Surrogate relaxation of a fuzzy multidimensional 0–1 knapsack model by surrogate constraint normalization rules and a methodology for multi-attribute project portfolio selection

Abstract

In this paper, a multidimensional 0–1 knapsack model with fuzzy parameters is defuzzified using triangular norm (t-norm) and t-conorm fuzzy relations. In the first part of the paper, the surrogate relaxation models of the defuzzified models are developed, and the use of surrogate constraint normalization rules is proposed as the surrogate multipliers. A methodology is proposed to evaluate some surrogate constraint normalization rules proposed in the literature as well as one rule proposed in this paper. Three distance metrics are used to find the distance of fuzzy objective function from the surrogate models to the distance of fuzzy objective function from the original models. A numerical experiment shows that the rule proposed in this paper dominates the other rules considered in this paper for three distance metrics given the whole assumptions. In the second part of the paper, a methodology is proposed for multi-attribute project portfolio selection, and optimal solutions from the original defuzzified models as well as near-optimal solutions from their surrogate relaxation models are considered as alternatives. The aggregation of evaluation results is managed using a simple yet effective method so-called fuzzy Simple Additive Weighting (SAW) method. Then, the methodology is applied to a hypothetical construction project portfolio selection problem with multiple attributes.