Analytical aspects of combining holistic evaluation and decomposition elicitation for preference modeling in the FITradeoff method

Combining the traditional elicitation by decomposition with holistic evaluations within a decision process with multiple criteria is a peculiar aspect of the Flexible and Interactive Tradeoff (FITradeoff) method since two paradigms in preference modeling are integrated. Even though this integration leads to significant benefits to the decision process, it brings several implications that deserve a deep and detailed analysis with regard to some analytical aspects of the mathematical modeling of the method. Integrating the information obtained by these two different protocols causes significant modifications in the space of weights that may have noteworthy impacts on the results. Hence, this paper focuses its efforts on tackling and investigating such aspects of the FITradeoff method. We analyze properties and analytical aspects of FITradeoff in depth, in order to investigate how the information of holistic judgments can be inserted into the mathematical model of FITradeoff and to determine the potential implications of such integration, such as defining preference relationships and identifying potentially optimal alternatives. In addition, a new heuristic to reduce the number of questions in the elicitation by decomposition of FITradeoff is proposed. We also address situations of inconsistencies that may arise due to the conflicting information provided by decomposition and holistic judgments, as well as ways to solve such inconsistencies.