Use Of Fuzzy Sets Research Articles

ТЕОРИЯ НЕЧЕТКИХ МНОЖЕСТВ В ИНТЕЛЛЕКТУАЛЬНОМ АНАЛИЗЕ ДАННЫХ

The article is devoted to the application of data mining (KDD) and fuzzy sets to work with large amounts of data. The digital revolution has led to a significant increase in the volume and speed of data, which makes traditional analysis methods ineffective. Data mining covers the stages of purification, integration, transformation and extraction of knowledge from data. Fuzzy logic, which extends Boolean logic, allows for uncertainty and approximate reasoning, which makes it especially useful for processing complex and noisy data. The article discusses in detail the applications of fuzzy sets in tasks such as clustering, associative rule detection, data generalization, time series analysis, and web applications. Fuzzy logic helps solve problems related to incomplete or inaccurate data by providing more flexible and understandable solutions. The author also notes that the use of fuzzy sets improves the adaptation of systems to specific data requirements and features, which contributes to more accurate analysis and decision-making in areas such as healthcare, finance and telecommunications. These advantages make fuzzy sets an important tool for improving the efficiency of data mining and improving user interaction.

Multi-factor fuzzy sets decision system forecasting consumer insolvency risk

The objective of this study is to develop a multi-factor decision system predicting insolvency risk for natural persons with the use of fuzzy sets. Considering that the financial situation of households is affected by various endogenous and exogenous factors, the main assumption of this study is that the system for predicting financial difficulties should not be limited to the use of only a few financial variables concerning consumers, but also include variables describing the environment. The author proposes a system consisting of three different forecasting models that connect the macroeconomic and microeconomic environments. It monitors the economic situation of households by also identifying those environmental variables, which may directly, or indirectly, endanger the consumer, such as unemployment rate (job market situation), inflation and interest rates, exchange rates, or economic situation in the country (GDP growth rate, the dynamics of retail sales, etc.). Moreover, the created cause-and-effect tool is in the form of a flexible application that can be easily adapted to changing economic conditions. Another unique feature of the study is the proposed use of newly developed ratios in household finance, similar to that in financial ratio analysis, which is commonly used in corporate finance. The proposed ratios demonstrated high predictive abilities. The paper also identifies the predictive capabilities of selected macroeconomic variables from the perspective of their impact on the risk of consumer insolvency. The research relies on four samples consisting of a total of 2400 consumers from Taiwan and Poland. The author created three forecasting models separately for the South-East Asian and Central European regions, and two multi-factor systems, each consisting of 1260 decision rules. The findings clearly showed that fuzzy logic is a significantly more effective method compared to traditional models based on classical logic.

The use of fuzzy sets to form the staffing of a medical institution

The timely provision of medical care directly depends on the well-planned time of the medical staff. The use of information systems and decision support systems can improve efficiency and reduce healthcare costs. A difficult problem to solve in medical information systems is the uncertainty of information associated with the failure to meet the conditions for completeness and reliability of incoming information when organizing the work of a medical institution. The use of a fuzzy logic mechanism in decision support systems to assess the staffing of a medical institution will allow taking into account the influence of many factors at the initial decision-making stage, which will contribute to improving the efficiency of the personnel of a medical organization.

A Fuzzy Inference Model to Identify the Current Industry Maturity Stage in the Transformation Process to Industry 4.0

