The Hierarchical and Stochastic VIKOR to Deal with Imprecise and Missing Information

A great majority of the Multiple Criteria Decision Aiding methods assume that all assessment criteria are considered at the same hierarchical level. However, decision problem often configure hierarchy among criteria with different structures configurations. Another difficulty of real decision problems, is the frequently questioned subjectivity of elicitation of preference information. These challenges have been highly discussed in the literature, but not duly addressed when they to come to VIKOR (Multi-criteria Optimization and Compromise Solution) method.Therefore, this paper proposes a new VIKOR-HSMAA method to deal simultaneously with indirect elicitation and hierarchy of criteria. A variant of the Multiple Criteria Hierarchy Process (MCHP) is integrated to VIKOR to consider multiple levels for the decision criteria. The Stochastic Multicriteria Acceptability Analysis (SMAA) is considered for the indirect elicitation, allowing a robust weight analyses and priority decision. The conditions of solution acceptance of VIKOR are adapted as SMAA new descriptive measures. The novelty of the whole methodology consists of a joint consideration of hierarchical assessments of alternatives performances for hierarchical criteria, considering imprecise criteria weights and analysis of compromise solution resulting from VIKOR method.An example regarding the assessment of Sustainability, Economic, Environmental and Social dimensions of Brazilian states shows the method application. The VIKOR-HSMAA provided information at the Sustainability level with the state of Santa Catarina (SC) as the most sustainable. Considering each macro-criteria, SC is the first in the Economic dimension, Roraima and Distrito Federal (DF) are the first in the Environmental rank and DF and SC are the first in the Social rank. By enabling the consideration of missing or imprecisedata, the VIKOR-HSMAA method proves to be a robust tool to reduce subjectivity in decision-making, providing a reliable support system for the assessment of institutions and governments