While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.

This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.

--Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger traction outside of fuzzy venues, because users sometimes do not know about fuzzy and because fuzzy partitions are not so easy to interpret in some situations. In this work, we propose a methodology to reduce fuzzy rule-based classifiers to crisp rule-based classifiers. We study different possible crisp descriptions and implement an algorithm to obtain them. Also, we analyze the complexity of the resulting crisp classifiers. We believe that our results can help both fuzzy and non-fuzzy practitioners understand better the way in which fuzzy rule bases partition the feature space and how easily one system can be translated to another and vice versa. Our complexity metric can also help to choose between different fuzzy classifiers based on what the equivalent crisp partitions look like.

Breast cancer remains one of the leading causes of mortality among women worldwide, with early diagnosis being critical for effective treatment and improved survival rates. However, timely detection continues to be a challenge due to the complex nature of the disease and variability in patient risk factors . This study presents a fuzzy soft set theory - based expert system designed to assess the risk of breast cancer in patients using measurable clinical and physiological parameters. The proposed system integrates Body Mass Index (BMI), Insulin Level (IL), Lep tin Level (LL), Adiponectin Level (AL), and age as input variables to estimate breast cancer risk through a set of fuzzy inference rules and soft set computations. These parameters can be obtained from routine blood analyses, enabling a non - invasive and ac cessible method for preliminary assessment. The dataset used for model development and validation was obtained from the UCI Machine Learning Repository. The proposed expert system aims to support healthcare professionals in identifying high - risk patients a nd determining the necessity of further diagnostic procedures such as biopsies.

Abstract--Dempster-Shafer Theory (DST) provides a powerful framework for modeling uncertainty and has been widely applied to multi-attribute classification tasks. However, traditional DST - based attribute fusion-based classifiers suffer from oversimplified membership function modeling and limited exploitation of the belief structure brought by basic probability assignment (BPA), reducing their effectiveness in complex real-world scenarios. This paper presents an enhanced attribute fusion-based classifier that addresses these limitations through two key innovations. First, we adopt a selective modeling strategy that utilizes both single Gaussian and Gaussian Mixture Models (GMMs) for membership function construction, with model selection guided by cross-validation and a tailored evaluation metric. Second, we introduce a novel method to transform the possibility distribution into a BPA by combining simple BPAs derived from normalized possibility distributions, enabling a much richer and more flexible representation of uncertain information. Furthermore, we apply the belief structure-based BPA generation method to the evidential K-Nearest Neighbors (EKNN) classifier, enhancing its ability to incorporate uncertainty information into decision-making. Comprehensive experiments on benchmark datasets are conducted to evaluate the performance of the proposed attribute fusion-based classifier and the enhanced evidential K-Nearest Neighbors classifier in comparison with both evidential classifiers and conventional machine learning classifiers. The results demonstrate that the proposed classifier outperforms the best existing evidential classifier, achieving an average accuracy improvement of 4.86%, while maintaining low variance, thus confirming its superior effectiveness and robustness.

Modern anthropomorphic upper limb bioprostheses are typically controlled by electromyographic (EMG) biosignals using a pattern recognition scheme. Unfortunately, there are many factors originating from the human source of objects to be classified and from the human-prosthesis interface that make it difficult to obtain an acceptable classification quality. One of these factors is the high susceptibility of biosignals to contamination, which can considerably reduce the quality of classification of a recognition system. In the paper, the authors propose a new recognition system intended for EMG based control of the hand prosthesis with detection of contaminated biosignals in order to mitigate the adverse effect of contaminations. The system consists of two ensembles: the set of one-class classifiers (OCC) to assess the degree of contamination of individual channels and the ensemble of K-nearest neighbours (KNN) classifier to recognise the patient's intent. For all recognition systems, an original, coherent fuzzy model was developed, which allows the use of a uniform soft (fuzzy) decision scheme throughout the recognition process. The experimental evaluation was conducted using real biosignals from a public repository. The goal was to provide an experimental comparative analysis of the parameters and procedures of the developed method on which the quality of the recognition system depends. The proposed fuzzy recognition system was also compared with similar systems described in the literature.

Credit card fraud is assuming growing proportions as a major threat to the financial position of American household, leading to unpredictable changes in household economic behavior. To solve this problem, in this paper, a new hybrid analysis method is presented by using the Enhanced ANFIS. The model proposes several advances of the conventional ANFIS framework and employs a multi-resolution wavelet decomposition module and a temporal attention mechanism. The model performs discrete wavelet transformations on historical transaction data and macroeconomic indicators to generate localized economic shock signals. The transformed features are then fed into a deep fuzzy rule library which is based on Takagi-Sugeno fuzzy rules with adaptive Gaussian membership functions. The model proposes a temporal attention encoder that adaptively assigns weights to multi-scale economic behavior patterns, increasing the effectiveness of relevance assessment in the fuzzy inference stage and enhancing the capture of long-term temporal dependencies and anomalies caused by fraudulent activities. The proposed method differs from classical ANFIS which has fixed input-output relations since it integrates fuzzy rule activation with the wavelet basis selection and the temporal correlation weights via a modular training procedure. Experimental results show that the RMSE was reduced by 17.8% compared with local neuro-fuzzy models and conventional LSTM models.

Air pollution in cities and the possibilities of reducing this pollution represents one of the most important factors that today's society has to deal with. This paper focuses on a systemic approach to traffic emissions with their relation to meteorological conditions, analyzing the effect of weather on the quantity and dispersion of traffic emissions in a city. Using fuzzy inference systems (FIS) the model for prediction of changes in emissions depending on various conditions is developed. The proposed model is based on traffic, meteorology and emission data measured in Prague, Czech Republic. The main objective of the work is to provide insight into how urban planners and policymakers can plan and manage urban transport more effectively with environmental protection in mind.

Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications.

Background: Wisdom is a superordinate construct that embraces perspective taking, reflectiveness, prosocial orientation, reflective empathetic action, and intellectual humility. Unlike conventional models of reasoning that are rigidly bound by binary thinking, wisdom unfolds in shades of ambiguity, requiring both graded evaluation and self-reflective humility. Current measures depend on self-reports and seldom reflect the humility and uncertainty inherent in wise reasoning. A computational framework that takes into account both multidimensionality and confidence has the potential to improve psychological science and allow humane AI. Method: We present a fuzzy inference system with Z numbers, each of the decisions being expressed in terms of a wisdom score (restriction) and confidence score (certainty). As part of this study, participants (N = 100) were exposed to culturally neutral pictorial moral dilemma tasks to which they generated think-aloud linguistic responses, which were mapped into five theoretically based components of wisdom. The scores of each individual component were combined using a base of 21 rules, with membership functions tuned via Gaussian kernel density estimation. Results: In a proof of concept study, the system produced dual attribute wisdom representations that correlated modestly but significantly with established scales while showing negligible relations with unrelated traits, supporting convergent and divergent validity. Contribution: The contribution is to formalize wisdom as a multidimensional, uncertainty-conscious construct, operationalized in the form of Z-numbers. In addition to progressing measurement in psychology, it calculates how fuzzy Z numbers can provide AI systems with interpretable, confidence-sensitive reasoning that affords a safe, middle ground between rigorous computation and human-like judgment.