Fuzzy Variables Research Articles

Modeling a Multimodal Routing Problem with Flexible Time Window in a Multi-Uncertainty Environment

In this study, we extend the research on the multimodal routing problem by considering flexible time window and multi-uncertainty environment. A multi-uncertainty environment includes uncertainty regarding the demand for goods, the travel speed of the transportation mode, and the transfer time between different transportation modes. This environment further results in uncertainty regarding the delivery time of goods at their destination and the earliness and lateness caused by time window violations. This study adopts triangular fuzzy numbers to model the uncertain parameters and the resulting uncertain variables. Then, a fuzzy mixed integer nonlinear programming model is established to formulate the specific problem, including both fuzzy parameters and fuzzy variables. To make the problem easily solvable, this study employs chance-constrained programming and linearization to process the proposed model to obtain an equivalent credibilistic chance-constrained linear programming reformulation with an attainable global optimum solution. A numerical case study based on a commonly used multimodal network structure is presented to demonstrate the feasibility of the proposed method. Compared to hard and soft time windows, the numerical case analysis reveals the advantages of the flexible time window in reducing the total costs, avoiding low reliability regarding timeliness, and providing confidence level-sensitive route schemes to achieve flexible routing decision-making under uncertainty. Furthermore, the numerical case analysis verifies that it is necessary to model the multi-uncertainty environment to satisfy the improved customer requirements for timeliness and enhance the flexibility of the routing, and multimodal transportation is better than unimodal transportation when routing goods in an uncertain environment. The sensitivity analysis in the numerical case study shows the conflicting relationship between the economic objective and the reliability regarding the timeliness of the routing, and the result provides a reference for the customer to find a balance between them.

Intuitionistic fuzzy twin proximal SVM with fuzzy hyperplane and its application in EEG signal classification

Twin support vector machine (TSVM) is a contemporary machine learning technique to tackle classification and regression problems. However, TSVM lacks the ability to differentiate between support vectors and noises since it neglects the positional information of input data samples, and hence it is sensitive to noises. Additionally, it fails to consider uncertainties associated with the data, which reduces its capacity for generalization. To address these drawbacks, we propose a novel fuzzy hyperplane based intuitionistic fuzzy twin proximal support vector machine. The first significant feature of the proposed approach is that it gives an intuitionistic fuzzy number based on the relevance to each data vector. This efficiently reduces the impact of noise and outliers by leveraging the local neighborhood information within the data points by incorporating membership and non-membership weights. Secondly, all the parameters present in the model are fuzzy variables, including the offset term and the elements of the normal vector. The suggested fuzzy hyperplane successfully reflects the inherent ambiguity prevalent in real-world categorization problems by reflecting vagueness in the input data through the use of fuzzy variables. The model’s efficiency is enhanced by solving two systems of linear equations to obtain two non-parallel classifiers rather than solving two quadratic programming problems as in standard TSVM. Utilizing non-linear kernel functions within the feature space enables the method to effectively identify complex patterns or non-linear relationships within the datasets. In order to demonstrate the effectiveness of the suggested approach, extensive computer experiments have been conducted on a set of eighteen benchmark datasets with both linear and non-linear kernels. In addition, rigorous statistical analysis, including Friedman and post-hoc Nemenyi tests, have been employed to assess the significance of the observed performance differences. Furthermore, we also performed numerical experiments utilizing linear, Gaussian, and polynomial kernels to classify electroencephalogram (EEG) signals. The outcomes of the experiment are analyzed in terms of average accuracy, processing time, and F-measure. The results demonstrate that the proposed method outperforms existing methods and achieves better generalization.

Fuzzy decision-making model for automatic mail sorting line

The object of this research is the implementation of fuzzy control in an automated mail sorting line. To decrease the processing time of postal items, automated sorting lines with conveyor belts are used, which carry out transportation to predefined loading points. The principal limitation of such systems is the decision-making model's inherent ambiguity when implementing the designated sorting logic. To overcome these shortcomings, a fuzzy decision-making model for automated sorting lines has been developed. This model allows implementing the sorting logic of postal items to specified loading points under predefined conditions. For this, the fuzzy classification of objects based on their parameters has been formalized, with loading points determined for each class. The fuzzy inference process stages have been formalized based on the Takagi-Sugeno-Kanga algorithm. The input and output fuzzy linguistic variables have been identified, and a rulebase for fuzzy inference has been formalized for fuzzification. For defuzzification, the center of gravity calculation for singletons has been chosen. Three criteria have been defined to implement the sorting logic, facilitated by the fuzzy inference rulebase. The first criterion sorts items to loading points considering cost evaluation, irrespective of weight and dimensions. The second criterion considers weight evaluation independent of dimensions. The third one takes into account the combined evaluation of weight and dimensions. The developed model was tested using the Matlab environment. The simulation confirmed the model's functionality and the sorting management criteria for postal items to loading points.

