Normal distribution interval numbers-based multiple attribute decision-making with unknown attribute weights

Abstract

With the rapid development of the society, decision-making methods with single attribute are becoming increasingly difficult to satisfy the needs of practical problems. And in real life, it is usually only possible to obtain the range of attribute values because of the measurement error or the complexity and uncertainty of objective things, that is, the interval number values of decision information are easily obtainable. Interval number multi-attribute decision-making problems have gradually become a research hotspot for scholars. However, most current studies have not discussed the distribution on interval numbers, resulting in partial loss of decision information. Therefore, this paper considers the case of normal distribution interval numbers (NDINs) and proposes a multi-attribute decision-making method based on symmetric relative entropy with completely unknown attribute weights. Firstly, based on the idea of maximal deviation, a model for determining attribute weights is established by the symmetric relative entropy of NDINs. Secondly, the possibility degree formula for comparison between two NDINs is used to determine the positive ideal solution (PIS) and negative ideal solution (NIS) under each attribute. Thirdly, the total closeness degree between each scheme and the ideal point is calculated using the TOPSIS method and symmetric relative entropy. Then, the ranking of schemes is obtained based on the total closeness degree. Finally, a numerical example is offered to prove the feasibility and validity of the proposed method.