Accurately predicting insurance claims is crucial for insurance companies as it directly impacts cash flow, pricing strategies and overall profitability. This paper addresses the critical need for distributional forecasting, particularly for regulatory requirements that necessitate understanding the variability of the claims. To this end, a hybrid model is proposed that integrates the chain ladder (CL) method, machine learning (ML) and fuzzy logic for enhanced claims reserve prediction through three major modules. In the first module, a multi-layer perceptron (MLP) is employed to capture patterns of the losses’ location, and then, CL estimations are imported to a second module using the adaptive neuro-fuzzy inference system (ANFIS). The outputs of the MLP and ANFIS are integrated into a recurrent neural network (RNN), as a kind of ensemble learning approach, in the third module. Specifically, a long short-term memory (LSTM) model is employed to obtain the mean and standard deviation of the loss distribution for each cell in the claims development triangle. Moreover, a module-wise explainability strategy is adopted that combines intrinsically interpretable components with post-hoc analyses for neural networks. Through comprehensive simulations, parameter optimization is addressed, the importance of its key components is validated, and the competitive performance of the method in accurately predicting the outstanding loss liabilities is demonstrated.

A comparative analysis of Reinforcement Learning (RL) and heuristic methods in solving the classic Tetris game, specifically using the Atari Learning Environment (ALE) implementation, is presented in this paper. Three state-of-the-art RL algorithms – Deep Q-Network (DQN), Categorical DQN (C51), and Proximal Policy Optimization (PPO) – alongside a custom heuristic agent are examined. Considerable disparities in performance and computational efficiency between these approaches are revealed by our study. The heuristic agent consistently outperformed the RL methods in both achieved score and computational efficiency within the constraints of our experimental setup. The paper provides insights into the fundamental challenges of applying RL to environments with delayed rewards and demonstrates the advantages of well-designed heuristics in specific problem domains. The challenges faced by RL agents in the Tetris environment, including sparse rewards and high-dimensional state spaces, are discussed. The complexities of applying RL to environments with delayed rewards and the potential advantages of well-designed heuristics in specific problem domains are highlighted by our findings. This research therefore contributes to the ongoing discourse on the applicability and limitations of different AI approaches in complex, real-time decision-making scenarios.

Monitoring healthcare processes, such as surgical outcomes, with a keen focus on detecting changes and unnatural conditions at an early stage is crucial for healthcare professionals and administrators. In line with this goal, control charts, which are the most popular tool in the field of Statistical Process Monitoring, are widely employed to monitor therapeutic processes. Healthcare processes are often characterized by a multistage structure in which several components, states or stages form the final products or outcomes. In such complex scenarios, Multistage Process Monitoring (MPM) techniques become invaluable for monitoring distinct states of the process over time. However, the healthcare sector has seen limited studies employing MPM. This study aims to fill this gap by developing an MPM control chart tailored for healthcare data to promote early detection, confirmation, and patient safety. As it is important to detect unnatural conditions in healthcare processes at an early stage, the statistical control charts are combined with machine learning techniques (i.e., we deal with Intelligent Control Charting, ICC) to enhance detection ability. Through Monte Carlo simulations, our method demonstrates better performance compared to its statistical counterparts. To underline the practical application of the proposed ICC framework, real data from a two-stage thyroid cancer surgery is utilized. This real-world case serves as a compelling illustration of the effectiveness of the developed MPM control chart in a healthcare setting.

The widespread implementation of computer technology has led to an increased use of Machine Vision Systems (MVS) for quality control in advanced manufacturing industries. The application of Statistical Process Control (SPC) techniques, especially control charts, is one of the most important and effective ways for fault detection in this field. Several statistical control charts have been extended to monitor images in the framework of MVS where the major aim is to improve the on-line detection ability, which is equivalent to avoid production of nonconforming products. In various industrial and non-industrial applications, control charts have been shown to be better able to detect anomalies in the underlying process(es) by integrating machine and ensemble learning techniques. However, in the field of image monitoring, approaches based on intelligent techniques have rarely been proposed. To bridge this gap and to improve the detection ability of control charts in monitoring image-based quality characteristics, this paper presents a novel control chart that combines machine learning, ensemble learning and image partitioning. In order to reach the maximum performance in Phase II SPC applications, specific designing and parameter tuning procedures are provided. The superiority of the proposed Partitioning Ensemble Control Chart (PECC) is verified by comparative analysis including conventional monitoring schemes by means of extensive simulations, in which different fault sizes and fault locations are applied to the images. Finally, a real MVS for quality control of O-rings is discussed to illustrate the practical application of the PECC.

