Investigating the theory, operationalization, and practical applications of complex fuzzy logic

该提案要求为正在进行的研究计划提供资金，研究复杂模糊逻辑（CFL）的理论基础，可操作性和应用。这个研究领域是我的研究小组十多年来的主要重点。在过去的五年里，我和我的学生1）为CFL定义并描述了一组新的逻辑连接词，包括否定和反义词; 2）开发并描述了一个基于CFL的机器学习架构（ANCFIS），用于时间序列预测; 3）改进了ANCFIS设计，以实现更快的训练和数据流挖掘应用。在这些成功的基础上，我们现在询问，如果有CFL实例，以及它们的操作化，会导致更好的性能，更紧凑和可解释的大规模学习模型;以及这些新模型与现有模型相比，最有效地解决了哪些问题。** 我们的提案将支持两个博士学位。学生和五名USRA学生谁将调查基于CFL的否定和反义词。我们将探讨命题和谓词CFL，捕捉两者，确定它们是否是健全的模糊系统和他们的应用推荐系统和互联网广告。 ** 我们将反义词建模为一个概念的符号反转，将否定建模为一个概念的正交;这些都得到了认知心理学和功能性MRI研究中大量证据的支持。然而，深度网络并不包含这些机制。也几乎没有关于深度神经模糊混合的工作，也没有关于深度网络的解释机制。我们不知道在经典逻辑中有任何关于反义词连接词的工作;在模糊逻辑中，它们是算法，不是连接词。因此，拟议的研究探索了数学逻辑和深度学习的突破性方向。我们将在我们的工业合作伙伴的指导下，研究上述开发的高价值应用。我们与HybridForge，Inc.（沿着J.米勒，ECE大学）专注于推荐引擎和点击率预测器。我们正在准备与另外两个阿尔伯塔中小企业的资金申请：Xcarts技术和Addos系统（后者与J. Salmon，A ECE的U）在推理传感和状态监测的深度模糊系统（M.Sc.和PDF将分别支持）。所有这些都是有商业价值的产品，通过这些产品，将培训4名HQP-总共11名。

This proposal requests funding for an ongoing program of research investigating the theoretical foundations, operationalization, and application of Complex Fuzzy Logic (CFL). This area of study has been a primary focus of my research group for over ten years. In the past five years, my students and I have 1) defined and characterized a new set of logical connectives for CFL, incorporating both negation and antonym; 2) developed and characterized a CFL-based machine-learning architecture (ANCFIS) for time series forecasting; and 3) refined the ANCFIS design for faster training and applications in data stream mining. Building on these successes, we now inquire which if any CFL instances, and their operationalizations, lead to better-performing, and more compact and interpretable models for large-scale learning; and what classes of problems are most effectively solved by these new models versus existing ones. ******Our proposal will support two Ph.D. students and five USRA students who will investigate CFL-based negation and antonym. We will explore the propositional and predicate CFLs that capture both, determining whether they are sound zzy systems and their applications to recommender systems and Internet advertising. ******We model antonym as a sign reversal of, and negation as orthogonal to, a concept; these are supported by a body of evidence in cognitive psychology and functional MRI studies. Deep networks, however, do not incorporate these mechanisms. There is also virtually no work on deep neural-fuzzy hybrids, nor on explanation mechanisms for deep networks. We are not aware of any work on antonym connectives in classical logics; in fuzzy logic, they are algorithms, not connectives. The proposed research thus explores ground-breaking directions in mathematical logic and deep learning.******We will investigate high-value applications of the above developments, guided by our industrial partners. Our CRD grant with HybridForge, Inc. (along with J. Miller, U of A ECE) is focused on recommender engines and click-through-rate predictors. We are preparing funding applications with two more Alberta SMEs: XSENSOR Technologies and Addos Systems (the latter with J. Salmon, U of A ECE) on deep fuzzy systems in inferential sensing and condition monitoring (an M.Sc. and a PDF to be supported, respectively). All of these are commercially valuable products, through which 4 more HQP will be trained - 11 total.