Interval-valued fuzzy permutation method and experimental analysis on cardinal and ordinal evaluations

This paper presents interval-valued fuzzy permutation (IVFP) methods for solving multiattribute decision making problems based on interval-valued fuzzy sets. First, we evaluate alternatives according to the achievement levels of attributes, which admits cardinal or ordinal representation. The relative importance of each attribute can also be measured by interval or scalar data. Next, we identify the concordance, midrange concordance, weak concordance, discordance, midrange discordance and weak discordance sets for each ordering. The proposed method consists of testing each possible ranking of the alternatives against all others. The evaluation value of each permutation can be computed either by cardinal weights or by solving programming problems. Then, we choose the permutation with the maximum evaluation value, and the optimal ranking order of alternatives can be obtained. An experimental analysis of IVFP rankings given cardinal and ordinal evaluations is conducted with discussions on consistency rates, contradiction rates, inversion rates, and average Spearman correlation coefficients.