The fourth industrial revolution has been developed and promoted unlike any other. In this regard, the measurement of achievements on every Industry IX.0 is subject to two major sources of imprecision, namely ambiguity and vagueness. In this paper, we introduce an Industry X.0 Fuzzy Inference Engine that, for a given industrial plant, it computes the technological footprint on Industries I1.0–I4.0; i.e., how much technology of each Industry IX.0 is present in that plant, therefore revealing its current maturity level in the transformation process to become an Industry 4.0. The model is scalable, and implements a control strategy inspired in resource allocation problems. It addresses the overlap issues common to I3.0 and I4.0, and assigns each criterion with a distinct importance. Our work stands out for bringing formal analytical methods supported by a theoretical background. To date, no work in the field has ever faced this problem as approached in the paper. Simulation results applied to hypothetical plants show the consistency and effectiveness of the proposed model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The need for leveraging all of the technologies currently available has made industrial plants to retrofit their facilities towards Industry 4.0. In order to properly assess the current stage of this transformation process, in real-world heterogeneous plants, we should measure the implementation extent of each automation technology, while considering where they fit in the industrial timeline. Existing models overlook important features of automated systems, such as control architecture and communication protocols, that among others determine whether a plant qualifies for one or more IX.0. Thus, in this paper we propose a Fuzzy inference engine that allows a thorough assessment and treatment of information, in order to state the current maturity stage (technological footprint) of a given plant with respect to Industries I1.0–4.0. The matrices are scalable, i.e., various plants may be evaluated all together for comparative purposes, the knowledge base can be improved, and other future IX.0 may be incorporated. The use of Fuzzy set and Fuzzy logic provided a suitable framework for modeling, quantifying, and reasoning under imprecise and unclear development stages of a transition for I4.0.

MEDICAL FUZZY-EXPERT SYSTEM FOR PREDICTION OF ENGRAFTMENT DEGREE OF DENTAL IMPLANTS IN PATIENTS WITH CHRONIC LIVER DISEASE

The paper presents an information technology for assessing the degree of engraftment of dental implants in the event of a pathology violation through the use of fuzzy sets, which allows using this method for medical diagnostic tasks. Main scientific results: developed algorithms and mathematical models that formalize the process supporting diagnostic decisions based on fuzzy logic; developed mathematical models of membership functions that formalize the presentation of qualitative and qualitative informational features based on the rules of fuzzy logic, which can be used in information expert systems when assessing the degree of engraftment of dental implants in case of disease with pathological diseases.

Multi-criteria decision methods applied to the assessment of photovoltaic technologies

The aim of this paper is the study and analysis of the decision criteria to be used when searching for the best technology for manufacturing photovoltaic modules, considering both technical and non-technical criteria such as social and environmental factors. Multi-criteria decision making (MCDM) methods will be used for the modelling of the selection problem of the best technology for manufacturing photovoltaic cells. Combining these techniques with the use of fuzzy sets will mean that linguistic labels can be used to value the criteria used.

Simulation model of a patient with type 1 diabetes using fuzzification

Type 1 diabetes is one of the most common diseases. The disease is caused by a lack of insulin secretion from the beta cells of the pancreas, which leads to improper regulation of blood glucose levels. The article presents a simulation model for determining changes in glucose-insulin levels using fuzzy logic techniques. The work concerns a quite simple deterministic simulation model of a digital twin of a type 1 diabetes patient, and fuzzification can significantly improve the efficiency of this model. A series of numerical experiments showed that enriching a simple deterministic patient model with a fuzzy approach gives much more accurate results than the simple deterministic model. The use of fuzzy sets opens up a number of possibilities and is a completely natural approach, resulting from, among others, the specificity of the simulated phenomenon - vital parameters of people with type 1 diabetes.

Multidimensional Analysis of Health Factors and Their Association With Food Insecurity

Objectives: In Mexico, food insecurity is one of the main problems identified as factors that intervene in the decline of population health. For this reason, an analysis of this relationship between food insecurity and loss of health is imperative. The objective of this work can be divided into 2 elements: (1) the analysis of the relationship between food insecurity and factors associated with loss of health, and (2) promoting an alternative methodological tool based on the use of fuzzy inference system. Methods: Two multidimensional indices were calculated: (1) the multidimensional health index, constructed using 6 factors ‐ excess weight, diabetes, high blood pressure, symptoms of depression, kidney problems and heart problems, and (2) the food insecurity index with 3 levels ‐ mild, moderate, and severe. The multidimensional health index is constructed with the use of fuzzy sets, through the National Health and Nutrition Survey (ENSANUT 2019 its acronym in Spanish) in Mexico. Results: There is a close relationship between these indices and a specific profile of individuals in which there is a higher prevalence of health loss in relation to severe food insecurity. Conclusions: This study aims to elucidate the current state of health of the population in Mexico using the most up-to-date data provided by the autonomous public body for statistics and geography to build a multidimensional panorama, as well as the close relationship between food security and the loss of health.

