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Fuzzy constraints are a popular approach to handle preferences andover-constrained problems in scenarios where one needs to be cautious, such asin medical or space applications. We consider here fuzzy constraint problemswhere some of the preferences may be missing. This models, for example,settings where agents are distributed and have privacy issues, or where thereis an ongoing preference elicitation process. In this setting, we study how tofind a solution which is optimal irrespective of the missing preferences. Inthe process of finding such a solution, we may elicit preferences from the userif necessary. However, our goal is to ask the user as little as possible. Wedefine a combined solving and preference elicitation scheme with a large numberof different instantiations, each corresponding to a concrete algorithm whichwe compare experimentally. We compute both the number of elicited preferencesand the "user effort", which may be larger, as it contains all the preferencevalues the user has to compute to be able to respond to the elicitationrequests. While the number of elicited preferences is important when theconcern is to communicate as little information as possible, the user effortmeasures also the hidden work the user has to do to be able to communicate theelicited preferences. Our experimental results show that some of our algorithmsare very good at finding a necessarily optimal solution while asking the userfor only a very small fraction of the missing preferences. The user effort isalso very small for the best algorithms. Finally, we test these algorithms onhard constraint problems with possibly missing constraints, where the aim is tofind feasible solutions irrespective of the missing constraints.

Elicitation strategies for fuzzy constraint problems with missing preferences: algorithms and experimental studies