Membership Functions Of Fuzzy Sets Research Articles

Intelligent decision support system for pulmonary tuberculosis detection using bipolar fuzzy utility matrix and bipolar Mamdani fuzzy inference system

Tuberculosis (TB) stands as the second leading global infectious cause of death, following closely behind the impact of COVID-19. The standard approach to diagnose TB involves skin tests, but these tests can yield inaccurate results due to limited access to healthcare and insufficient diagnostic resources. To enhance diagnostic accuracy, this study introduces a novel approach employing a Bipolar Fuzzy Utility Matrix Inference System (BFUMIS) and a Bipolar Mamdani Fuzzy Inference System (BMFIS) to assess TB disease levels. By considering factors associated with the causation of TB, the study devises suitable membership functions for bipolar fuzzy sets (BFS) using both triangular and trapezoidal fuzzy numbers. Using a point factor scale, the study clusters the rules systematically and assesses the level of uncertainty within these grouped rules by utilizing bipolar triangular fuzzy numbers (BTFN). To handle the BTFN, this study proposes converting bipolar triangular fuzzy into bipolar crisp score (CBTFBCS) algorithm as a defuzzification method. The optimal bipolar fuzzy utility sets (BFUS) are determined from the bipolar fuzzy utility matrix to identify patients’ TB disease levels. These sets play a pivotal role in characterizing the severity of TB disease levels in patients. Additionally, rigorous validation of the utility framework is accomplished through measures of bipolar fuzzy satisfactory factors and sensitivity analyses. Furthermore, the study introduces the BMFIS, which presents a novel perspective on the conventional fuzzy inference system. This innovative system integrates the Mamdani fuzzy inference system (MFIS) into a bipolar fuzzy context, enriching the diagnostic process with enhanced insights. To demonstrate the efficacy of the proposed methods, extensive validation is carried out using actual clinical data. The performance metrics used in this validation effectively demonstrate the superiority of the proposed approach.

Neural network analysis of the productivity of biogas plants for small agricultural enterprises

The article is devoted to the problem of assessing the productivity of biogas plants. The aim of the work is to build intelligent tools for evaluating the performance of biogas plants by determining the output of biogas depending on the properties of raw materials based on the fuzzy inference method according to the Sugeno algorithm. First of all, the output of biogas is influenced by the chemical composition of the raw materials used. The chemical composition indicators were obtained by the authors in the framework of experimental studies. To carry out the analysis, a knowledge base was built on the following parameters: humidity, crude ash content, crude fat content, crude protein content, crude fiber content, nitrogen-free extractive substances content. The fuzzification of its vertices in the section of 2- and 3-term sets has been carried out. Membership functions of fuzzy sets for each parameter are constructed. The fuzzification of the root is defined in 5 categories. A system of rules was compiled based on experimental data, and the biogas yield was calculated depending on the initial parameters. The results obtained can be used in the organization of biogas plants.

Исследование методов модификации функций принадлежности нечетких множеств на основе эталонов

Fuzzy set membership functions are widely used to reflect expert preferences in situations of uncertainty. Procedures for modifying membership functions provide the opportunity to obtain new functions based on existing ones without the additional involvement of experts. The work examines existing and proposes new approaches to the construction of modification procedures, methods for their implementation and compensation for the difficulties arising in this case.

Structuring and determining the influence of stakeholders on the innovation ecosystem

In this paper, criteria for the distribution of stakeholders of the innovation ecosystem (IE), such as subsystems, functional features and positions, are formed. Stakeholder matrices and maps have been constructed for monitoring and identifying trends in changes in the rank of stakeholders in the innovation ecosystem. According to the conducted calculations, in addition to quantitative calculations, their qualitative assessments were provided according to linguistic sets. In the process of research, the method of constructing membership functions of discrete fuzzy sets, as cognitive modeling, was used to determine the influence of cause-and-effect relationships. The elements of the matrix of mutual influences of the cognitive map were expertly formed in the modeling process. The purpose of the paper is to identify the stakeholders of the innovation ecosystem, structure them by subsystem categories, sphere and level of influence, to model the interaction of stakeholders within the innovation ecosystem. Understanding the systemic roles and interactions of stakeholders is critical to gaining a more accurate and detailed view of their contributions. A purposeful approach to building an innovative ecosystem allows you to form stakeholders to ensure their effective interaction.