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

Matheuristics for mixed-model assembly line balancing problem with fuzzy stochastic processing time

Our work aims to investigate methods for solving the mixed-model assembly line balancing problem (MALBP) under uncertainty with the objective of minimizing the number of workstations. Specifically, we model task processing time as fuzzy stochastic variables (FRVs) due to the inherent uncertainties and variations in the manufacturing environment. Additionally, we introduce a ranking method for FRVs and propose a mathematical model to address MALBP. The recently developed Red Fox Optimization (RFO) algorithm is also discretized for the first time to support solving this problem. Finally, matheuristic algorithms combine a metaheuristic such as the popular Genetic Algorithm (GA), Particle Swarm Optimization (PSO), or the Discretized Red Fox Optimization (DRFO) algorithm with the Mixed-Integer Programming (MIP) model to generate the best solution in a reasonable time. Our comparative results demonstrate that the GA-MIP combination outperforms the others in both objective value and computational time.

A prediction method for aircraft icing severity forecast based on probability model and meteorological observation data

Aircraft flight performance and safety are inevitably affected by adverse meteorological conditions, one such weather is icing. Aircraft icing can cause severe aerodynamic and flight mechanical effects, thus threatens aircraft flight safety. This study presents an aircraft icing severity prediction method with probabilistic model, in which meteorological observation data are described as random variables and the airplane icing severity level is defined as fuzzy variables with membership function. When the information of aircraft flying cloud type, altitude, speed, temperature, pressure and dew point temperature is known, the probability of aircraft icing severity during aircraft fly can be effectively predicted by a weighted icing forecasting method. Using the proposed method into two aircraft icing cases, the analysis results show that the proposed method is accurate and valid. It can provide technical support for aircraft icing forecasting.

Multi-objective multi-item fuzzy inventory and production management problem involving fuzzy decision variables

Multi-objective multi-item fuzzy inventory and production management problem involving fuzzy decision variables

Global sensitivity analysis and optimization of multi-stage TEG based on random and fuzzy mixed input variables

In practical engineering, uncertainties in thermoelectric power generation arise from various factors such as material properties, geometric dimensions, assembly processes, and operational fluctuations of the thermoelectric components. Addressing subjective and objective uncertainties in the design parameters of multi-stage thermoelectric generators (TEGs), this study establishes a robust TEG model incorporating non-equilibrium thermodynamics. Fuzzy and stochastic theories are employed for uncertainty representation, and a variance-based global sensitivity analysis is conducted. The results indicate that the uncertainties in the design variables have varying effects on the output responses of the three-stage TEG. Among them, the temperature of the hot and cold sources has the most significant impact on the output responses（STHP: 0.5018, STLP:0.2199, STHη: 0.5436, STLη: 0.3336）, Parameters like Seebeck coefficient, thermal resistance, thermal conductivity, and operating current exhibit relatively minor effects. The coefficient of variation of the output response varies consistently with changes in the standard deviation or coefficient of variation of input variables, following a similar order as the sensitivity indicators. The variations in the distribution parameters of the key design variable, i.e., the temperature of the hot and cold sources, do not affect the sensitivity index rankings of the variables concerning the system output responses. As the distribution parameters of the hot and cold source temperatures gradually increase, the sensitivity indices of the design variables to the system output responses exhibit different trends, indicating a change in the degree of sensitivity to the variations in distribution parameters of the design variables. Optimization based on global sensitivity analysis enhances power output by 43.37 %, reaching a maximum of 11.37 W under constraints compared to the original 7.93 W. This research provides guidance for designing and optimizing thermoelectric power systems under mixed uncertainties.

Projection depth and Lr-type depths for fuzzy random variables

Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate case) and there is a lack of parametric models, a fuzzy extension of depth-based methods is very interesting. In this paper, we adapt the multivariate depths projection depth and Lr-type depth functions to the fuzzy setting, proposing different generalizations for the Lr-type depths. We prove that the proposed fuzzy depth functions have very good properties, obtaining that the fuzzy projection depth is the second example in the literature to satisfy simultaneously the notion of semilinear and of geometric depth. This implies that the fuzzy projection depth is extremely well behave, to order fuzzy sets with respect to fuzzy random variables. Furthermore, we illustrate the good empirical behavior of the proposed fuzzy depth functions with a real data example of trapezoidal fuzzy sets and the used of fuzzy depths in depth-based classification procedures. Finally, as trapezoidal fuzzy sets can be represented by elements of R4, we justify our proposals by also showing empirically the superiority of the fuzzy depths over the multivariate projection depth applied to fuzzy sets.

