Decision aid system founded on nonlinear valuation, dispersion-based weighting and correlative aggregation for wire rope selection in slope stability cable nets

• A decision aid system to address hierarchical decision-making problems is developed.
• Levels of satisfaction are valuated using the Beta Cumulative Distribution Function.
• Subcriteria are weighted based on their variability using measures of dispersion.
• Dependencies between subcriteria are quantified through correlation coefficients.
• The system is applied to the selection of wire rope in slope stability cable nets.

This paper presents a decision aid system to address hierarchically structured decision-making problems based on the determination of the satisfaction provided by a group of alternatives in relation to multiple conflicting subcriteria grouped into criteria. The system combines the action of three new methods related to the following concepts: nonlinear valuation, dispersion-based weighting and correlative aggregation. The first includes five value functions that allow the conversion of the ratings of the alternatives regarding the subcriteria into the satisfaction they produce in a versatile and simple manner through the Beta Cumulative Distribution Function. The use of measures of dispersion to weight the subcriteria by giving more importance to those factors that can make a difference due to their heterogeneity is revised to validate it when the values are not normally distributed. Dependencies between subcriteria are taken into account through the determination of their correlation coefficients, whose incorporation adjusts the results provided by the system to favour those alternatives having a balanced behaviour with respect to conflicting aspects. The overall satisfaction provided by each alternative is determined using a prioritisation operator to avoid compensation between criteria when aggregating the subcriteria. The system was tested through a novel field of application such as the selection of wire rope to form slope stability cable nets.