Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations
The interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov’s intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2016-01-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25868678/view |
| _version_ | 1811252535272407040 |
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| author | Hua Zhao Zeshui Xu Zeqing Yao |
| author_facet | Hua Zhao Zeshui Xu Zeqing Yao |
| author_sort | Hua Zhao |
| collection | DOAJ |
| description | The interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov’s intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under interval-valued intuitionistic fuzzy environment. Firstly, we discuss the four change directions (the addition, subtraction, multiplication and division directions) of the interval- valued intuitionistic fuzzy values (IVIFVs); Secondly, we propose four kinds of limits (the addition, subtraction, multiplication and division limits) for different sequences of IVIFVs, and then we define the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and study the continuities of IVIFFs; Thirdly, we develop two kinds of derivatives (the subtraction and division derivatives) of IVIFFs and give an equivalent condition for the existence of the derivative of an IVIFF. At last, we define the concepts of two kinds of differentials (the subtraction and division differentials) of IVIFFs and discuss the approximate computations of IVIFFs by the developed differentials. |
| first_indexed | 2024-04-12T16:37:01Z |
| format | Article |
| id | doaj.art-d69e42360da14c9ab8e4b6ccb4bb8fb6 |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-12T16:37:01Z |
| publishDate | 2016-01-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-d69e42360da14c9ab8e4b6ccb4bb8fb62022-12-22T03:24:58ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832016-01-019110.1080/18756891.2016.1144152Interval-Valued Intuitionistic Fuzzy Derivative and Differential OperationsHua ZhaoZeshui XuZeqing YaoThe interval-valued intuitionistic fuzzy set (IVIFS) generalizes Atanassov’s intuitionistic fuzzy set (A-IFS) with the membership and non-membership degrees being intervals instead of real numbers, so it can contain more information. In this paper, we study the derivatives and differentials under interval-valued intuitionistic fuzzy environment. Firstly, we discuss the four change directions (the addition, subtraction, multiplication and division directions) of the interval- valued intuitionistic fuzzy values (IVIFVs); Secondly, we propose four kinds of limits (the addition, subtraction, multiplication and division limits) for different sequences of IVIFVs, and then we define the concepts of interval-valued intuitionistic fuzzy function (IVIFF) and study the continuities of IVIFFs; Thirdly, we develop two kinds of derivatives (the subtraction and division derivatives) of IVIFFs and give an equivalent condition for the existence of the derivative of an IVIFF. At last, we define the concepts of two kinds of differentials (the subtraction and division differentials) of IVIFFs and discuss the approximate computations of IVIFFs by the developed differentials.https://www.atlantis-press.com/article/25868678/viewInterval-valued intuitionistic fuzzy set (IVIFS)Interval-valued intuitionistic fuzzy function (IVIFF)LimitContinuityDerivativeDifferential |
| spellingShingle | Hua Zhao Zeshui Xu Zeqing Yao Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations International Journal of Computational Intelligence Systems Interval-valued intuitionistic fuzzy set (IVIFS) Interval-valued intuitionistic fuzzy function (IVIFF) Limit Continuity Derivative Differential |
| title | Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations |
| title_full | Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations |
| title_fullStr | Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations |
| title_full_unstemmed | Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations |
| title_short | Interval-Valued Intuitionistic Fuzzy Derivative and Differential Operations |
| title_sort | interval valued intuitionistic fuzzy derivative and differential operations |
| topic | Interval-valued intuitionistic fuzzy set (IVIFS) Interval-valued intuitionistic fuzzy function (IVIFF) Limit Continuity Derivative Differential |
| url | https://www.atlantis-press.com/article/25868678/view |
| work_keys_str_mv | AT huazhao intervalvaluedintuitionisticfuzzyderivativeanddifferentialoperations AT zeshuixu intervalvaluedintuitionisticfuzzyderivativeanddifferentialoperations AT zeqingyao intervalvaluedintuitionisticfuzzyderivativeanddifferentialoperations |