A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems
The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for...
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| Published in | Computers & mathematics with applications (1987) Vol. 60; no. 6; pp. 1557 - 1570 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2010
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| Subjects | |
| Online Access | Get full text |
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| Abstract | The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example. |
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| AbstractList | The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example. |
| Author | Li, Deng-Feng |
| Author_xml | – sequence: 1 givenname: Deng-Feng surname: Li fullname: Li, Deng-Feng email: lidengfeng65@hotmail.com, dengfengli@sina.com organization: School of Management, Fuzhou University, No. 2, Xueyuan Road, Daxue New District, Fuzhou District, Fuzhou, Fujian 350108, China |
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| Snippet | The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult... |
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| SubjectTerms | Ambiguity Decision making Fuzzy set Fuzzy systems Intuitionistic fuzzy number Mathematical analysis Mathematical models Methodology Preference modeling Ranking Ratings Uncertainty |
| Title | A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems |
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