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

这项提案要求为一个正在进行的研究项目提供资金，该项目调查复杂模糊逻辑(CFL)的理论基础、可操作性和应用。十多年来，这一研究领域一直是我的研究小组的主要重点。在过去的五年里，我和我的学生们1)为CFL定义和表征了一组新的逻辑连接词，包括否定和反义词；2)开发并表征了基于CFL的机器学习体系结构(ANCFIS)，用于时间序列预测；以及3)改进了ANCFIS设计，以便在数据流挖掘中更快地进行培训和应用。在这些成功的基础上，我们现在询问，如果有任何CFL实例及其可操作性，将为大规模学习带来更好的性能、更紧凑和可解释的模型；以及与现有模型相比，这些新模型最有效地解决了哪些类别的问题。*我们的提案将支持两名博士生和五名USRA学生，他们将调查基于CFL的否定和反义词。我们将探索捕捉两者的命题和谓词CFL，确定它们是否是声音模糊系统及其在推荐系统和互联网广告中的应用。*我们将反义词建模为概念的符号反转，并将否定视为与概念正交；认知心理学和功能磁共振研究中的大量证据支持这些观点。然而，深层网络并不包含这些机制。也几乎没有关于深层神经-模糊混合体的工作，也没有关于深层网络的解释机制的工作。我们不知道在经典逻辑中有任何关于反义连接词的工作；在模糊逻辑中，它们是算法，而不是连接词。因此，拟议的研究探索了数理逻辑和深度学习的开创性方向。*我们将在我们的工业合作伙伴的指导下，研究上述发展的高价值应用。我们与Hybridge Forge，Inc.(与A ECA大学的J.Miller一起)的CRD赠款专注于推荐引擎和点击率预测器。我们正在准备另外两家艾伯塔省中小企业的融资申请：XSENSOR Technologies和Addos Systems(后者与A.Salmon，A ECA大学的J.Salmon一起)关于推理传感和状态监测中的深度模糊系统(M.SC。和要分别支持的PDF)。所有这些都是有商业价值的产品，通过这些产品将再培训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.