A study on fundamentals of refined intuitionistic fuzzy set with some properties
Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and...
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Ayandegan Institute of Higher Education,
2020
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/1a96d2b494d74d06b2fb9d11b892547c |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:1a96d2b494d74d06b2fb9d11b892547c |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:1a96d2b494d74d06b2fb9d11b892547c2021-11-13T08:42:02ZA study on fundamentals of refined intuitionistic fuzzy set with some properties2783-14422717-345310.22105/jfea.2020.261946.1067https://doaj.org/article/1a96d2b494d74d06b2fb9d11b892547c2020-12-01T00:00:00Zhttp://www.journal-fea.com/article_120762_fbb95382675187e2d4cae7c799ea5348.pdfhttps://doaj.org/toc/2783-1442https://doaj.org/toc/2717-3453Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding.Atiqe RahmanMuhammad AhmadMuhammad SaeedMuhammad AhsanMuhammad ArshadMuhammad IhsanAyandegan Institute of Higher Education,articlefuzzy setintuitionistic fuzzy setrefined intuitionistic fuzzy setMathematicsQA1-939ENJournal of Fuzzy Extension and Applications, Vol 1, Iss 4, Pp 279-292 (2020) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
fuzzy set intuitionistic fuzzy set refined intuitionistic fuzzy set Mathematics QA1-939 |
| spellingShingle |
fuzzy set intuitionistic fuzzy set refined intuitionistic fuzzy set Mathematics QA1-939 Atiqe Rahman Muhammad Ahmad Muhammad Saeed Muhammad Ahsan Muhammad Arshad Muhammad Ihsan A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| description |
Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding. |
| format |
article |
| author |
Atiqe Rahman Muhammad Ahmad Muhammad Saeed Muhammad Ahsan Muhammad Arshad Muhammad Ihsan |
| author_facet |
Atiqe Rahman Muhammad Ahmad Muhammad Saeed Muhammad Ahsan Muhammad Arshad Muhammad Ihsan |
| author_sort |
Atiqe Rahman |
| title |
A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| title_short |
A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| title_full |
A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| title_fullStr |
A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| title_full_unstemmed |
A study on fundamentals of refined intuitionistic fuzzy set with some properties |
| title_sort |
study on fundamentals of refined intuitionistic fuzzy set with some properties |
| publisher |
Ayandegan Institute of Higher Education, |
| publishDate |
2020 |
| url |
https://doaj.org/article/1a96d2b494d74d06b2fb9d11b892547c |
| work_keys_str_mv |
AT atiqerahman astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadahmad astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadsaeed astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadahsan astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadarshad astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadihsan astudyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT atiqerahman studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadahmad studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadsaeed studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadahsan studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadarshad studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties AT muhammadihsan studyonfundamentalsofrefinedintuitionisticfuzzysetwithsomeproperties |
| _version_ |
1718430239998083072 |