In multiple criteria decision making (MCDM) with interval-valued belief distributions (IVBDs), individual IVBDs on multiple criteria are combined explicitly or implicitly to generate the expected utilities of alternatives, which can be used to make decisions with the aid of decision rules. To analyze an MCDM problem with a large number of criteria and grades used to profile IVBDs, effective algorithms are required to find the solutions to the optimization models within a large feasible region. An important issue is to identify an algorithm suitable for finding accurate solutions within a limited or acceptable time. To address this issue, four representative evolutionary algorithms, including genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and gravitational search algorithm, are selected to combine individual IVBDs of alternatives and generate the minimum and maximum expected utilities of alternatives. By performing experiments with different numbers of criteria and grades, a comparative analysis of the four algorithms is provided with the aid of two indicators: accuracy and efficiency. Experimental results indicate that particle swarm optimization algorithm is the best among the four algorithms for combining individual IVBDs and generating the minimum and maximum expected utilities of alternatives.
Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships
