Všechny publikace
Fuzzy–Probabilistic Inference Systems Based on Piecewise Linear Weighted Quantiles
In this work, we consider a particular construction of IF--THEN rules and the associated inference mechanism, which coincide with the so-called quantile fuzzy transform (or L1-fuzzy transform). Given …
In this work, we consider a particular construction of IF--THEN rules and the associated inference mechanism, which coincide with the so-called quantile fuzzy transform (or L1-fuzzy transform). Given a suitable fuzzy partition of the underlying universe and a random variable defined on a probability space, the system is formulated through rules stating that if the input belongs to the $k$-th fuzzy set, then the output is modeled by a corresponding quantile function.The consequent is represented by weighted quantile functions that provide statistical estimates of the output distribution conditioned on the input's membership in the respective fuzzy set. A crucial step in the inference process is the estimation of these quantile functions from data. Traditionally, weighted quantiles are computed via linear programming. We have recently introduced an alternative and computationally efficient method for evaluating weighted quantiles based on the analysis of the right derivative of the associated convex objective function.Although classical weighted quantiles are computationally efficient, they may be inadequate for accurately capturing the local positions of output quantiles over fuzzy inputs. To overcome this limitation, we have extended the weighted quantile approach into a piecewise linear functional form. In this contribution, we propose a slight modification of this construction to enhance its applicability to forecasting tasks. We describe the modified approach, demonstrate its improved inference performance compared to scalar weighted quantiles, and highlight its relevance for forecasting applications.
On Inference Mechanisms of Fuzzy-Probabilistic Inference Systems
This work studies the inference mechanism of fuzzy-probabilistic inference systems (FPIS), a class of rule-based models where antecedents encode fuzzy information and consequents represent conditional…
This work studies the inference mechanism of fuzzy-probabilistic inference systems (FPIS), a class of rule-based models where antecedents encode fuzzy information and consequents represent conditional probability distributions of the output variable. A system of m rules is considered: if the input belongs to a fuzzy set A_k, then the output follows a probability distribution described by an empirical quantile function. The antecedents form a covering fuzzy partition of the universe, ensuring that every input has positive membership in at least one fuzzy set. In practice, uniform or generalized partitions are typically employed. Local quantile functions are estimated from data as weighted quantiles, with weights given by membership degrees. The inference mechanism produces an empirical quantile function for any input as a linear combination of these local quantile functions, using normalized membership weights. Fuzzy rule-based systems capture input-output relationships in a rough manner, while the inference mechanism refines this into a complete mapping usable in practice. Previous studies compared the standard weighted average of quantile functions with several alternatives on synthetic and real datasets. However, a theoretical analysis of these mechanisms, including the original weighted average and related L1-based minimization approaches, remains open. This gap motivates a deeper investigation of the foundations of the inference mechanism for FPIS.
A General Framework for Multiplets Selection: Algorithmization and Complexity Analysis
In this contribution, we present the multiplets algorithm for constructing and selecting optimal sets of disjoint hyperedges across multiple groups in tabular data. We describes main computational ste…
In this contribution, we present the multiplets algorithm for constructing and selecting optimal sets of disjoint hyperedges across multiple groups in tabular data. We describes main computational steps and provide a complexity analysis covering both the edge construction and optimization phases, based on the Linear Sum Assignment method and the Constraint Programming SAT-based solver.
