Reward-Penalty Assignments and Genetic Algorithms for Ordinal Interval Number Group Decision Making

Abstract

Ordinal interval number group decision making GDM is implemented using the closed interval preferences provided by the decision makers DMs for the potential courses of action. Two reward-penalty assignments RPAs are introduced, which express the compatibility between the ordinal intervals provided by the DMs in a purely binary and a fully graded manner, respectively. Genetic algorithms are employed for establishing a collectively preferred ranking, with chromosome-validity-enforcing crossover and gene-swapping mutation being appropriately combined for efficient convergence. The effect that the consensus function, as derived from two RPAs, has on the fitness landscape and, consequently, on the preferred courses of action is illustrated in a number of GDM problems derived from the relevant literature covering a complete and incomplete problems, b perturbations of the relative importance values assigned to the DMs, c full and partial preferences, and d increasing numbers of DMs and/or available courses of action scaling potential.