614000, ChinaSchool of Physics and Electronic Engineering, Leshan Normal University, Leshan, Sichuan 614000, ChinaState Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610064, ChinaThe intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.http://dx.doi.org/10.1155/2019/3947261 |
| spellingShingle | Zhenghai Ai Xiaoqin Shu Zeshui Xu Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data Complexity |
| title | Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data |
| title_full | Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data |
| title_fullStr | Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data |
| title_full_unstemmed | Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data |
| title_short | Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data |
| title_sort | foundation of interval valued intuitionistic fuzzy limit and differential theory and an application to continuous data |
| url | http://dx.doi.org/10.1155/2019/3947261 |
| work_keys_str_mv | AT zhenghaiai foundationofintervalvaluedintuitionisticfuzzylimitanddifferentialtheoryandanapplicationtocontinuousdata AT xiaoqinshu foundationofintervalvaluedintuitionisticfuzzylimitanddifferentialtheoryandanapplicationtocontinuousdata AT zeshuixu foundationofintervalvaluedintuitionisticfuzzylimitanddifferentialtheoryandanapplicationtocontinuousdata |