Combinatorial design of the MAUT and PAMSSEM II methods for multiple attributes group decision making with probabilistic linguistic information

Abstract

This paper considers the application of Probabilistic Linguistic Term Sets (PLTS) in Multiple Attribute Group Decision Making (MAGDM) when the weights cannot be determined. Firstly, as an improvement of PROMETHEE, the PAMSSEM method has substantial advantages in handling mixed data and missing data. It can not only make use of the preference threshold as well as the irrelevant threshold to express the preference degree of the decision-maker (DM) but likewise express the compensation limit that DM is willing to accept through the rejection threshold. Simultaneously, the MAUT method cleverly employs the marginal utility function to redistribute the evaluation values under the same attribute within a fixed interval, making the decision matrix standard and reliable. To comprehensively utilize the advantages of these two methods, we integrated the PAMSSEM II and MAUT methods in the probabilistic linguistic environment to form the PL-MAUT-PAMSSEM II method followed by applying it to the problem of inbound tourism destination selection. Secondly, in the process of data processing, an equivalent conversion function will be used to convert the PLTS and the probabilistic hesitant fuzzy set (HPFS) to each other to make the calculation between the matrices feasible and use the entropy method to calculate the weights to ensure the decision-making process. Finally, taking the sample deviation value as the inspection standards, the big data analysis compared with other methods is carried out through a large number of sample examples to scientifically validate the superiority of the newly proposed method.