Aggregation of aggregating modes in MCDM: Synthesis of Type 2 and Level 2 fuzzy sets

A new approach to MCDM in a fuzzy setting based on the aggregation of aggregating modes is proposed. The problem of appropriate common scale for representation of objective and subjective criteria is solved using the simple subsethood measure based on α-cut representation of fuzzy values. To elaborate an appropriate method for such aggregation, we use the synthesis of the tools of Type 2 and Level 2 fuzzy sets. As the result the final assessments of compared alternatives are presented in form of fuzzy-valued membership function defined on the support composed of considered alternatives. To compare obtained fuzzy assessments we use the probabilistic approach to fuzzy values comparison. Well known Tool Steel Material Selection problem is used as the test task.