ДОСЛІДЖЕННЯ ІНТЕЛЕКТУАЛЬНИХ МОДЕЛЕЙ КЛАСИФІКАЦІЇ НЕВИЗНАЧЕНИХ ДАНИХ З ВИМОГАМИ ДОСТОВІРНОСТІ РЕЗУЛЬТАТІВ

The report contains the results of research and development of intellectual models for managing complex systems under conditions of data uncertainty based on classification procedures, which ensure reliable solution of tasks considering the assessment of the boundary dimensionality of models. The possibilities of improving Hamming neural networks for data classification in formats of fuzzy variables and certainty factor CF(A) are investigated. The features of the mathematical model of classification tasks based on a set of feature templates are determined. A software complex of information technology for assignment/selection of performers, as well as determination of authorship of Ukrainian-language works based on classification of sets of templates with certain fuzzy features, is presented. The software complex utilizes the reduction and Cohen's kappa statistics procedures proposed in the report.

Fuzzy Influence Maximization in Social Networks

Influence maximization is a fundamental problem in social network analysis. This problem refers to the identification of a set of influential users as initial spreaders to maximize the spread of a message in a network. When such a message is spread, some users may be influenced by it. A common assumption of existing work is that the impact of a message is essentially binary: A user is either influenced (activated) or not influenced (non-activated). However, how strongly a user is influenced by a message may play an important role in this user’s attempt to influence subsequent users and spread the message further; existing methods may fail to model accurately the spreading process and identify influential users. In this article, we propose a novel approach to model a social network as a fuzzy graph where a fuzzy variable is used to represent the extent to which a user is influenced by a message (user’s activation level). By extending a diffusion model to simulate the spreading process in such a fuzzy graph, we conceptually formulate the fuzzy influence maximization problem for which three methods are proposed to identify influential users. Experimental results demonstrate the accuracy of the proposed methods in determining influential users in social networks.

Fire Risk Assessment Method of Energy Storage Power Station Based on Cloud Model

In response to the randomness and uncertainty of the fire hazards in energy storage power stations, this study introduces the cloud model theory. Six factors, including battery type, service life, external stimuli, power station scale, monitoring methods, and firefighting equipment, are selected as the risk assessment set. The risks are divided into five levels. Membership function is constructed using cloud model. The forward generator is responsible for calculating the complete coefficient matrix and the comprehensive evaluation matrix, while the reverse generator handles the same calculations separately. By utilizing fuzzy synthesis operators and cloud computing, the numerical attributes of the evaluation cloud model are derived, resulting in the creation of a visual representation that illustrates the fire hazard level for energy storage power stations. The results show that the cloud model can be used for fire risk assessment in energy storage power stations. Fuzzy variables can be accurately and clearly represented and corresponded to different safety levels. The effectiveness and feasibility of this assessment method have been verified through case analysis.

Strategic Priorities for the Development of Food Security of the State Taking into Account Hybrid Threats and Challenges

Relevance. Food security is one of the most urgent and complex problems of the modern world. In the context of globalization, climate change, economic fluctuations and other factors, ensuring the stability and reliability of food security is becoming a complex task that requires effective strategies.The purpose is to analyze and evaluate strategic priorities in the field of food security, taking into account complex hybrid threats and challenges. Objectives: identification of strategic alternatives; development of a mathematical model with fuzzy variables and rules for evaluating strategic alternatives; analysis of evaluation results to identify the most effective strategic directions.Methodology. The research methodology included the use of fuzzy logic methods to build a mathematical model for evaluating strategic alternatives.Results. As a result of the study, it was revealed that the strategic alternative S1 received the highest rating, emphasizing its key importance for the sustainability of the food system. Alternatives S7, S9, S4 and S3 also have high ratings, which makes them potentially effective for ensuring food security. Alternatives S10, S8, S2, S6 and S5 are less of a priority, but are important for reducing various risks associated with food security, such as lack of food and vulnerability of supplies.Conclusions. The results of the study allowed us to conclude that the use of the fuzzy logic tool provides an opportunity to conduct a deeper and more comprehensive analysis of complex factors affecting food security. This approach allows us to take into account the uncertainty and multidimensionality of data related to the food system and introduce more accurate modeling of this dynamic area. Such a method enriches the decision-making process in the field of food security, contributing to the development of more effective strategic decisions and management approaches that take into account a variety of factors and their interaction. This contributes to improving the quality of research and helps to form more rational and informed strategies that contribute to ensuring the stability and reliability of food security.

Fuzzy Logic In The Digital Travel Era: Enhancing Tourist Experience Through Comprehensive Hotel Reviews And Sentiment Analysis

In today's society, social media is becoming a more and more important part of our everyday lives as it continues to evolve. Lot of of users assess and tourist rate attractions daily, and hotels play a significant part in travel. Following reviews can be implicated to fuzzy logic, which will be beneficial for resolving the fame of tourist attractions and hotel reviews. Tourists can choose their accommodation and travel destinations with ease based on the outcome of the fuzzy control system. In this research, fuzzy logic has been used to implement sentiment analysis. To provide precise pass on relating to a few aspects chosen by the end user, the system uses attributes including food quality, service, locations, and ratings. This method enables customers to assess a certain hotel service's quality using a variety of factors. Additionally, a user can compare various hotels in depth. To accomplish this, a membership task that specifies how a smooth value maps to the term on a scale of 0 to 1 is used in the proposed system of fuzzy logic. It essentially outlines "how good" something is and how to produce complex behaviour from a condensed, understandable set of professional guidelines before passing these variables to a fuzzy control system. Using a set of rules, a fuzzy control system connects fuzzy variables. These laws are merely mappings that explain the relationships between one or more fuzzy variables. After specifying the inputs and obtaining the priority of the alternatives, the control system is finally simulated. As food preferences, service quality, and user-specific amounts vary, the system is scaled for each individual user. As a result, the system offers more accurate outcomes and increased classification method accuracy for the supplied review data set. Future research will use the Trapezoidal Fuzzy Number (TpFNs) as an evaluation tool to reflect clearly the variation of an element from 0 to 1 in order to increase the model's accuracy.

Optimizing Unit Scheduling with Fuzzy Logic: A Strategic Approach for Efficient Power Network Operations

This study delves into addressing the challenge of resolving the Unit Commitment (UC) problem, which focuses on enhancing the efficiency of production units and devising their operational schedules to accommodate fluctuations in consumption spanning from a day to a month. Given the intricate, combinatorial, and nonlinear constraints associated with each production unit, this study advocates an optimization approach rooted in fuzzy logic. A Langrangian function was established to simplify the UCP and to transform the different inequality into a linear unconstrained problem. The choice of fuzzy inputs was established using the partial derivatives of a Lagrangian function as a function of the powers injected into each node of the electrical network. This combination of the Lagrangian function and the input of the fuzzy regulator made it possible to control the different constraints in the total production cost function and to improve the operating efficiency of the different production units. This method was effectively applied to a 14-bus IEEE power network encompassing 5 generating units, to address the UC problem by optimizing generator load capacity (LCG) and minimizing Incremental Losses (IL). The numerical processing of the fuzzy linguistic variables was implemented using Mamdani-type fuzzy rules. This strategy stands out for its robust exploratory capability, facilitating the identification of optimal solutions to reduce production costs while ensuring optimal planning of production units.

On the Transformation of a Stationary Fuzzy Random Process by a Linear Dynamic System

In this paper, stationary random processes with fuzzy states are studied. The properties of their numerical characteristics—fuzzy expectations, expectations, and covariance functions—are established. The spectral representation of the covariance function, the generalized Wiener–Khinchin theorem, is proved. The main attention is paid to the problem of transforming a stationary fuzzy random process (signal) by a linear dynamic system. Explicitform relationships are obtained for the fuzzy expectations (and expectations) of input and output stationary fuzzy random processes. An algorithm is developed and justified to calculate the covariance function of a stationary fuzzy random process at the output of a linear dynamic system from the covariance function of a stationary input fuzzy random process. The results rest on the properties of fuzzy random variables and numerical random processes. Triangular fuzzy random processes are considered as examples.

Innovative methodology for predicting pipe thickness loss based on electromagnetic flaw detection results

The paper proposes an innovative approach to forecasting based on the results of electromagnetic flaw detection to determine maximum pipe thickness losses over 10-m intervals of the immersion depth of the lower part of a pipe into a well. The main model uses rank transformation applied to a fuzzy regression model with fuzzy input variables and fuzzy output. The input variables include the main parameters of the reservoir in the well (temperature, density, and dynamic viscosity of the hydrocarbon mixture), while the output variable is the maximum loss of pipe thickness in the above–mentioned immersion intervals of the lower part of the pipe. The error of the output forecasts is determined using a numerical procedure to estimate the difference between fuzzy numbers. The forecasting is performed using a sliding method that combines rank fuzzy regression with clear nonlinear regression until the prediction error reaches the specified threshold value. The use of fuzzy regression with fuzzy input and output makes it possible to assess the impact of reservoir parameters on the condition of pipes and the potential for emissions and critical situations. Keywords: Fuzzy LR-type numbers; rank transformation; fuzzy regression; electromagnetic flaw detection; fuzzy outliers; sliding prediction; membership function; pipe thickness loss.