Predicting Subgoals in Ricochet Robots with a Graph Neural Network
Tato práce aplikuje grafové neuronové sítě na predikci podcílů ve hře s názvem Ricochet Robots, NP-úplné logické hře. Herní stavy …
Tato práce aplikuje grafové neuronové sítě na predikci podcílů ve hře s názvem Ricochet Robots, NP-úplné logické hře. Herní stavy jsou reprezentovány jako orientované grafy, kde uzly odpovídají políčkům mřížky a hrany reprezentují pohyby robotů. Rekurentní architektura Graph Attention Network je trénována k napodobení hierarchické vyhledávací heuristiky, která identifikuje slibné pozice (podcíle), kterých by cílový robot měl dosáhnout. Vyhodnoceny jsou dva klasifikační úkoly: identifikace políček, ze kterých je cíl nezávisle dosažitelný, a predikce optimálních podcílů. Model dosahuje téměř dokonalého výkonu u jednoduššího úkolu dosažitelnosti a prokazuje významné učení u komplexnějšího úkolu predikce optimálních podcílů. Výsledky potvrzují, že grafové neuronové sítě dokážou zachytit prostorové uvažování potřebné pro identifikaci podcílů ve výpočetně náročných problémových doménách, čímž vytvářejí základ pro autonomní objevování podcílů v komplexních stavových prostorech.
On the Dissimilarity of Fuzzy Information Granules
In this work, we pose the question of how to assess the dissimilarity of pairs of information granules that may be exemplified with I1 and I2. We focus on two representative types of information granu…
In this work, we pose the question of how to assess the dissimilarity of pairs of information granules that may be exemplified with I1 and I2. We focus on two representative types of information granules, namely fuzzy association rules (FAR) and fuzzy linguistic summaries, and aim to (1) propose a unified notation for the construction and selection of the most meaningful fuzzy information granules, and (2) analyze and discuss the assessment of dissimilarity across the considered types.
Qualitative Criteria for Fuzzy Linguistic Summaries with Absolute Linguistic Expressions
This contribution builds upon previous achievements in the theories of generalized and intermediate quantifiers, and the evaluative linguistic expressions. In this work, we study the antonym property …
This contribution builds upon previous achievements in the theories of generalized and intermediate quantifiers, and the evaluative linguistic expressions. In this work, we study the antonym property of fuzzy linguistic summaries with absolute linguistic expressions. First, we briefly review qualitative evaluation criteria with a particular focus on the degree of truth (as baseline) and the degrees of imprecision and specificity. Next, we consider the property of antonym and investigate its adequacy for the selected criteria.
Few-shot learning in industrial applications
This paper reports on the empirical performance of few-shot learning (FSL) for visualdefect classification using confidential industrial datasets. We evaluate 16 combinations offour backbone models (P…
This paper reports on the empirical performance of few-shot learning (FSL) for visualdefect classification using confidential industrial datasets. We evaluate 16 combinations offour backbone models (Perception Encoder, DINOv2, DINOv3, ConvNeXt-v2) and fourFSL classifiers (Prototypical Networks, Neighborhood Component Analysis, Relation Networks,Linear Adapter). The evaluation covers three conditions: a baseline comparison,deterministic support set augmentation, and a learnable attention preprocessor. Resultsdemonstrate that support set augmentation is a highly effective strategy, improving performancein nearly all configurations. Furthermore, the DINOv2 and ConvNeXt-V2-T backbonesemerged as top performers, achieving the most competitive and highest-accuracyresults, respectively. These findings suggest that for industrial FSL applications, combininga strong, pre-trained backbone with a simple augmentation strategy is a practicalapproach for building data-efficient classification systems.
Linguistic interpretation of natural data using new forms of intermediate quantifiers
This paper examines the application of fuzzy natural logic in the analysis of scientific data and their representation through special linguistic expressions. We use the theory of evaluative linguisti…
This paper examines the application of fuzzy natural logic in the analysis of scientific data and their representation through special linguistic expressions. We use the theory of evaluative linguistic expressions, which makes it possible to describe quantitative data using imprecise expressions such as ``very small'', ``medium'', ``large'', and similar. They occur in the definition of the so-called intermediate quantifiers, using which we characterize given data.
Verification of Validity of Syllogisms Related to Graded Peterson Cube of Opposition
In this article, we will examine the validity of selected forms of logical syllogisms with intermediate quantifiers. We will focus in particular on forms related to the graded Peterson's cube of oppos…
In this article, we will examine the validity of selected forms of logical syllogisms with intermediate quantifiers. We will focus in particular on forms related to the graded Peterson's cube of opposition. Our verification will be based on the application of graded Peterson's rules using the distribution index.