In this article, the common arithmetic operations of left–right ($LR$) fuzzy numbers are extended to cases where the left and right shape functions of$LR$fuzzy numbers are different. Extending arithmetic operations to$LR$fuzzy numbers with different left and right shape functions offers several advantages, including a more realistic representation of uncertainty, enhanced expressiveness, flexibility in modeling, improved accuracy, compatibility with real data, and robustness in decision-making. These benefits make such extensions valuable in various applications where uncertainty plays an important role. The addition, difference, multiplication, and division of such$LR$fuzzy numbers are defined as$LR$fuzzy numbers. It is shown that the proposed arithmetic operations satisfy main properties, such as the distributive property of the multiplication operator over addition. The results of these new operators are examined through a numerical evaluation.

In this article, we extend the popular supervised learning technique radial basis function network (RBFN) for regression modeling based on fuzzy responses and exact predictors. For this purpose, we suggest a penalized squared error ridge-based method to estimate the model components including fuzzy parameters and exact tuning constants. The performance of the newly proposed model is examined via established goodness-of-fit criteria and the effectiveness is demonstrated within some numerical application examples. Following the obtained results it is indicative that the fuzzy RBFN regression model outperforms conventional fuzzy nonlinear and multiple regression models and provides more accurate results for nonlinear regression problems.

Abstract In profile monitoring, it is usually assumed that the observations between or within each profile are independent of each other. However, this assumption is often violated in manufacturing practice, and it is of utmost importance to carefully consider autocorrelation effects in the underlying models for profile monitoring. For this reason, various statistical control charts have been proposed to monitor profiles when between- or within-data is correlated in Phase II, in which the main aim is to develop control charts with quicker detection ability. As a novel approach, this study aims to employ machine learning techniques as control charts instead of statistical approaches in monitoring profiles with between-profile autocorrelations. Specifically, new input features based on conventional statistical control chart statistics and normalized estimated parameters are defined that are capable of adequately accounting for the between-autocorrelation effect of profiles. In addition, six machine learning techniques are extended and compared by means of Monte Carlo simulations. The simulation results indicate that machine learning techniques can obtain more accurate results compared with statistical control charts. Moreover, adaptive neuro-fuzzy inference systems outperform other machine learning techniques and the conventional statistical control charts.

Abstract Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on $$\alpha $$ α -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples.

The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID-19 in HIV-infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test.

Nonparametric tests do not rely on data belonging to any particular parametric family of probability distributions, which makes them preferable in case of doubt about the underlying population. Although the two-tailed sign test is likely the most common nonparametric test for location problems, practitioners face serious drawbacks, such as its lack of statistical power and its inapplicability when information regarding data and hypotheses is uncertain or imprecise. In this paper, we generalize the two-tailed sign test by embedding fuzzy hypotheses caused by uncertainty/imprecision regarding linguistic statements on fractions of underlying quantiles. By achieving this objective, (1) crucial limitations of the common two-tailed sign test are mitigated/overcome, (2) various further strengths are incorporated into the sign test (e.g., meeting the trade-off between point- and interval-valued hypotheses, facilitated formulation of fuzzy hypotheses, standardization of membership functions), and (3) shortcomings that often come along with fuzzy hypothesis testing are avoided (e.g., higher complexity, fuzzy test decision, possibilistic interpretation of test results). In addition, we conduct a comprehensive case study using a real data set on the psychosocial status during the COVID-19 pandemic. The results of the case study clearly indicate that the generalized two-tailed sign test is preferable to the two-tailed sign test with point- or interval-valued hypotheses.