Implicit and hybrid methods for attribute weighting in multi-attribute decision-making: a review study

Attribute weighting is a task of paramount relevance in multi-attribute decision-making (MADM). Over the years, different approaches have been developed to face this problem. Despite the effort of the community, there is a lack of consensus on which method is the most suitable one for a given problem instance. This paper is the second part of a two-part survey on attribute weighting methods in MADM scenarios. The first part introduced a categorization in five classes while focusing on explicit weighting methods. The current paper addresses implicit and hybrid approaches. A total of 20 methods are analyzed in order to identify their strengths and limitations. Toward the end, we discuss possible alternatives to address the detected drawbacks, thus paving the road for further research directions. The implicit weighting with additional information category resulted in the most coherent approach to give effective solutions. Consequently, we encourage the development of future methods with additional preference information.