Experimental analysis on objective weights with intuitionistic fuzzy entropy measures in multi-attribute decision problems

In the multiple attribute decision making (MADM) problem, it is crucial to properly assess the weights of attribute because the changes in the attribute weights would affect the ranking of alternatives. In addition, although the intuitionistic fuzzy (IF) set is widely extended to MADM problems, it turns out that the data and decision matrix get more complex and uncertain. Therefore, it is important to pay much attention to the credibility of data itself. However, there is little investigation on MADM with the credibility of data being explicitly taken into account. In this research, we propose a new objective weighting method by using IF entropy measures for MADM under the intuitionistic fuzzy environment. In terms of the nature of IF entropy, the attribute weights are assessed by the credibility of data. Moreover, several IF entropy measures are used and examined to figure out the difference between them with a series of simulation experiments. Four indices are employed to compare the ranking results by objective weights, including the contradiction rate, the inversion rate, the consistency rate and Spearman correlation coefficients. The experimental results indicate that different IF entropy measures would cause a totally different ranking result for attributes. In addition, when the numbers of alternative and attributes become large, the difference between rankings of attributes expands gradually.