Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction

Abstract

Decision making problems are becoming increasingly complicated. Consequently, the developed methods to support decision makers are more and more general. Group decision-making is a very common scenario. When a team of decision makers is faced with a problem, it is natural to assume that due to diversity of their backgrounds and experience they may require different ways of providing their evaluations and opinions. A very common, and quite unreasonable, assumption made by decision-making methods that deal with groups of decision makers is to consider that all decision makers agreed on a unique criteria set to evaluate given alternatives. Criteria interaction is another common issue in multi-criteria decision making and it is normally addressed using Choquet integral, which alone brings another serious problem of capacity identification. In addition, the decision-making environments are rarely static. Aiming to address all these issues at once, we propose two generalized approaches based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and the TODIM (an acronym in Portuguese for Interactive and Multi-Criteria Decision Making). The new methods are able to consider groups of decision makers with all their different opinions, heterogeneous types of information, criteria interaction, fuzzy measure identification and dynamic environments. The methods are applied in two examples and two case studies showing their feasibility in solving complex real world problems.