Measuring the Temporal Stability of Fuzzy Linguistic Summaries about Time Series with Drifts
We thoroughly analyse the stability of sequences of FLSs with various quantifiers and various drifts, aiming to identify patterns between the statistical properties in observed multivariate time serie…
We thoroughly analyse the stability of sequences of FLSs with various quantifiers and various drifts, aiming to identify patterns between the statistical properties in observed multivariate time series and the calculated stability indexes. The secondary goal is to characterise the group of fuzzy linguistic summaries that may serve as promising explanations of changes detected in the original time series.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
Intermediate quantifiers and the problems of non-monotonic logic
Intermediate quantifiers and valid syllogisms on EQ-algebras
Abstract Intermediate quantifiers are expressions of natural language, for example “most, almost all, many, a few” using which we quantify a number of some objects in a given univer…
Abstract Intermediate quantifiers are expressions of natural language, for example “most, almost all, many, a few” using which we quantify a number of some objects in a given universe. We have shown in [23] that all valid syllogisms with intermediate quantifiers are a consequence of only two algebraic inequalities and one equality. The result was obtained in the formalism of Lukasiewicz fuzzy type theory whose truth values form a linearly ordered complete MV-algebra. In this paper we will prove that the same holds if we replace MV-algebra by a much more general IEQ-algebra (involutive EQ-algebra).
Dyslipidemia in Anorexia Nervosa Is Associated with Decreased Plasma Tauroursodeoxycholic Acid and a Specific Fatty Acid Pattern
Abstract Background: Dyslipidemia and distorted fatty acid (FA) metabolism are frequent biochemical abnormalities associated with anorexia nervosa (AN). Gut microbiota is supposed to play an important…
Abstract Background: Dyslipidemia and distorted fatty acid (FA) metabolism are frequent biochemical abnormalities associated with anorexia nervosa (AN). Gut microbiota is supposed to play an important role in the etiopathogenesis of AN. Apart from the digestive function of bile acids (BAs), these compounds have multiple metabolic functions due to the activation of specific receptors. Objective/aims: The aims of the study were to investigate biochemical measures, including plasma lipids (lipoproteins, respectively), fatty acid (FA) patterns, and the profile of plasma Bas, in AN patients and healthy controls (CON). Methods: Plasma phospholipid FA and BAs profiles were analyzed in 39 women with a restrictive type of AN (AN-R; median age 17 years) and in 35 CON women (median age 20 years). Results: Compared to CON, AN had an increased concentration of HDL-C, increased content of palmitic acid, and decreased proportion of linoleic acid. Moreover, AN had a drop in the level of the sum of PUFAn-6 and increased delta 9 desaturase activity for stearic acid. In AN, we found decreased levels of plasma tauroursodeoxycholic acid (TUDCA). In AN, concentrations of 22:5n-6, 16:0, 20:3n-6 and fat mass index were predic-tors of HDL-C levels (R2 = 0.43). Conclusions: Patients with AN-R had an increased concentration of HDL-C, decreased levels of total PUFA n-6, and increased activity of D9D for stearic acid. Furthermore, AN exerted decreased levels of TUDCA. Therefore, a decreased level of TUDCA could potentially serve as a marker of AN.
