Abstract
•The general scheme of multicriteria decision making under uncertainty is discussed.•The possibilistic approach produces robust solutions to multiobjective problems.•An approach to quantitative and qualitative information fusion is proposed.•The results are applied to multiobjective allocation of resources or their shortages.•An approach to the homogeneous formulation of allocation objectives is proposed.
This study is concerned with a multiobjective allocation of resources (or their shortages), delivering an answer to the fundamental question “How to do?” arising in different types of planning activities (strategic, innovation, new business, research and development, expansion, operational, maintenance, etc. planning). The solution to the problem is associated with the extension of the general scheme of multicriteria decision making under uncertainty. This scheme is based on a possibilistic approach and involves a fuzzy set-based generalization of the classic approach to deal with the uncertainty to produce solutions, including robust solutions, in multicriteria analysis. Its usage, in the original form, helps one to use available quantitative information to the highest extent to reduce the decision uncertainty regions. If the quantitative information does not lead to a unique solution, the scheme presumes the application of information of qualitative character (based on knowledge, experience, and intuition of experts) used at the final decision stage. However, increasingly, we encounter problems whose essence requires the consideration of the objectives (investment attractiveness, political effect, maintenance flexibility, etc.) formed on the basis of qualitative information, at all decision process stages. Considering this, the study is aimed at generating multicriteria solutions, including multicriteria robust solutions, by constructing representative combinations of initial data, states of nature or scenarios with direct using qualitative information (with the possibility for experts to apply diverse preference formats processed by transformation functions) presented along with quantitative information, realizing a process of information fusion within the multiobjective models. The corresponding results are of a universal character and applicable to diverse classes of multiobjective problems. The paper also proposes a new approach to the homogeneous and expert-acceptable formulation of specific allocation objectives. Examples are presented to illustrate the study results.