The aim of this paper is to develop a simulated annealing-based permutation method for multiple criteria decision analysis within the environment of interval type-2 fuzzy sets. The outranking methodology constitutes one of the most fruitful approaches in multiple criteria decision making and has been applied in numerous real-world problems. The permutation method is a classical outranking model, which generalizes Jacquet–Lagreze's permutation method and is based on a pairwise criterion comparison of the alternatives. Because modeling of the uncertainty in the decision-making process becomes increasingly important, an extension to the interval type-2 fuzzy environment is a useful generalization of the permutation method and is appropriate for handling uncertain and imprecise information in practical decision-making situations. This paper produces a signed-distance-based comparison among the comprehensive rankings of alternatives for concordance and discordance analyses. An integrated nonlinear programming model is constructed for estimation of the criterion weights and the optimal ranking order of the alternatives under incomplete preference information. To enhance the implementation efficiency, a simulated annealing-based permutation method and its meta-heuristic algorithm are developed to produce a polynomial time solution for the total completion time problem. Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result. 
A simulated annealing-based permutation method and experimental analysis for multiple criteria decision analysis with interval type-2 fuzzy sets