Novel developments in computational intelligence with applications to data stream mining

复模糊逻辑是传统模糊逻辑的一种新的推广。复模糊真值是来自复平面的幅值小于或等于1的向量。在阐明复杂模糊逻辑的性质方面进展有限，并且已经出现了一些基于它的机器学习方法（我们的工作在两个研究领域都很突出）。然而，人们认为，复杂的模糊逻辑实际上是一个多值逻辑的无限家族，并且基于它的学习算法的设计空间相应地是巨大的。显然，在理解这一领域方面还有大量的工作要做，我们的研究也有明显的机会在这一领域留下持久的印记。我们提出的未来五年的研究计划将继续我们在这一领域的理论和应用研究，解决关键的开放性问题，如：什么类的运营商，形成复杂的模糊合取，析取和影响？它们的性质是什么？什么样的函数构成有用的复模糊集？我们如何用语言解释复杂的模糊集？复杂的模糊集和逻辑如何在机器学习算法中最有效地实现，它们最适合解决哪些类别的问题？

Complex fuzzy logic is a recent generalization of the traditional fuzzy logic. Complex fuzzy truth values are vectors from the complex plane with a magnitude less than or equal to 1. There has been limited progress in elucidating the properties of complex fuzzy logic, and a few machine-learning approaches based on it have appeared (with our work prominent in both strands of research). However, it is believed that complex fuzzy logic is actually an infinite family of multivalued logics; and that the design space for learning algorithms based on it is correspondingly vast. Plainly, there is still an enormous amount of work to be done in understanding this area, and a clear opportunity for our research to make a lasting mark on the field. Our proposed program of research for the coming five years will continue our theoretical and applied research in this field, tackling key open questions such as: what are the classes of operators that form complex fuzzy conjunctions, disjunctions, and implications? What are their properties? What functions form useful complex fuzzy sets? How do we linguistically interpret complex fuzzy sets? How are complex fuzzy sets and logic most usefully realized in machine-learning algorithms, and what classes of problems are they best-suited to solve?