Aristotle's square for mining fuzzy concepts
Abstract Aristotle's Square also known as Square of Opposition, is a mathematical diagram dating back to Greek philosophy and exhibiting the connection between four logical propositions in a…
Abstract Aristotle's Square also known as Square of Opposition, is a mathematical diagram dating back to Greek philosophy and exhibiting the connection between four logical propositions in a simple graphical form. Fuzzy Relational Concept Analysis (FRCA) is a technique for extracting special clusters called fuzzy concepts from a Fuzzy Relational Context Family (FRCF), which is a dataset organized as multiple fuzzy object-attribute and object-object relations. The primary FRCA tools to obtain information from data are special fuzzy quantifiers viewed as interpretations in a model of formulas of the formal theory of the intermediate generalized quantifiers. This work focuses on the issue of generating a collection of fuzzy concepts from a certain FRCF, by choosing one of four particular FRCA quantifiers: the positive universal quantifier 𝒮1, the negative universal quantifier 𝒮−1, the positive existential quantifier 𝒮∃, and the negative existential quantifier 𝒮−∃. Certainly, the selection of the quantifier is crucial in the FRCA procedure since it affects the final concept classification: diverse fuzzy concepts arise from varying quantifiers. As the initial objective, this article introduces the logical relations involving 𝒮1,𝒮−1, 𝒮∃, and 𝒮−∃, in order to arrange them in a graded version of the Aristotelian square. The second goal of this study is to examine the connections among fuzzy concepts produced by distinct quantifiers in {𝒮1,𝒮−1,𝒮∃,𝒮−∃}. Therefore, our findings provide a twofold contribution to the advancement of Aristotle's square. Indeed, they reveal a novel interpretation of the square of opposition within the framework of Fuzzy Relational Concept Analysis, emphasizing its potential as a valuable tool for the analysis of data.
Block-Coordinate Descent Algorithm for Interventional Data in Directed Graphical Models
Computing maximum likelihood estimates in linear structural equation models is generally a difficult problem. The critical equations are usually non-linear and have numerous solutions, even for purely…
Computing maximum likelihood estimates in linear structural equation models is generally a difficult problem. The critical equations are usually non-linear and have numerous solutions, even for purely observational data. The block-coordinate descent (BCD) algorithm proposed by Drton et al. (2019)[1] is an efficient way to solve the optimization problem by decomposing it into a series of sub-problems with closed-form solutions, and which works with observational data. In this work, we describe the general problem of a BCD-type scheme for computing maximum likelihood estimates in linear structural equation models without hidden variables, integrating multiple observational and interventional environments. With interventional data, the degrees of both the original likelihood equations and the block-coordinate update equations could increase greatly. We study special setups in which the block optimization subproblems have a degree of at most 2 and provide closed-form solutions in these cases. Additionally, we discuss the potential applications of the model and algorithm to health and well-being data.
On Approximation of Lattice-valued Functions Using Lattice Integral Transforms
This paper examines the approximation capabilities of lattice integral transforms and their compositions in reconstructing lattice-valued functions. By introducing an integral kernel 𝑄 on the function…
This paper examines the approximation capabilities of lattice integral transforms and their compositions in reconstructing lattice-valued functions. By introducing an integral kernel 𝑄 on the function domain, we define the concept of a 𝑄-inverse integral kernel, which generalizes the traditional inverse kernel defined as a transposed integral kernel. Leveraging these 𝑄-inverses, we establish upper and lower bounds for a transformed version of the original function induced by the integral kernel 𝑄. The quality of approximation is analyzed using a lattice-based modulus of continuity, specifically designed for functions valued in complete residuated lattices. Additionally, under specific conditions, we demonstrate that the approximation quality for extensional functions with respect to the kernel 𝑄 can be estimated through the integral of the square of 𝑄, and in certain cases, these extensional functions can be perfectly reconstructed. The theoretical findings, illustrated through examples, provide a strong foundation for further theoretical advancement and practical applications.
Virtual neural networks: hundreds of souls in a body
A new concept, termed virtual neural networks, is introduced, where the count of trainable parameters is kept constant, and scalability is attained purely through computational resources. This concept…
A new concept, termed virtual neural networks, is introduced, where the count of trainable parameters is kept constant, and scalability is attained purely through computational resources. This concept is an abstract framework that can be realized using any standard convolutional neural network. It merges siamese neural networks with a deep ensemble technique by generating numerous virtual models that share weights derived from a small set of physical models. The ensemble comprises up to hundreds of trained models simultaneously. All virtual networks take the same input, and their interconnected structure induces an internal distortion that boosts the entire ensemble robustness. The accuracy of the ensemble improves as the number of virtual networks increases, without changing the capacity. Virtual neural networks outperform larger capacity models, typical deep ensembles, and contemporary approaches like SWA and Masksembles. Additionally, the highest performing individual model from the ensemble surpasses other models trained individually, even those with a greater number of parameters.
