Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty
It is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately,...
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| Format: | Article |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2361 |
| _version_ | 1797442720744079360 |
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| author | Vladik Kreinovich Olga Kosheleva Patricia Melin Oscar Castillo |
| author_facet | Vladik Kreinovich Olga Kosheleva Patricia Melin Oscar Castillo |
| author_sort | Vladik Kreinovich |
| collection | DOAJ |
| description | It is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher-order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty to come up with a new algorithm for the type-3 case. |
| first_indexed | 2024-03-09T12:46:04Z |
| format | Article |
| id | doaj.art-a6ef5785ed8248a7b0807a5617b3a396 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:46:04Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a6ef5785ed8248a7b0807a5617b3a3962023-11-30T22:12:30ZengMDPI AGMathematics2227-73902022-07-011013236110.3390/math10132361Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy UncertaintyVladik Kreinovich0Olga Kosheleva1Patricia Melin2Oscar Castillo3Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USADepartment of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USADivision of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, MexicoDivision of Graduate Studies and Research, Tijuana Institute of Technology, Tomas Aquino, Tijuana 22685, Baja California, MexicoIt is known that, to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher-order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher-order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty to come up with a new algorithm for the type-3 case.https://www.mdpi.com/2227-7390/10/13/2361fuzzy techniquestype-2 fuzzy setstype-3 fuzzy setsdata processingZadeh’s extension principleefficient algorithms |
| spellingShingle | Vladik Kreinovich Olga Kosheleva Patricia Melin Oscar Castillo Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty Mathematics fuzzy techniques type-2 fuzzy sets type-3 fuzzy sets data processing Zadeh’s extension principle efficient algorithms |
| title | Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty |
| title_full | Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty |
| title_fullStr | Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty |
| title_full_unstemmed | Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty |
| title_short | Efficient Algorithms for Data Processing under Type-3 (and Higher) Fuzzy Uncertainty |
| title_sort | efficient algorithms for data processing under type 3 and higher fuzzy uncertainty |
| topic | fuzzy techniques type-2 fuzzy sets type-3 fuzzy sets data processing Zadeh’s extension principle efficient algorithms |
| url | https://www.mdpi.com/2227-7390/10/13/2361 |
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