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This paper studies fuzzy coalition formation for self-interested agents in cooperative superadditive games. In particular, we consider the situation, where, given a number of tasks, service provider agents seek partners from those available in the environment. These potential partners can commit their resources to multiple coalitions and, in so doing, aim to maximise the sum of the expected Shapley value in the coalitions in which they participate. Specifically, we develop a novel auction-based fuzzy coalition formation algorithm that enables each agent to choose its most preferred coalitions and then to find the coalitions it will actually participate in through simultaneous multiple entry English auctions. When the auction closes, the active bids in each auction represent the set of agents that will perform the task jointly. We then show, by empirical evaluation, that our algorithm outperforms two benchmarks (that allow only crisp coalitions and a greedy approach to fuzzy coalitions) by up to 61.3% with respect to the total value of the coalition structure.