Superiority-comparison-based transformation, consensus, and ranking methods for heterogeneous multi-attribute group decision-making.

• The paper explores a new family of methods for heterogeneous MAGDM. • Diversified opinions are unified into random values to retain structural feature. • The SPM is developed to measure the superiority probability between alternatives. • Probabilistic rank is introduced to fit with heterogeneous decision environment. Heterogeneous multi-attribute group decision making (heterogeneous MAGDM) is a hot topic in complicated decision-making environment. This paper proposes a new approach for heterogeneous MAGDM problems, including three main research points. Firstly, different from the commonly used unified transformation process, the study provides a randomization method to transform heterogeneous opinions into random values, which can keep the structural features of the original data as much as possible. Secondly, the random values are integrated into superiority-probability-based pairwise comparison matrix (SPM) by combining stochastic simulation and multi-attribute decision making methods. Then, a maximization-similarity-based consensus approach is developed to obtain the collective SPM. The collective SPM can not only objectively present the superiority relationship between any two alternatives, but also balance the opinions of multiple experts. Thirdly, a new type of ranking, probabilistic rank order, is proposed, which is more consistent with the heterogeneous and uncertain characteristics of the decision-making opinions. At last, an example regarding missile weapon system selection is chosen from previous studies to illustrate the validity of the proposed methods. Another example about the predictive evaluation of city development potential is constructed to further illustrate the practical application prospects of the research methods. [ABSTRACT FROM AUTHOR]