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A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. (English) Zbl 1202.91054
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.

MSC:
91B06 Decision theory
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
62C86 Statistical decision theory and fuzziness
90B50 Management decision making, including multiple objectives
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