An extended ITARA-TOPSIS method for multi-criteria group decision-making problems based on R-number

With the continuous improvement and development of various decision-making methods, it has led to the widespread use of fuzzy sets and fuzzy numbers. At the same time, the application of decision-making methods in different fuzzy environments has been very effective in addressing the deficiencies in existing research. At present, triangular fuzzy numbers have been widely used in the evaluation aspects of various decision making methods, and the proposed R-number effectively solve the uncertainty involving problems related to future events, but the existing research based on the TOPSIS method in the R-number environment has not yet been clearly applied to the triangular fuzzy number environment, and the indifference threshold-based attribute ratio analysis (ITARA) method in the fuzzy environment has yet to be extended. Therefore, this paper proposes a fuzzy indifference threshold-based attribute ratio analysis (FITARA) method based on triangular fuzzy numbers for solving the problem of determining attribute weights in the multi-attribute decision-making process. Secondly, the various risks of the decision environment and the impact on future events are considered and R-number are used to solve this puzzle. In addition, the incorporation of risk perception factors in the context of the existing RTOPSIS method considering multiple risk factors and the use of Manhattan distances to optimize the large number of operations in the process of the method resulted in the development of the FITARA-RTOPSIS model. Finally, the proposed FITARA-RTOPSIS method is applied to the problem of siting emergency supplies storage depots, and the effectiveness of the proposed method is verified through comparative analysis.

Mathematical Modeling Method for Detecting the Fuzzy Occurrence of Dangerous Events

The article describes a mathematical modeling method for detecting the fuzzy occurrence of dangerous events. A distinctive feature of this study is the assessment of the occurrence of dangerous events based on the use of fuzzy sets. Each dangerous event is associated with a subset of the set of sensors. The data is converted into some characteristics of the occurrence of an event, which are then fed to the input of the membership function of a set of dangerous events. In addition, an example of the application of this mathematical model is given, demonstrating its advantages and possibilities for its expansion. The appendix contains a table of possible dangerous events associ­ated with the functioning of the forest robot. The presented model can also be used to detect the fuzzy occurrence of dangerous events associated with human movement. The developed mathematical modeling method for detecting the occurrence of dangerous events has many applications. In particular, it contributes to the creation of a digital assistant to expand the capabilities of the senses of a remote human operator, and can also be used to control a mobile robot.

FUZZY MODEL FOR TIME SERIES FORECASTING

Abstract: In 2007, in Kazakhstan, there was a transition of TDM (Time Division Multiplexing) circuit-switched technologies to IP (Internet Protocol) packet technology, which created a modern infrastructure for the ICT (information communication technologies) sphere. The advent of the IoT (Internet of Things) concept has led to the growth of a functioning network at a faster rate. It is currently developing in the direction of a cognitive infocommunication network. Its evolutionary development is characterized by a change in the volume of transmitted information, types of its presentation, methods of transmission and storage, the number of sources and consumers, distribution among users, requirements for timeliness and reliability (quality) [1]. Types of traffic and their structure are changing, therefore data processing becomes more complicated. For this reason, the tasks of analyzing and predicting network traffic remain relevant.&#x0D; In this work, the prediction of the measured traffic on a real network is performed. The series under study shows the totality of packets transmitted over the backbone network for each second. Forecasting of a one-dimensional time series is carried out on the basis of fuzzy logic methods. This class of models is well suited for modeling nonlinear systems and time series forecasting. The use of fuzzy sets is based on the ability of fuzzy models to approximate functions, as well as on the readability of rules using linguistic variables. The results of the software algorithm of fuzzy inference models were obtained using the Python environment. Membership functions, predictive graphs were built and their evaluation was carried out. The numerical values of the root mean square error (MSE) are calculated. As a result, it was found that the Cheng fuzzy prediction model has higher forecast accuracy than the Chen forecasting method.

