量子模糊集：模糊集理论与量子计算的融合
Quantum Fuzzy Sets: Blending Fuzzy Set Theory and Quantum Computation
摘要：
在这篇文章中，我们研究了一种方法，量子计算可以用来扩展类的模糊集。其核心思想是将量子寄存器的状态看作是给定集合的量子模糊子集的特征函数。当实单位区间嵌入Bloch球面时，每个模糊集自动成为量子模糊集。然而，一个通用的量子模糊集可以被看作是许多模糊集的叠加（可能是纠缠的），为建模不确定性提供了新的机会。在介绍了量子模糊集理论的主要框架之后，我们从我们的角度分析了模糊化和去模糊化的标准运算。最后，我们列出了量子模糊集在模式识别中的可能应用，以及量子模糊集理论纯研究的未来方向。
英文摘要：
In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the real unit interval is embedded in the Bloch sphere, every fuzzy set is automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be seen as a (possibly entangled) superposition of many fuzzy sets at once, offering new opportunities for modeling uncertainty. After introducing the main framework of quantum fuzzy set theory, we analyze the standard operations of fuzzification and defuzzification from our viewpoint. We conclude this preliminary paper with a list of possible applications of quantum fuzzy sets to pattern recognition, as well as future directions of pure research in quantum fuzzy set theory.
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