Day-ahead dispatch of electricity-hydrogen systems under solid-state transportation mode of hydrogen energy via FV-IGDT approach

Hydrogen energy has the advantages of being clean and carbon-free, convenient storage, and easy conversion to electrical energy. The use of renewable energy electrolysis for hydrogen production is an important solution to promote clean energy utilization and decarburization in the power and transportation industries. However, hydrogen has a low hydrogen storage density and is prone to explosion. The high cost and risk of hydrogen transportation pose challenges to the promotion and utilization of hydrogen. To address these difficulties, this paper proposes a day-ahead dispatch of electricity-hydrogen systems (EHS) under the solid-state transportation mode of hydrogen energy. Firstly, based on the Van't Hoff equation, the relationship between gas pressure and the reaction temperature is established during the gas-solid conversion process, and a hydrogen energy solid-state transport model based on a magnesium-based hydrogen transport vehicle (MHTV) is proposed. Secondly, a renewable energy uncertainty set is established based on the information-gap decision theory (IGDT) envelope constraint for addressing the uncertainty of renewable energy and a day-ahead bi-level dispatch model of the EHS is constructed based on the solid-state transportation mode of hydrogen energy. Finally, the IGDT approach considering fuzzy variables (FV-IGDT) is presented by using a fuzzy variable membership function, and the proposed bi-level model is transformed into a single-level model for a solution based on this approach. The effectiveness of the proposed model and solution method is verified through simulation on an EHS consisting of a modified IEEE-118 power system, 2 hydrogen production stations (HPS), and 10 hydrogen refueling stations (HRS).

A Multisource Uncertainty Fusion Reliability Evaluation Method for the Control Rod Drive Mechanism of Nuclear Power Plants

The reliability of a pressurized water reactor power plant’s control rod drive mechanism (CRDM) is affected by many factors, such as operation states, unit performance, and dynamic environments. Multiple sources of uncertainties, including random, interval, and fuzzy, exist when analyzing the reliability of CRDMs. Modeling reliability without considering the fusion of multisource uncertainties may result in model distortion and may not provide realistic assessment results. This paper proposes a multisource uncertainty fusion method powered by the margin-based variable transformation and the Bayesian network propagation. The interval and fuzzy variables are transformed into random variables to obtain the corresponding generalized probability density function of the CRDM’s feature parameters. After that, the CRDM’s reliability can be evaluated via probability quantization of the Bayesian network inference result through sampling algorithms. A magnetic-jack type CRDM case is presented to verify the proposed method, and the results show that this method can fuse three types of uncertainty variable in a unified way and effectively obtain reliability evaluation results.

Profiling Social Sentiment in Times of Health Emergencies with Information from Social Networks and Official Statistics

Social networks and official statistics have become vital sources of information in times of health emergencies. The ability to monitor and profile social sentiment is essential for understanding public perception and response in the context of public health crises, such as the one resulting from the COVID-19 pandemic. This study will explore how social sentiment monitoring and profiling can be conducted using information from social networks and official statistics, and how this combination of data can offer a more complete picture of social dynamics in times of emergency, providing a valuable tool for understanding public perception and guiding a public health response. To this end, a three-layer architecture based on Big Data and Artificial Intelligence is presented: the first layer focuses mainly on collecting, storing, and governing the necessary data such as social media and official statistics; in the second layer, the representation models and machine learning necessary for knowledge generation are built, and in the third layer the previously generated knowledge is adapted for better understanding by crisis managers through visualization techniques among others. Based on this architecture, a KDD (Knowledge Discovery in Databases) framework is implemented using methodological tools such as sentiment analysis, fuzzy 2-tuple linguistic models and time series prediction with the Prophet model. As a practical demonstration of the proposed model, we use tweets as data source (from the social network X, formerly known as Twitter) generated during the COVID-19 pandemic lockdown period in Spain, which are processed to identify the overall sentiment using sentiment analysis techniques and fuzzy linguistic variables, and combined with official statistical indicators for prediction, visualizing the results through dashboards.