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Application of interval-valued intuitionistic fuzzy \(R\)-norm entropy in multiple attribute decision making. (English) Zbl 1412.90067

Summary: The theory of interval-valued intuitionistic fuzzy sets (IVIFSs) is well suitable to deal with the vagueness and hesitancy. In the present communication, we have considered an interval-valued intuitionistic fuzzy (IVIF) \(R\)-norm entropy with both uncertainty and hesitancy degrees expressed in terms of IVIFS. Using this IVIF R-norm entropy, we have solved a multiple attribute decision making (MADM) problem in which attribute values are expressed as IVIFSs. In MADM problem, we mainly encounter with two types of problems. First is when we don’t have any information regarding attribute weights and second is when we have little information about attribute weights, i.e., they are partially known to us. In this paper, we have considered both the cases with examples. For the first case, we have used an extension of entropy weight method to calculate the attribute weights and in second case attribute weights are calculated by using the minimum entropy principle method which is based on solving a linear programming model. The two methods are effectively explained by taking real life examples.

MSC:

90B50 Management decision making, including multiple objectives
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