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In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed $\zeta$-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-algebras). We introduce and examine the concepts of $\zeta$-Lukasiewicz fuzzy SBE-subalgebras and $\zeta$-Lukasiewicz fuzzy SBE-ideals, with a focus on their algebraic properties. Furthermore, we define three specific types of subsets, referred to as ∈-sets, q-sets, and O-sets, and investigate the necessary conditions for these subsets to constitute subalgebras or ideals within the SBE-algebraic context. Full article

Applied sensing technology has made it possible for human beings to experience a revolutionary aspect of the science and technology world. Along with many other fields in which this technology is working wonders, human locomotion activity recognition, which finds applications in healthcare, smart homes, life-logging, and many other fields, is also proving to be a landmark. The purpose of this study is to develop a novel model that can robustly handle divergent data that are acquired remotely from various sensors and make an accurate classification of human locomotion activities. The biggest support for remotely sensed human locomotion activity recognition (RS-HLAR) is provided by modern smartphones. In this paper, we propose a robust model for an RS-HLAR that is trained and tested on remotely extracted data from smartphone-embedded sensors. Initially, the system denoises the input data and then performs windowing and segmentation. Then, this preprocessed data goes to the feature extraction module where Parseval’s energy, skewness, kurtosis, Shannon entropy, and statistical features from the time domain and the frequency domain are extracted from it. Advancing further, by using Luca-measure fuzzy entropy (LFE) and Lukasiewicz similarity measure (LS)–based feature selection, the system drops the least-informative features and shrinks the feature set by 25%. In the next step, the Yeo–Johnson power transform is applied, which is a maximum-likelihood-based feature optimization algorithm. The optimized feature set is then forwarded to the multilayer perceptron (MLP) classifier that performs the classification. MLP uses the cross-validation technique for training and testing to generate reliable results. We designed our system while experimenting on three benchmark datasets namely, MobiAct_v2.0, Real-World HAR, and Real-Life HAR. The proposed model outperforms the existing state-of-the-art models by scoring a mean accuracy of 84.49% on MobiAct_v2.0, 94.16% on Real-World HAR, and 95.89% on Real-Life HAR. Although our system can accurately differentiate among similar activities, excessive noise in data and complex activities have shown an inverse effect on its performance. Full article

The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension of fuzzy sets, we will try to define a conditional mean value for the intuitionistic fuzzy case. The conditional mean value in crisp intuitionistic fuzzy events was first studied by V. Valenčáková in 2009. She used Gödel connectives. Her approach can only be used for special cases of intuitionistic fuzzy events, therefore, we want to define a conditional mean value for all elements of a family of intuitionistic fuzzy events. In this paper, we define the conditional mean value for intuitionistic fuzzy events using Lukasiewicz connectives. We use a Kolmogorov approach and the notions from a classical probability theory for construction. B. Riečan formulated a conditional intuitionistic fuzzy probability for intuitionistic fuzzy events using an intuitionistic fuzzy state in 2012. In classical cases, there exists a connection between the conditional probability and the conditional mean value, therefore we show a connection between the conditional intuitionistic fuzzy probability induced by the intuitionistic fuzzy state and the conditional intuitionistic fuzzy mean value. Full article