Assessing quality of selection procedures: Lower bound of false positive rate as a function of inter-rater reliability
Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters…
Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome - the applicant is either selected or not. This final outcome is not considered in IRR, which instead focuses on the ratings of the individual subjects or objects. We outline the connection between the ratings' measurement model (used for IRR) and a binary classification framework. We develop a simple way of approximating the probability of correctly selecting the best applicants which allows us to compute error probabilities of the selection procedure (i.e., false positive and false negative rate) or their lower bounds. We draw connections between the IRR and the binary classification metrics, showing that binary classification metrics depend solely on the IRR coefficient and proportion of selected applicants. We assess the performance of the approximation in a simulation study and apply it in an example comparing the reliability of multiple grant peer review selection procedures. We also discuss other possible uses of the explored connections in other contexts, such as educational testing, psychological assessment, and health-related measurement, and implement the computations in the R package IRR2FPR.
Graded hexagon of opposition in fuzzy natural logic with new intermediate quantifiers
Logical syllogisms with "Almost all, Most, Many, A few" and "Several"
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
From competence to care: digital leadership in eHealth
This article examines the role of digital skills in the health sector, where healthcare social workers perform their professional work, using the Delphi method in two rounds: 2020 (pre-Covid-19 contex…
This article examines the role of digital skills in the health sector, where healthcare social workers perform their professional work, using the Delphi method in two rounds: 2020 (pre-Covid-19 context) and 2021 (Covid-19 context). Experts point out three major transformations in organisations resulting from digitalisation: (i) the growing importance of digital skills; (ii) the relevance of developing a leadership adapted to a digitalisated context, and (iii) the key role of health managers and their organisations. Based on the results obtained, a conceptual approach based on the Shaw et al. (2017) model is proposed to face the challenges of e-Health, explicitly centred on fostering both organisational and individual wellbeing. This leadership model aims to improve the wellbeing of workers in the healthcare sector, including healthcare social workers.
DXAnalyzer
DXAlyzer is a desktop tool for extracting, reviewing, validating, and exporting DXA measurement data from Hologic DXA PDF reports and OCR text exports. The application runs locally, stores data in a l…
DXAlyzer is a desktop tool for extracting, reviewing, validating, and exporting DXA measurement data from Hologic DXA PDF reports and OCR text exports. The application runs locally, stores data in a local SQLite database, and prepares cohort-level CSV tables and SVG figures for research and publication workflows. Features Import DXA reports from .pdf, .txt, .text, and .ocr files. Extract patient identifiers, scan dates, BMD, BMC, T-score, Z-score, fat mass, lean mass, and total mass values. Review and edit extracted records before saving them. Validate measurements with QC status and notes. Compare repeated measurements for the same patient. Export full measurement data to CSV. Generate publication summary tables and subject-level change tables. Export cohort figures as SVG. Manage parser templates for different report formats. Requirements For running from source: Python 3.11 or newer Windows, macOS, or Linux with Tkinter support Python dependencies are listed in requirements.txt. Run From Source python -m pip install -r requirements.txt python main.py Application data is stored locally in: ~/DXAlyzer/dxa.db ~/DXAlyzer/templates/ Windows Executable The Windows executable is built with PyInstaller and published through GitHub Actions. To download it: Open the repository on GitHub. Go to Releases. Download DXAlyzer.exe from the latest release. If there is no release yet, open Actions, run the Windows Release workflow manually, and download the windows-DXAlyzer artifact. Build On Windows From a Windows command prompt in the project folder: build.bat Expected output: dist\DXAlyzer.exe More release and code-signing details are documented in WINDOWS_RELEASE.md. Basic Workflow Import PDF reports or OCR text exports. Review extracted records before saving. Check measurement quality in the QC tab. Run cohort analysis. Export CSV tables and SVG figures. Acknowledgements This software was developed as part of the project Research of Excellence on Digital Technologies and Wellbeing, CZ.02.01.01/00/22_008/0004583, co-funded by the European Union. License This project is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Reference and Solution Architecture for GenAI- and GIS-Enhanced Physical Activity Interventions: Towards Implementing the AI4Motion Platform
