Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

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 & complete. We will design deep fuzzy systems, which we expect will yield more interpretable models than existing deep networks. Deep complex fuzzy systems will be an extension that employs negation and antonym to also create more compact networks (just as negative rules are known to lead to more compact rulebases). We will apply these architectures to several high-value problems we have explored in previous research. Two other Ph.D. students, supported by a CRD grant, will examine shallow complex fuzzy 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.