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Motivated by Zadeh's paradigm of computing with words (CWs) rather than numbers, several formal models of CWs have recently been proposed. These models are based on automata and, thus, are not well suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, which is called the Petri net, together with fuzzy-set theory and, thereby, establish a concurrency model of CWs-fuzzy Petri nets for CWs (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW that makes computing with more words possible. The language expressiveness of the two formal models of CWs, i.e., fuzzy automata for CWs as well as FPNCWs, is compared. A few small examples are provided to illustrate the theoretical development.