Abstract Digital Behaviour Change Interventions (DBCIs) aim at improving individual health by engaging various means of Information and Communication Technology (ICT), including mobile apps and weara…
Abstract Digital Behaviour Change Interventions (DBCIs) aim at improving individual health by engaging various means of Information and Communication Technology (ICT), including mobile apps and wearables. Participant intervention fatigue may happen when DBCIs become too frequent, repetitive, demanding, or lack perceived relevance, and this may result in participants’ reduced motivation and adherence over time. Advancing technology-supported engagement mechanisms is therefore of utmost importance. To address this problem, we present a reference and solution architecture based on open-source technologies and open Application Programming Interfaces (Open APIs). First, we integrated a Large Language Model (LLM) component into the DBCI design. Second, to support context-awareness, we enhanced this integration by adding a Geographic Information Systems (GIS) element. Our pilot implemented AI4Motion platform targets both personalization and contextualization aspects of DBCIs. Our work contributes to the emerging discussion on LLM/GIS-related system design patterns for digital platforms supporting Ecological Momentary Assessment (EMA), Experience Sampling Method (ESM), and Just-in-Time Adaptive Interventions (JITAIs).
Leveraging Generative Artificial Intelligence to Enhance Carbon Performance in Supply Chains Through Green Product Innovation and End-of-Life Product Management: AI-Driven Carbon Performance
ABSTRACT This study illustrates how organizations reconcile their information processing capabilities with uncertainty within the supply chain (SC) through generative artificial intelligence (GAI) to…
ABSTRACT This study illustrates how organizations reconcile their information processing capabilities with uncertainty within the supply chain (SC) through generative artificial intelligence (GAI) to achieve carbon performance (CP). A quantitative research methodology is applied, and 155 responses from manufacturing firms are analyzed through structural equation modeling (SEM) for hypothesis testing. The findings suggest that GAI for process automation and cognitive engagement has a positive influence on business intelligence (BI), whereas end-of-life (EOL) product management mediates the relationship between green product innovation (GPI) and CP. This study contributes to the SC context, focusing on GAI and BI in mitigating uncertainties within SCs to foster GPI and improve CP. This study highlights actionable frameworks for leveraging digital technologies in sustainable SCs by addressing technological challenges and integrating green innovation practices
Assoc Rules Mining and Modeling
Analysis of Participant-Level Characteristics Predicting Adherence to Long-Term EMA and Fitbit Monitoring
This directory contains R scripts, data files, and analysis reports relatedto the analysis of adherence. FILE OVERVIEW DATA FILES* data.xlsx Main subject-level dataset. * data-fitbit.xlsx …
This directory contains R scripts, data files, and analysis reports relatedto the analysis of adherence. FILE OVERVIEW DATA FILES* data.xlsx Main subject-level dataset. * data-fitbit.xlsx Dataset with detailed Fitbit-derived measures. DATA LOADING AND PREPROCESSING* data.R R script for loading and preprocessing the main dataset. * data-fitbit.R R script for loading and preprocessing the detailed Fitbit dataset. DESCRIPTIVE AND BASELINE ANALYSES* summary.Rmd R Markdown document providing a basic description of the datasets. * baseline.Rmd R Markdown document with baseline characteristics and missing-value analysis, including evaluation and imputation of missing values in SWL (new variable SWLlm.predicted). * baseline-by-burst.Rmd R Markdown document with baseline characteristics stratified by burst number. MODELING AND VARIABLE IMPORTANCE* importance.Rmd R Markdown analysis template for evaluating variable importance using stepwise regression and random forest models. PROJECT CONFIGURATION AND BUILD SYSTEM* Makefile.R Project definition for the rmake package; generates the GNU Makefile. * Makefile File dependencies and compilation commands used by GNU Make to generate all project results. * Rproject.Rproj RStudio project file. ------------------------------------------------------------------------------REQUIREMENTS------------------------------------------------------------------------------ 1) INSTALL REQUIRED R PACKAGES Run the following commands in R: install.packages(c( "tidyverse", "knitr", "rmake", "caret", "randomForest", "fastDummies", "broom", "devtools" )) devtools::install_github("beerda/hammer") devtools::install_github("beerda/mbrtools") 2) GENERATE PROJECT ANALYSES Run the analysis pipeline using rmake: make() This command generates all results defined in the project Makefile.------------------------------------------------------------------------------
