Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields approximation operators that satisfy cautious monotony, while pi-groupoidal approximations (that additionally involve strategic choice and algebraic operators) have nicer properties. The study is primarily motivated by possible structure of concepts in distributed cognition perspectives, real or virtual classroom learning contexts, and student-centric teaching. Rough clustering techniques for datasets that involve up-directed relations (as in the study of Sentinel project image data) are additionally proposed. This research is expected to see significant theoretical and practical applications in related domains.

The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's extension principle for determining the degree of membership of a function of fuzzy numbers is corrected for this generalization. An analogue of the concept of mean value is also suggested. The use of partially ordered values in cognitive maps with comparison of expert assessments is considered.

Human beings have an inherent capability to use linguistic information (LI) seamlessly even though it is vague and imprecise. Computing with Words (CWW) was proposed to impart computing systems with this capability of human beings. The interest in the field of CWW is evident from a number of publications on various CWW methodologies. These methodologies use different ways to model the semantics of the LI. However, to the best of our knowledge, the literature on these methodologies is mostly scattered and does not give an interested researcher a comprehensive but gentle guide about the notion and utility of these methodologies. Hence, to introduce the foundations and state-of-the-art CWW methodologies, we provide a concise but a wide-ranging coverage of them in a simple and easy to understand manner. We feel that the simplicity with which we give a high-quality review and introduction to the CWW methodologies is very useful for investigators, especially those embarking on the use of CWW for the first time. We also provide future research directions to build upon for the interested and motivated researchers.

The electricity consumption of buildings composes a major part of the city's energy consumption. Electricity consumption forecasting enables the development of home energy management systems resulting in the future design of more sustainable houses and a decrease in total energy consumption. Energy performance in buildings is influenced by many factors like ambient temperature, humidity, and a variety of electrical devices. Therefore, multivariate prediction methods are preferred rather than univariate. The Honda Smart Home US data set was selected to compare three methods for minimizing forecasting errors, MAE and RMSE: Artificial Neural Networks, Support Vector Regression, and Fuzzy Rule-Based Systems for Regression by constructing many models for each method on a multivariate data set in different time terms. The comparison shows that SVR is a superior method over the alternatives.

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an $O(\sqrt{T})$ regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games. We also propose several extensions of our algorithm, including an algorithm with Bernstein-type bonus that can achieve a tighter regret bound, and another algorithm for model misspecification that can be applied to neural function approximation.

Load balancing (LB) is a challenging issue in the hybrid light fidelity (LiFi) and wireless fidelity (WiFi) networks (HLWNets), due to the nature of heterogeneous access points (APs). Machine learning has the potential to provide a complexity-friendly LB solution with near-optimal network performance, at the cost of a training process. The state-of-the-art (SOTA) learning-aided LB methods, however, need retraining when the network environment (especially the number of users) changes, significantly limiting its practicability. In this paper, a novel deep neural network (DNN) structure named adaptive target-condition neural network (A-TCNN) is proposed, which conducts AP selection for one target user upon the condition of other users. Also, an adaptive mechanism is developed to map a smaller number of users to a larger number through splitting their data rate requirements, without affecting the AP selection result for the target user. This enables the proposed method to handle different numbers of users without the need for retraining. Results show that A-TCNN achieves a network throughput very close to that of the testing dataset, with a gap less than 3%. It is also proven that A-TCNN can obtain a network throughput comparable to two SOTA benchmarks, while reducing the runtime by up to three orders of magnitude.

This paper presents an open-source Python toolbox called Ensemble Feature Importance (EFI) to provide machine learning (ML) researchers, domain experts, and decision makers with robust and accurate feature importance quantification and more reliable mechanistic interpretation of feature importance for prediction problems using fuzzy sets. The toolkit was developed to address uncertainties in feature importance quantification and lack of trustworthy feature importance interpretation due to the diverse availability of machine learning algorithms, feature importance calculation methods, and dataset dependencies. EFI merges results from multiple machine learning models with different feature importance calculation approaches using data bootstrapping and decision fusion techniques, such as mean, majority voting and fuzzy logic. The main attributes of the EFI toolbox are: (i) automatic optimisation of ML algorithms, (ii) automatic computation of a set of feature importance coefficients from optimised ML algorithms and feature importance calculation techniques, (iii) automatic aggregation of importance coefficients using multiple decision fusion techniques, and (iv) fuzzy membership functions that show the importance of each feature to the prediction task. The key modules and functions of the toolbox are described, and a simple example of their application is presented using the popular Iris dataset.

The requirement to trace and process moving objects in the contemporary era gradually increases since numerous applications quickly demand precise moving object locations. The Map-matching method is employed as a preprocessing technique, which matches a moving object point on a corresponding road. However, most of the GPS trajectory datasets include stay-points irregularity, which makes map-matching algorithms mismatch trajectories to irrelevant streets. Therefore, determining the stay-point region in GPS trajectory datasets results in better accurate matching and more rapid approaches. In this work, we cluster stay-points in a trajectory dataset with DBSCAN and eliminate redundant data to improve the efficiency of the map-matching algorithm by lowering processing time. We reckoned our proposed method's performance and exactness with a ground truth dataset compared to a fuzzy-logic based map-matching algorithm. Fortunately, our approach yields 27.39% data size reduction and 8.9% processing time reduction with the same accurate results as the previous fuzzy-logic based map-matching approach.

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $\epsilon$-Nash equilibrium with $O(1/\epsilon^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/\epsilon^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoys convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments.

Online streaming feature selection (OSFS), which conducts feature selection in an online manner, plays an important role in dealing with high-dimensional data. In many real applications such as intelligent healthcare platform, streaming feature always has some missing data, which raises a crucial challenge in conducting OSFS, i.e., how to establish the uncertain relationship between sparse streaming features and labels. Unfortunately, existing OSFS algorithms never consider such uncertain relationship. To fill this gap, we in this paper propose an online sparse streaming feature selection with uncertainty (OS2FSU) algorithm. OS2FSU consists of two main parts: 1) latent factor analysis is utilized to pre-estimate the missing data in sparse streaming features before con-ducting feature selection, and 2) fuzzy logic and neighborhood rough set are employed to alleviate the uncertainty between estimated streaming features and labels during conducting feature selection. In the experiments, OS2FSU is compared with five state-of-the-art OSFS algorithms on six real datasets. The results demonstrate that OS2FSU outperforms its competitors when missing data are encountered in OSFS.