Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated with Keras that can do computations within TensorFlow and PyTorch. It provides Dense and Convolutional 1D, 2D, and 3D layers architectures.

Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main statements, and we also create a dataset that provides a counterexample to the ELM learning algorithm and explain its design, which leads to many such counterexamples. Finally, we provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.

Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on admittance of new objects. In particular, one may obtain new objects whose sets of values of features are new to the system. In this case the problem is to assign a decision value to any such new object. This problem is somehow resolved in the rough set theory, e.g., on the basis of similarity of the value set of a new object to value sets of objects already assigned a decision value. It is crucial for online learning when each new object must have a predicted decision value.\ There is a vast literature on various methods for decision prediction for new yet unseen object. The approach we propose is founded in the theory of rough mereology and it requires a theory of sets/concepts, and, we root our theory in classical set theory of Syllogistic within which we recall the theory of parts known as Mereology. Then, we recall our theory of Rough Mereology along with the theory of weight assignment to the Tarski algebra of Mereology.\ This allows us to introduce the notion of a part to a degree. Once we have defined basics of Mereology and rough Mereology, we recall our theory of weight assignment to elements of the Boolean algebra within Mereology and this allows us to define the relation of parts to the degree and we apply this notion in a procedure to select a decision for new yet unseen objects.\ In selecting a plausible candidate which would pass its decision value to the new object, we employ the notion of Vapnik - Chervonenkis dimension in order to select at the first stage the candidate with the largest VC-dimension of the family of its $\varepsilon$-components for some choice of $\varepsilon$.

In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in 3-dimensional space. To avoid falling into the local minimum, we assist with a weighted Euclidean distance. Moreover, a searching path from the start point to the target, with respect to avoiding the obstacles was applied. The environment was created by connecting two cameras working in real-time. To determine the gate and elements of the world inside the map was responsible the Python Library OpenCV [1] which recognized shapes and colors. The main purpose of this paper is to apply the given results to drones.

The three classes of architectures for time series prediction were tested. They differ by input layers which contain either convolutional, LSTM, or dense hypercomplex layers for 4D algebras. The input was four related Stock Market time series, and the prediction of one of them is expected. The optimization of hyperparameters related to the classes of architectures was performed in order to compare the best neural networks within the class. The results show that in most cases, the architecture with a hypercomplex dense layer provides similar MAE accuracy to other architectures, however, with considerably less trainable parameters. Thanks to it, hypercomplex neural networks can be learned and process data faster than the other tested architectures. Moreover, the order of the input time series has an impact on effectively.

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.

Real estate markets depend on various methods to predict housing prices, including models that have been trained on datasets of residential or commercial properties. Most studies endeavor to create more accurate machine learning models by utilizing data such as basic property characteristics as well as urban features like distances from amenities and road accessibility. Even though environmental factors like noise pollution can potentially affect prices, the research around this topic is limited. One of the reasons is the lack of data. In this paper, we reconstruct and make publicly available a general purpose noise pollution dataset based on published studies conducted by the Hellenic Ministry of Environment and Energy for the city of Thessaloniki, Greece. Then, we train ensemble machine learning models, like XGBoost, on property data for different areas of Thessaloniki to investigate the way noise influences prices through interpretability evaluation techniques. Our study provides a new noise pollution dataset that not only demonstrates the impact noise has on housing prices, but also indicates that the influence of noise on prices significantly varies among different areas of the same city.

The study analyzes the impact of constant and alternating magnetic fields and alternating electric fields on various growth parameters of soy plants: the germination energy and capacity, plants emergence and number, the Yield(II) of the fresh mass of seedlings, protein content, and photosynthetic parameters. Four cultivars were used: MAVKA, MERLIN, VIOLETTA, and ANUSZKA. Moreover, the advanced Machine Learning processing pipeline was proposed to distinguish the impact of physical factors on photosynthetic parameters. It is possible to distinguish exposition on different physical factors for the first three cultivars; therefore, it indicates that the EM factors have some observable effect on soy plants. Moreover, some influence of physical factors on growth parameters was observed. The use of ELM (Electromagnetic) fields had a positive impact on the germination rate in Merlin plants. The highest values were recorded for the constant magnetic field (CMF) - Merlin, and the lowest for the alternating electric field (AEF) - Violetta. An increase in terms of emergence and number of plants after seed stimulation was observed for the Mavka cultivar, except for the AEF treatment (number of plants after 30 days) (...)

Among the many merits of Roman Słowiński in his so long and so rich scientific carrier, we have to consider his pioneering approach to the use of artificial intelligence methodologies to decision support, and, in particular, to Multiple Criteria Decision Aiding (MCDA) (for an updated state of the art see [48]). In this perspective, the proposal and the development of the Dominance-based Rough Set Approach (DRSA) is a cornerstone in the domain. The DRSA basic idea of a decision support procedure based on a decision model expressed in natural language and obtained from simple preference information in terms of exemplary decisions has attracted the interest of experts and it is now considered one of the three main approaches to MCDA, together with the classical Multiple Attribute Utility Theory (MAUT) [58] and the outranking approach [75]. In fact, DRSA is not a mere application to MCDA of concepts and tools already proposed and developed in the domain of artificial intelligence, knowledge discovery, data mining and machine learning. Indeed, consideration of preference orders typical for MCDA problems required a reformulation of many important concepts and methodologies, so that DRSA became a methodology viable and interesting per se also in these domains. Consequently, after more or less 25 years from the proposal of DRSA, we try to present a first assessment taking into consideration the basic ideas and the main developments.