Data analysis using system modeling

Expert systems are increasingly being used to format safe operations. But the functions of expert systems can perform not only assistance in making decisions, but also analyze processes and help at various stages. These actions are possible when considering a system with fuzzy data. The work is devoted to solving the problem of fuzzy inference knowledge in intelligent systems based on the use of fuzzy logic. The scheme of construction of continuous logic, the computation of values of membership functions of linguistic variables of output knowledge. The proposed approach is based on the use of continuous logic, which allows for a more accurate representation of fuzzy data compared to traditional logic. The construction of the continuous logic scheme involves the use of fuzzy sets for both input and output variables, which are then used to compute the values of membership functions of linguistic variables of output knowledge. In this approach, the expert system is able to analyze processes and assist at various stages by making use of fuzzy inference knowledge. The fuzzy inference mechanism is based on the use of fuzzy logic, which allows for a more nuanced understanding of complex systems and processes. The expert system is able to analyze data from various sources and make informed recommendations based on the available information. Overall, the use of expert systems based on fuzzy logic is becoming increasingly popular in a variety of industries. By improving the accuracy of data analysis and decision-making, these systems can help to ensure safe and efficient operations.

РАСЧЕТ ПОКАЗАТЕЛЕЙ НАДЕЖНОСТИ ЗАДНЕГО МОСТА АВТОБУСА В УСЛОВИЯХ НЕЧЕТКОЙ ФОРМАЛИЗАЦИИ ПАРАМЕТРОВ ОТКАЗОВ

The article deals with the issues of constructing a rear axle reliability scheme. On the basis of statistical analysis, estimates of the parameters of the Weibull reliability model for individual axle nodes are obtained, which are the basis for calculating rear axle reliability schemes. For the main nodes that are used in the reliability scheme, the proximity to the Rayleigh model is shown, which is used as the base model. The article proposes an approach for calculating the reliability of a bridge based on the use of fuzzy sets. It is assumed that the parameters of reliability models represent fuzzy numbers. To calculate the scheme on the basis of classical methods, transformations of the membership functions of the parameters of the reliability models of parts are obtained. As a result, reliability indicators such as the probability of failure-free operation, the probability of failure, and others are also fuzzy numbers or fuzzy functions.

Optimization of the structure of filter-compensating devices in networks with powerful non-linear power consumers based on fuzzy logic

&lt;span lang="EN-US"&gt;The article presents a solution to the problem of optimizing the structure of filter-compensating devices (FCD) when installed in high-voltage mine networks with powerful nonlinear electrical receivers. The urgency of the problem of choosing a rational structure of the FCD. The problem of choosing the design and installation location of the FCD is presented. The main technical means of compensation of higher harmonics of currents and voltages in high-voltage networks with powerful nonlinear electrical receivers are considered. Analysis of different types of passive filters (PF) and their frequency properties showed that the choice of specific types of PF refers to the multi-criteria optimization problem. The main methods of optimization of FCD design are considered. The variant of FCD construction based on the solution of multi-criteria optimization problem with the use of fuzzy sets is proposed and justified. To this end, the calculation of PF parameters and frequency characteristics of equivalent systems of the "filter-external network" type for four possible combinations of PF is performed. The optimal is a FCD with two resonant PF tuned to the 11&lt;sup&gt;th&lt;/sup&gt; and 13&lt;sup&gt;th&lt;/sup&gt; harmonics, and a second-order broadband PF tuned to compensate harmonics starting from the 23&lt;sup&gt;rd&lt;/sup&gt; and above. The analysis of simulation results showed effective compensation of higher harmonic currents and voltages.&lt;/span&gt;

Methodology for Determining the Probability of Damage to UAV as a Result of Exposure to Atmospheric Environmental Factors

