The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems
Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/459508 |
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| _version_ | 1832562836466827264 |
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| author | Shan Zhao Hongxing Li |
| author_facet | Shan Zhao Hongxing Li |
| author_sort | Shan Zhao |
| collection | DOAJ |
| description | Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings
by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an
algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First,
we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in
accordance with different input subdomains under certain conditions. And then different techniques are discussed
to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation
equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that
of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning
relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be
obtained as the special case of the proposed algorithm. |
| format | Article |
| id | doaj-art-b88a8da037e64c83a829990e57233ccd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b88a8da037e64c83a829990e57233ccd2025-02-03T01:21:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/459508459508The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic SystemsShan Zhao0Hongxing Li1School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, ChinaSchool of Control Science and Engineering, Dalian University of Technology, Dalian 116024, ChinaType-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.http://dx.doi.org/10.1155/2014/459508 |
| spellingShingle | Shan Zhao Hongxing Li The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems Journal of Applied Mathematics |
| title | The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems |
| title_full | The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems |
| title_fullStr | The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems |
| title_full_unstemmed | The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems |
| title_short | The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems |
| title_sort | construction of type 2 fuzzy reasoning relations for type 2 fuzzy logic systems |
| url | http://dx.doi.org/10.1155/2014/459508 |
| work_keys_str_mv | AT shanzhao theconstructionoftype2fuzzyreasoningrelationsfortype2fuzzylogicsystems AT hongxingli theconstructionoftype2fuzzyreasoningrelationsfortype2fuzzylogicsystems AT shanzhao constructionoftype2fuzzyreasoningrelationsfortype2fuzzylogicsystems AT hongxingli constructionoftype2fuzzyreasoningrelationsfortype2fuzzylogicsystems |