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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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2010-09, Vol.60 (6), p.1557-1570
Main Author: Li, Deng-Feng
Format: Article
Language:English
Subjects:
Ambiguity
Decision making
Fuzzy set
Fuzzy systems
Intuitionistic fuzzy number
Mathematical analysis
Mathematical models
Methodology
Preference modeling
Ranking
Ratings
Uncertainty
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.06.039