The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions
In this paper we have frstly defned a metric in intuitionistic fuzzy environment and studied its properties.Then we have proved that the metric spaceof fuzzy number valued functions is complete under this metric. We havestudied the concept of Aumann integration for intuitionistic fuzzy numbervalued...
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| Format: | Article |
| Language: | English |
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Kyrgyz Turkish Manas University
2018-12-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/604856 |
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| author | Ömer Akın Selami Bayeğ |
| author_facet | Ömer Akın Selami Bayeğ |
| author_sort | Ömer Akın |
| collection | DOAJ |
| description | In this paper we have frstly defned a metric in intuitionistic fuzzy environment and studied its properties.Then we have proved that the metric spaceof fuzzy number valued functions is complete under this metric. We havestudied the concept of Aumann integration for intuitionistic fuzzy numbervalued functions in terms of α and β cuts. We have given the relationbetween Hukuhara derivative and Aumann integral for intuitionistic fuzzyvalued functions by using the fundamental theorem of calculus. |
| format | Article |
| id | doaj-art-0d5e2c28bb90443ba1c5797d2d9b34a0 |
| institution | OA Journals |
| issn | 1694-7398 |
| language | English |
| publishDate | 2018-12-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-0d5e2c28bb90443ba1c5797d2d9b34a02025-08-20T02:03:04ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982018-12-01621431631437The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functionsÖmer Akın0Selami Bayeğ1Department of Mathematics, TOBB University of Economics and Technology, Ankara, Turkey Kyrgyz – Turkish Manas University, Faculty of Science, Department of Applied Mathematics and Informatics, Bishkek, KyrgyzstanDepartment of Mathematics, TOBB University of Economics and Technology, Ankara, TurkeyIn this paper we have frstly defned a metric in intuitionistic fuzzy environment and studied its properties.Then we have proved that the metric spaceof fuzzy number valued functions is complete under this metric. We havestudied the concept of Aumann integration for intuitionistic fuzzy numbervalued functions in terms of α and β cuts. We have given the relationbetween Hukuhara derivative and Aumann integral for intuitionistic fuzzyvalued functions by using the fundamental theorem of calculus.https://dergipark.org.tr/en/download/article-file/604856intuitionistic fuzzy setsintuitionistic fuzzy valued functionshukuhara differentiabilityaumann integralintuitionistic hausdorff metric |
| spellingShingle | Ömer Akın Selami Bayeğ The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions MANAS: Journal of Engineering intuitionistic fuzzy sets intuitionistic fuzzy valued functions hukuhara differentiability aumann integral intuitionistic hausdorff metric |
| title | The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions |
| title_full | The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions |
| title_fullStr | The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions |
| title_full_unstemmed | The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions |
| title_short | The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions |
| title_sort | concept of hukuhara derivative and aumann integrals for intuitionistic fuzzy number valued functions |
| topic | intuitionistic fuzzy sets intuitionistic fuzzy valued functions hukuhara differentiability aumann integral intuitionistic hausdorff metric |
| url | https://dergipark.org.tr/en/download/article-file/604856 |
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