Introduction. For the effective use of unmanned aerial vehicles (UAV), it is required to take into account the impact of atmospheric environmental factors. Based on the existing level of development of the research and methodological apparatus, it is impossible to determine the probability of damage to the UAV under the conditions of complex exposure to atmospheric environmental factors and to assess the feasibility of further performance of the flight task. Violation of the UAV operation process is caused by the influence of atmospheric precipitation, wind and temperature conditions of the environment. The work aims at the development of a methodology for determining the probability of damage to UAV as a result of exposure to atmospheric environmental factors, as well as to evaluate the performance of the software package implementing the developed algorithm using triangular, trapezoidal, pentagonal, and Gaussian membership functions.Materials and Methods. A technique is proposed that makes it possible, using the theory of fuzzy logic, to determine the probability of damage to the UAV with inaccuracies and uncertainties in the description of atmospheric effects of the environment. It takes into account possible atmospheric forcing and enables to determine the probability of damage to the UAV under various atmospheric influences. The computational complexity of the algorithm implementing the technique depends significantly on the number of qualitative assessments of atmospheric impacts on UAV.Results. A method for determining the probability of damage to UAV as a result of exposure to atmospheric environmental factors based on fuzzy sets (triangular, trapezoidal, pentagonal, Gaussian) was proposed and tested. The use of fuzzy sets for estimating the conditions of the UAV application environment was described. An algorithm was developed to determine the probability of damage to the UAV as a result of exposure to atmospheric environmental factors. A computational experiment was carried out to determine the complexity of calculating the probability of UAV damage as a result of atmospheric forcing under various environmental conditions: «moderate conditions» at a wind speed of 3 m/s, precipitation intensity of 0.8 mm/h, and air temperature of 5 °C; «very heavy conditions» of the external environment at a wind speed of 12 m/s, precipitation intensity 3.5 mm/h, and air temperature of –6 ºС. It was established that the use of triangular membership functions to calculate the probability of damage to the UAV as a result of atmospheric forcing provided higher performance compared to the rest ones (trapezoidal, pentagonal, Gaussian).Discussion and Conclusions. The values of the UAV damage probabilities obtained during the implementation of the methodology under atmospheric environmental influences can be used at the pre-flight preparation stage and during the flight to assess the feasibility of further performance of the flight task. Based on the analysis of the application of the considered forms of membership functions, recommendations for their application are given. The use of algorithms with triangular membership functions will provide high performance of UAV control systems (UAV CS).

Application of the fuzzy data theory in durability estimation

Aim. Problems associated with the study of material fatigue, while being relevant in terms of engineering practice, have a significant degree of uncertainty. The fatigue curve is censored (which indicates the presence of items that have passed the planned load cycle and destroyed by the end of the tests), while the load block made for calculating durability can be designed in a number of ways with a sufficient share of subjective decisions. The load block is intended for calculating durability and defining test plans. It is to fully reflect the entire expected operational history. Both factors are considered in the paper as elements of fuzzy logic. The author examines the creation of a scientifically substantiated load block that would take into account the possible operating modes in a right proportion and taking into account the variability. That is due to the fact that fatigue damage accumulates over the entire life of a machine and is to be scientifically evaluated for an adequate probabilistic assessment. Methods. As the modes of operation of a certain part are not precisely defined (and cannot be defined by virtue of the logic of random use of machines), projections of random fuzzy distributions are considered. A finite set of operating modes in a reasonable proportion was successfully scientifically substantiated. Using the example of load analysis of a critical part of rolling stock, distributions were constructed and the possible distribution of a part’s life was estimated. The output of the developed method will allow assessing the operational risks and predict the required number of spare parts. By taking into account the censored sample elements in the process of fatigue curve construction, the estimation of the fatigue curve parameters can be made more consistent. Conclusions. The use of fuzzy sets may prove to be very useful when examining fatigue curves and estimating durability variation. Examples are given of applying the proposed method.

Green Logistics Partner Selection Based on Pythagorean Hesitant Fuzzy Set and Multiobjective Optimization

With the deepening of the uncertainty and fuzziness of people’s understanding of things, it becomes more convenient to use fuzzy decision making in evaluating schemes. These schemes not only include quantitative data but also consider more and more uncertainty evaluation information. In fuzzy theory, the Pythagorean fuzzy set is extended, both of which are less than or equal to 1, which increases the scope of application. This paper mainly studies the selection of green logistics. Based on the original TOPSIS principle, this paper introduces a Pythagorean fuzzy symmetric cross entropy to describe the difference between two Pythagorean fuzzy numbers and proves its rationality. The model is applied to the selection of green logistics and compared with the results obtained by other different methods, which also shows the effectiveness and practicability of the model. It extends the use of fuzzy sets and can solve some problems that cannot be solved by intuitionistic fuzzy sets before.

