Introducing the difficulty of implementing alternatives in the multiple criteria decision problems

In this paper we propose methods that can help the decision-makers to find a compromise between willingness to do and ability to do by introducing the difficulty considerations in the multiple criteria decision analysis problems. Two problems are considered: ranking alternatives and improving existing solution. Usually, in the classical approaches of multiple criteria decision analysis, only the degree of satisfaction is considered to compare alternatives. However, sometimes a good alternative is difficult to implement by a decision-maker even if he spends necessary cost for it. First we give the definition of the concept of difficulty function, then we show how to introduce it in decision problems using operators based on fuzzy measures. This allows us to consider interactions between criteria under two aspects: 1) the overall satisfaction resulting from the simultaneous satisfaction or not of certain criteria; 2) the overall difficulty resulting from the difficulty or not of satisfying certain criteria simultaneously. After that, we present two examples of the difficulty function assessment in the case of a non-linear model. Finally, we propose an illustration concerning the problem of managing the students effort when improving their scores on a set of subjects. This illustration focus on the extension of the concept of worth index which quantifies the gain of improvement related to a subset of objectives when it is difficult to improve all the objectives simultaneously.