A Temporal Type-2 Fuzzy System for Time-dependent Explainable Artificial Intelligence

Explainable Artificial Intelligence (XAI) is a paradigm that delivers transparent models and decisions, which are easy to understand, analyze, and augment by a non-technical audience. Fuzzy Logic Systems (FLS) based XAI can provide an explainable framework, while also modeling uncertainties present in real-world environments, which renders it suitable for applications where explainability is a requirement. However, most real-life processes are not characterized by high levels of uncertainties alone; they are inherently time-dependent as well, i.e., the processes change with time. To account for the temporal component associated with a process, in this work, we present novel Temporal Type-2 FLS Based Approach for time-dependent XAI (TXAI) systems, which can account for the likelihood of a measurement’s occurrence in the time domain using (the measurement’s) frequency of occurrence. In Temporal Type-2 Fuzzy Sets (TT2FSs), a four-dimensional (4D) time-dependent membership function is developed where relations are used to construct the inter-relations between the elements of the universe of discourse and its frequency of occurrence. The proposed TXAI system with TT2FSs is exemplified with a step-by-step numerical example and an empirical study using a real-life intelligent environments dataset to solve a time-dependent classification problem (predict whether or not a room is occupied depending on the sensors readings at a particular time of day). The TXAI system performance is also compared with other state-of-the-art classification methods with varying levels of explainability. The TXAI system manifested better classification prowess, with 10-fold test datasets, with a mean recall of 95.40% than a standard XAI system (based on non-temporal general type-2 (GT2) fuzzy sets) that had a mean recall of 87.04%. TXAI also performed significantly better than most non-explainable AI systems between 3.95%, to 19.04% improve- ment gain in mean recall. Temporal convolution network (TCN) was marginally better than TXAI (by 1.98% mean recall improvement) although with a major computational complexity. In addition, TXAI can also outline the most likely time-dependent trajectories using the frequency of occurrence values embedded in the TXAI model; viz. given a rule at a determined time interval, what will be the next most likely rule at a subsequent time interval. In this regard, the proposed TXAI system can have profound implications for delineating the evolution of real-life time-dependent processes, such as behavioural or biological processe