Intuitionistic Type-2 Fuzzy Set and Its Properties
Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of im...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/6/808 |
| _version_ | 1798038089352871936 |
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| author | Surajit Dan Mohuya B. Kar Saibal Majumder Bikashkoli Roy Samarjit Kar Dragan Pamucar |
| author_facet | Surajit Dan Mohuya B. Kar Saibal Majumder Bikashkoli Roy Samarjit Kar Dragan Pamucar |
| author_sort | Surajit Dan |
| collection | DOAJ |
| description | Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of imprecision that necessitates different approaches for making a proper and legitimate decision. In this article, we propose the concept of the intuitionistic type-2 fuzzy set (IT2FS). Several arithmetic operations on IT2FS such as union, intersection, complement, containment, etc., are defined, and the related algebraic properties of IT2FS are also studied. Subsequently, we define two new operators, namely the necessity operator and the possibility operator, to convert an IT2FS into an ordinary T2FS, and then discuss some of their basic properties. Moreover, in this study, two distance measures, the Hamming distance and Euclidian distance of IT2FS, are proposed, and their applications are illustrated with an example. |
| first_indexed | 2024-04-11T21:35:27Z |
| format | Article |
| id | doaj.art-10ee074b43e5425fa329cce19ccb2539 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T21:35:27Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-10ee074b43e5425fa329cce19ccb25392022-12-22T04:01:46ZengMDPI AGSymmetry2073-89942019-06-0111680810.3390/sym11060808sym11060808Intuitionistic Type-2 Fuzzy Set and Its PropertiesSurajit Dan0Mohuya B. Kar1Saibal Majumder2Bikashkoli Roy3Samarjit Kar4Dragan Pamucar5Department of Master of Computer Application, Regent Education and Research Foundation, Kolkata 700121, IndiaDepartment of Computer Science, Heritage Institute of Technology, Kolkata 700107, IndiaDepartment of Computer Science and Engineering, National Institute of Technology Durgapur, Durgapur 713209, IndiaDepartment of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, IndiaDepartment of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, IndiaDepartment of Logistics, University of Defence in Belgrade Military Academy, 11000 Belgrade, SerbiaDecision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of imprecision that necessitates different approaches for making a proper and legitimate decision. In this article, we propose the concept of the intuitionistic type-2 fuzzy set (IT2FS). Several arithmetic operations on IT2FS such as union, intersection, complement, containment, etc., are defined, and the related algebraic properties of IT2FS are also studied. Subsequently, we define two new operators, namely the necessity operator and the possibility operator, to convert an IT2FS into an ordinary T2FS, and then discuss some of their basic properties. Moreover, in this study, two distance measures, the Hamming distance and Euclidian distance of IT2FS, are proposed, and their applications are illustrated with an example.https://www.mdpi.com/2073-8994/11/6/808type-2 fuzzy setintuitionistic type-2 fuzzy setpossibility and necessity operatorsdistance measure |
| spellingShingle | Surajit Dan Mohuya B. Kar Saibal Majumder Bikashkoli Roy Samarjit Kar Dragan Pamucar Intuitionistic Type-2 Fuzzy Set and Its Properties Symmetry type-2 fuzzy set intuitionistic type-2 fuzzy set possibility and necessity operators distance measure |
| title | Intuitionistic Type-2 Fuzzy Set and Its Properties |
| title_full | Intuitionistic Type-2 Fuzzy Set and Its Properties |
| title_fullStr | Intuitionistic Type-2 Fuzzy Set and Its Properties |
| title_full_unstemmed | Intuitionistic Type-2 Fuzzy Set and Its Properties |
| title_short | Intuitionistic Type-2 Fuzzy Set and Its Properties |
| title_sort | intuitionistic type 2 fuzzy set and its properties |
| topic | type-2 fuzzy set intuitionistic type-2 fuzzy set possibility and necessity operators distance measure |
| url | https://www.mdpi.com/2073-8994/11/6/808 |
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