ANALYSIS OF MODERN METHODS OF THE FINANCIAL CONDITION OF THE ENTERPRISE EVALUATION

The article investigates scientific approaches to the financial condition of enterprises analysis. The main methods of assessing the financial condition of enterprises are identified. The problem of financial recovery of enterprises in the context of strengthening their financial condition is considered. The essence of financial recovery of enterprises according to different approaches is analyzed, the ways of financial recovery in uncertainty conditions are given. The following methods of economic phenomena research and processes are used: scientific abstraction (theoretical generalizations of the most essential approaches to financial recovery), graphic (schematic visualization of algorithm of realization of financial recovery of the enterprises). The main tasks for a comprehensive assessment of the financial condition of enterprises are indicated. Different approaches to the definition of the category «comprehensive assessment of the financial condition of the enterprise» are analyzed. The advantages of introducing a comprehensive assessment of the financial condition of enterprises have been established. As a result of the existing methods and models analysis for assessing the financial condition of enterprises, it is determined that for the implementation of decision-making procedures there is a need to choose the optimal mathematical apparatus taking into account the specifics of solving a particular financial problem. It is proposed to formalize financial objects on the basis of artificial intelligence devices. In particular, the theory of fuzzy sets allows taking into account the different parameters of the object under study, as well as to stratify the evaluation process and analyze a powerful set of evaluation parameters. The theory of neural networks allows solving the problems of pattern recognition and formation, obtaining and storing knowledge (empirically found regular connections of images and influences on the object of control), qualitative characteristics of images evaluation, decision-making. The theory of genetic algorithms allows the debugging of models that solve the problem of compiling different schedules, forecasting economic processes, designing complex systems and more. It is substantiated that the use of fuzzy sets, neural networks and genetic algorithms in assessing the financial condition of the enterprise is a promising area of financial decision support systems development.

ПРИМЕНЕНИЕ НЕЧЕТКИХ ДАННЫХ В ЗАДАЧАХ ОЦЕНКИ ДОЛГОВЕЧНОСТИ

The author considers the creation of a scientifically based loading unit which would take into account the possible modes of operation in the correct proportion, with due regard for variability and unclearness (fuzziness). It is due to the fact that the fatigue damage accumulates throughout the life of the machine and must be scientifically evaluated for an adequate assessment in the probabilistic aspect. Since the operation of some specific part is not precisely defined (and cannot be determined by the logic of random use of machines during exploitation), projections of random fuzzy distributions are considered. It worked out possible to scientifically take into account a finite set of operating modes in their reasonable proportion. Analyzing the loading of a critical performance part of the rolling stock served as example for construction of distributions and in particular for estimation of the part’s resource distribution. The results obtained on the basis of the developed method will allow assessing the risks of operation and predicting the required number of spare parts. Consideration of the censored sample elements in the construction of the fatigue curve will make the estimation of the parameters of the fatigue curve more consistent. The use of fuzzy sets can be very useful when considering the fatigue curve and when evaluating the durability variation. Examples of application of the proposed approach are shown.

The use of fuzzy sets to determine the parameters of genetic algorithms that provide approximately the same execution time on the CPU and GPU

The problem under consideration consists in choosing the number of k individuals, so that the time for processing k individuals by the genetic algorithm (GA) on the CPU architecture is close to the time for processing l individuals on the GPU architecture by the genetic algorithm. The initial information is data arrays containing information about the processing time of a given number of individuals by the genetic algorithm on the available hardware architectures. Fuzzy numbers are determined based on these arrays?~? and?~?, describing the processing time of a given number of individuals, respectively, on the CPU and GPU architectures. The peculiarities of the subject area do not allow considering the well-known methods of comparison based on the equalities of the membership functions and the nearest clear sets as adequate. Based on the known formula “close to Y (around Y)” the way to compare fuzzy numbers?~? and?~? was developed in order to determine the degree of closeness of the processing time of k and l individuals, respectively, on the hardware architectures of the CPU and GPU.