Remarks on the Universal Approximation Property of Feedforward Neural Networks
Abstract This paper presents a structured overview and novel insights into the universal approximation property offeedforward neural networks. We categorize existing results based on the characteristi…
Abstract This paper presents a structured overview and novel insights into the universal approximation property offeedforward neural networks. We categorize existing results based on the characteristics of activation functions— ranging from strictly monotonic to weakly monotonic and continuous almost everywhere — and examinetheir implications under architectural constraints such as bounded depth and width. Building on classical resultsby Cybenko [1], Hornik [2], and Maiorov [3], we introduce new activation functions that enable even simplerneural network architectures to retain universal approximation capabilities. Notably, we demonstrate thatsingle-layer networks with only two neurons and fixed weights can approximate any continuous univariatefunction, and that two-layer networks can extend this capability to multivariate functions. These findings refinethe known lower bounds of neural network complexity and offer constructive approaches that preserve strictmonotonicity, improving upon prior work that relied on relaxed monotonicity conditions. Our results contributeto the theoretical foundation of neural networks and open pathways for designing minimal yet expressivearchitectures.
Fuzzy rules with quantifiers as weights
Abstract In this paper, we explore the use of General Unary Hypotheses Automaton quantifiers and provide representations for their specific subclasses. Furthermore, we focus explicitly on implication…
Abstract In this paper, we explore the use of General Unary Hypotheses Automaton quantifiers and provide representations for their specific subclasses. Furthermore, we focus explicitly on implicational quantifiers for analyzing specific relational dependencies. We discuss their suitability in fuzzy modeling and demonstrate their integration with appropriate fuzzy rules to create a new class of weighted fuzzy rules. This study contributes to the advancement of fuzzy modeling and offers a framework for further research and practical applications.
Lower and Upper Approximations of Real-Valued Functions and Their Applications to Differential Equations
Abstract This paper investigates the use of fuzzy set theory in approximating solutions to differential equations under uncertainty. By defining lower and upper bounds, a robust framework is develope…
Abstract This paper investigates the use of fuzzy set theory in approximating solutions to differential equations under uncertainty. By defining lower and upper bounds, a robust framework is developed for modeling transitions between function extrema, extending classical methods to fuzzy initial value problems. The study demonstrates universal approximation properties and proposes numerical techniques that ensure stability and convergence. Applications highlight the practical utility of this approach in engineering and computational mathematics, solidifying fuzzy set theory as a powerful tool for addressing uncertainty in mathematical modeling.
A Refined Approach to Interactive Division of Fuzzy Numbers Under Complete Correlation
Abstract This paper introduces an enhanced framework for performing division operations on interactive fuzzy numbers characterized by complete correlation. Unlike traditional methods reliant on the i…
Abstract This paper introduces an enhanced framework for performing division operations on interactive fuzzy numbers characterized by complete correlation. Unlike traditional methods reliant on the independence assumption, we build on the sup-J extension framework to support correlated input fuzzy values. The proposed method establishes precise conditions under which the result aligns with, diverges from, or subsumes conventional divisions such as Zadeh’s and the generalized Hukuhara division. Additionally, we investigate invertibility conditions for the proposed division with respect to multiplication. These refinements offer valuable theoretical insights and have implications for models involving uncertainty, including difference equations.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
Žádné publikace nenalezeny.
