This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent's fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.

中文翻译：

---

具有模糊偏好的纯交换经济均衡的存在性

本文重点研究了一种新模型，以在具有模糊偏好的纯交换经济（PXE-FP）中达到均衡的存在。所提出的模型在消费集合中整合了交换、消费和代理的模糊偏好。我们在消费集上建立了一个新的模糊二元关系来评估模糊偏好。此外，我们证明了在一定条件下，消费集合中存在一个连续的模糊保序函数。通过关于模糊非合作博弈的模糊纳什均衡存在的新结果，证实了 PXE-FP 模糊竞争均衡的存在。在模糊非合作博弈中，任何代理的所有策略配置文件的收益都是模糊数。最后，