Fuzzy Number Addition with the Application of Horizontal Membership Functions
The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/367214 |
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| _version_ | 1832562150021791744 |
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| author | Andrzej Piegat Marcin Pluciński |
| author_facet | Andrzej Piegat Marcin Pluciński |
| author_sort | Andrzej Piegat |
| collection | DOAJ |
| description | The paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods use α-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs. |
| format | Article |
| id | doaj-art-2f659b8365f24cc79634f3953e5f76c8 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-2f659b8365f24cc79634f3953e5f76c82025-02-03T01:23:19ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/367214367214Fuzzy Number Addition with the Application of Horizontal Membership FunctionsAndrzej Piegat0Marcin Pluciński1Faculty of Computer Science and Information Systems, West Pomeranian University of Technology, Żołnierska 49, 71-210 Szczecin, PolandFaculty of Computer Science and Information Systems, West Pomeranian University of Technology, Żołnierska 49, 71-210 Szczecin, PolandThe paper presents addition of fuzzy numbers realised with the application of the multidimensional RDM arithmetic and horizontal membership functions (MFs). Fuzzy arithmetic (FA) is a very difficult task because operations should be performed here on multidimensional information granules. Instead, a lot of FA methods use α-cuts in connection with 1-dimensional classical interval arithmetic that operates not on multidimensional granules but on 1-dimensional intervals. Such approach causes difficulties in calculations and is a reason for arithmetical paradoxes. The multidimensional approach allows for removing drawbacks and weaknesses of FA. It is possible thanks to the application of horizontal membership functions which considerably facilitate calculations because now uncertain values can be inserted directly into equations without using the extension principle. The paper shows how the addition operation can be realised on independent fuzzy numbers and on partly or fully dependent fuzzy numbers with taking into account the order relation and how to solve equations, which can be a difficult task for 1-dimensional FAs.http://dx.doi.org/10.1155/2015/367214 |
| spellingShingle | Andrzej Piegat Marcin Pluciński Fuzzy Number Addition with the Application of Horizontal Membership Functions The Scientific World Journal |
| title | Fuzzy Number Addition with the Application of Horizontal Membership Functions |
| title_full | Fuzzy Number Addition with the Application of Horizontal Membership Functions |
| title_fullStr | Fuzzy Number Addition with the Application of Horizontal Membership Functions |
| title_full_unstemmed | Fuzzy Number Addition with the Application of Horizontal Membership Functions |
| title_short | Fuzzy Number Addition with the Application of Horizontal Membership Functions |
| title_sort | fuzzy number addition with the application of horizontal membership functions |
| url | http://dx.doi.org/10.1155/2015/367214 |
| work_keys_str_mv | AT andrzejpiegat fuzzynumberadditionwiththeapplicationofhorizontalmembershipfunctions AT marcinplucinski fuzzynumberadditionwiththeapplicationofhorizontalmembershipfunctions |