The interval-valued fuzzy TOPSIS method and experimental analysis

The purpose of this paper is to extend the TOPSIS method based on interval-valued fuzzy sets in decision analysis. Hwang and Yoon developed the technique for order preference by similarity to ideal solution (TOPSIS) in 1981. TOPSIS has been widely used to rank the preference order of alternatives and determine the optimal choice. Considering the fact that it is difficult to precisely attach the numerical measures to the relative importance of the attributes and to the impacts of the alternatives on these attributes in some cases, therefore, the TOPSIS method has been extended for interval-valued fuzzy data in this paper. In addition, a comprehensive experimental analysis to observe the interval-valued fuzzy TOPSIS results yielded by different distance measures is presented. A comparative analysis of interval-valued fuzzy TOPSIS rankings from each distance measure is illustrated with discussions on consistency rates, contradiction rates, and average Spearman correlation coefficients. Finally, a second-order regression model is provided to highlight the effects of the number of alternatives, the number of attributes, and distance measures on average Spearmen correlation coefficients.