A neural fuzzy system can learn an agent profile of a user when it samples user question-answer data. A fuzzy system uses if-then rules to store and compress the agent's knowledge of the user's likes and dislikes. A neural system uses training data to form and tune the rules. The profile is a preference map or a bumpy utility surface defined over the space of search objects. Rules define fuzzy patches that cover the surface bumps as learning unfolds and as the fuzzy agent system gives a finer approximation of the profile. The agent system searches for preferred objects with the learned profile and with a new fuzzy measure of similarity. The appendix derives the supervised learning law that tunes this matching measure with fresh sample data. We test the fuzzyagent profile system on object spaces of flowers and sunsets and test the fuzzy agent matching system on an object space of sunset images. Rule explosion and data acquisition impose fundamental limits on the system designs.