Fuzzy Interpolation with Extensional Fuzzy Numbers
The article develops further directions stemming from the arithmetic of extensional fuzzy numbers. It presents the existing knowledge of the relationship between the arithmetic and the proposed orderings of extensional fuzzy numbers—so-called <inline-formula><math xmlns="http://www.w3....
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/170 |
| _version_ | 1797408388666097664 |
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| author | Michal Holčapek Nicole Škorupová Martin Štěpnička |
| author_facet | Michal Holčapek Nicole Škorupová Martin Štěpnička |
| author_sort | Michal Holčapek |
| collection | DOAJ |
| description | The article develops further directions stemming from the arithmetic of extensional fuzzy numbers. It presents the existing knowledge of the relationship between the arithmetic and the proposed orderings of extensional fuzzy numbers—so-called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-orderings—and investigates distinct properties of such orderings. The desirable investigation of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-orderings of extensional fuzzy numbers is directly used in the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-function—a natural extension of the notion of a function that, in its arguments as well as results, uses extensional fuzzy numbers. One of the immediate subsequent applications is fuzzy interpolation. The article provides readers with the basic fuzzy interpolation method, investigation of its properties and an illustrative experimental example on real data. The goal of the paper is, however, much deeper than presenting a single fuzzy interpolation method. It determines direction to a wide variety of fuzzy interpolation as well as other analytical methods stemming from the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-function and from the arithmetic of extensional fuzzy numbers in general. |
| first_indexed | 2024-03-09T03:58:43Z |
| format | Article |
| id | doaj.art-a57f33df0ccf474fbb47780d01502901 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:58:43Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a57f33df0ccf474fbb47780d015029012023-12-03T14:17:03ZengMDPI AGSymmetry2073-89942021-01-0113217010.3390/sym13020170Fuzzy Interpolation with Extensional Fuzzy NumbersMichal Holčapek0Nicole Škorupová1Martin Štěpnička2CE IT4Innovations–IRAFM, University of Ostrava, 70103 Ostrava, Czech RepublicCE IT4Innovations–IRAFM, University of Ostrava, 70103 Ostrava, Czech RepublicCE IT4Innovations–IRAFM, University of Ostrava, 70103 Ostrava, Czech RepublicThe article develops further directions stemming from the arithmetic of extensional fuzzy numbers. It presents the existing knowledge of the relationship between the arithmetic and the proposed orderings of extensional fuzzy numbers—so-called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-orderings—and investigates distinct properties of such orderings. The desirable investigation of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-orderings of extensional fuzzy numbers is directly used in the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-function—a natural extension of the notion of a function that, in its arguments as well as results, uses extensional fuzzy numbers. One of the immediate subsequent applications is fuzzy interpolation. The article provides readers with the basic fuzzy interpolation method, investigation of its properties and an illustrative experimental example on real data. The goal of the paper is, however, much deeper than presenting a single fuzzy interpolation method. It determines direction to a wide variety of fuzzy interpolation as well as other analytical methods stemming from the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>-function and from the arithmetic of extensional fuzzy numbers in general.https://www.mdpi.com/2073-8994/13/2/170extensional fuzzy numbersMI-algebrassimilarityarithmetics of fuzzy numbersorderingsfuzzy interpolation |
| spellingShingle | Michal Holčapek Nicole Škorupová Martin Štěpnička Fuzzy Interpolation with Extensional Fuzzy Numbers Symmetry extensional fuzzy numbers MI-algebras similarity arithmetics of fuzzy numbers orderings fuzzy interpolation |
| title | Fuzzy Interpolation with Extensional Fuzzy Numbers |
| title_full | Fuzzy Interpolation with Extensional Fuzzy Numbers |
| title_fullStr | Fuzzy Interpolation with Extensional Fuzzy Numbers |
| title_full_unstemmed | Fuzzy Interpolation with Extensional Fuzzy Numbers |
| title_short | Fuzzy Interpolation with Extensional Fuzzy Numbers |
| title_sort | fuzzy interpolation with extensional fuzzy numbers |
| topic | extensional fuzzy numbers MI-algebras similarity arithmetics of fuzzy numbers orderings fuzzy interpolation |
| url | https://www.mdpi.com/2073-8994/13/2/170 |
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