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In the literature on automated negotiation, very few negotiation agents are designed with the flexibility to slightly relax their negotiation criteria to reach a consensus more rapidly and with more certainty. Furthermore, these relaxed-criteria negotiation agents were not equipped with the ability to enhance their performance by learning and evolving their relaxed-criteria negotiation rules. The impetus of this work is designing market-driven negotiation agents (MDAs) that not only have the flexibility of relaxing bargaining criteria using fuzzy rules, but can also evolve their structures by learning new relaxed-criteria fuzzy rules to improve their negotiation outcomes as they participate in negotiations in more e-markets. To this end, an evolutionary algorithm for adapting and evolving relaxed-criteria fuzzy rules was developed. Implementing the idea in a testbed, two kinds of experiments for evaluating and comparing EvEMDAs (MDAs with relaxed-criteria rules that are evolved using the evolutionary algorithm) and EMDAs (MDAs with relaxed-criteria rules that are manually constructed) were carried out through stochastic simulations. Empirical results show that: 1) EvEMDAs generally outperformed EMDAs in different types of e-markets and 2) the negotiation outcomes of EvEMDAs generally improved as they negotiated in more e-markets.