A new approach to the Rough Set multicriteria optimisation method

Abstract

In the recent years, enormous amount of attention has been given to multicriteria optimisation problems. These are problems with conflicting objectives, to which it is impossible to obtain an optimum solution that contains the best value for every criterion simultaneously, therefore the decision maker must decide on a reasonable compromise. There have been numerous developments of optimisation methods to aid the decision-maker in addressing such problems. These methods can be divided to two categories based on the use or not of the Pareto domain (PD). The Pareto domain is the set of all non-dominated solutions to the multicriteria problem, where no solution is better or worse than any other in the set when all the criteria are considered equal in importance. This thesis is a collection of two papers that focuses on a new approach to the Rough Set multicriteria optimisation technique. Rough Set method (RSM) requires the determination of the PD as the first step to the optimisation process. In the suggested new approach to RSM, a more systematic way in the selection of points from the PD, that is given to the expert for ranking and then the generation of rules by which the entire PD is ranked, is presented. The RSM that operates based on this new approach was applied to three case studies in paper 1 and to "Beer quality optimisation" in the second paper. The results were compared to the ones obtained by the traditional RSM, Net Flow method and the simple Least Squares method. In conclusion, the new RSM showed to be the most reliable and robust method of all.