On Testing of Fuzzy Hypothesis for Mean and Variance Using Centroid-Based New Distance Function Under Symmetric Fuzzy Environment

This paper discusses the problem of testing fuzzy and statistical hypotheses of the observed data are from a symmetric fuzzy environment. In this approach, many fuzzy tests statistics are obtained based on fuzzy data with varied forms of membership functions of fuzzy sets. To accept or reject the hypothesis of interest, a decision rule based on a new distance function to find the distance between symmetric fuzzy numbers with many forms of membership functions is proposed. The proposed method is employed to test hypotheses for mean and variance, as well as the difference between the means of a normal distribution and two normal distributions, with both known and unknown variances.

Автоматизація підбору кадрового складу за принципами нечіткої логіки

This article discusses the development of an expert system for personnel selection using fuzzy logic. The system uses a fuzzy set structure and membership functions for each criterion to calculate how well a candidate matches the criteria. The algorithm was implemented in Python and the results show that the system can improve automated recruitment for vacant positions and be developed further as a software product.

Bipolar interval-valued fuzzy set in graph and hypergraph settings

Graphs and hypergraphs are popular models for data structured representation. For example, traffic data, weather data, and animal skeleton data are all described by graph structures. Interval-valued fuzzy sets change the membership function of general fuzzy sets from single value functions to interval-valued functions, and thus describe the fuzzy attributes of things in terms of fuzzy intervals, which is more in line with the characteristics of fuzzy objectives. This paper aims to define the bipolar interval-valued fuzzy hypergraph to reveal the inner relationship of fuzzy data, and give some characterizations of it. The characteristics of bipolar interval-valued intuitionistic fuzzy hypergraph and bipolar interval-valued Pythagorean fuzzy hypergraph are studied. In addition, we discuss the characteristics of the bipolar interval-valued fuzzy threshold graph. Finally, some instances are presented as the applications of bipolar interval-valued fuzzy hypergraphs.

Volatile time series forecasting on the example of the dynamics of the Dow Jones index

The paper discusses a new predictive model of a fuzzy volatile time series, in the framework of which a new approach to the data fuzzification is proposed as the results of observations based on “Sоft Measurements”. As an example, the index of the Dow Jones Industrial Average is chosen, the readings of which are established by usual arithmetic averaging of cоntextual indicators. This allows to consider the daily readings of the Dow Jones index as weakly structured, and to interpret the dynamics of its change as a fuzzy time series. The data fuzzification is realized by applying the fuzzy inference system that provides the values of the membership functions of the appropriate fuzzy sets on the universe covering the set of Dow Jones index for the period from June 15, 2018 to October 10, 2019. The prоpоsed predictive mоdel is based on the identified internal relatiоnships, designed as 1st оrder fuzzy relatiоns between evaluation criteria (or fuzzy sets) that describe weakly structured Dow Jones indexes. At the end of the study, the proposed model is evaluated for adequacy using the statistical criteria MAPE, MPE and MSE.

MODEL OF THE PROCESS OF GEOSPATIAL MULTI-CRITERIA DECISION ANALYSIS FOR TERRITORIAL PLANNING

Context. The process of multi-criteria decision analysis for territorial planning and rational placement of spatial objects, based on modeling the properties of the territory, is considered. Objective. Development of technology for multi-criteria decision analysis for territorial planning based on the apparatus of the theory of fuzzy sets and functions of geoinformation analysis. Method. An object-spatial approach to the formation of a set of alternatives and criteria is proposed, according to which the process of multicriteria decision analysis is divided into two stages: macro- and microanalysis.The macroanalysis stage involves the assessment of the ecological and socio-economic properties of the territory using geomodeling functions. The paper provides a formalized description of the macroanalysis stage, including methods for assessing the qualitative and quantitative impact of spatial objects on the properties of the territory and decomposing objects into thematic layers of criteria. At the stage of microanalysis, the ranking of alternatives is performed taking into account the chosen decision-making strategy. The method of standardization of criteria attributes using fuzzy set membership functions and the modification of the method for calculating the coefficients of relative importance (weights) of criteria, taking into account the spatial heterogeneity of the preferences of the decision maker, are considered. A comparative analysis of the methods for aggregating the estimates of alternatives according to different criteria has been carried out. A feature of the presented technology of geospatial multi-criteria decision analysis of decisions for territorial planning is the possibility of its integration into modern geographic information systems. Results. The procedure of geospatial multi-criteria decision analysis was implemented in the environment of the geographic information system ESRI ArcGIS 10.5 and was studied in solving the spatial problem of rational location of an enterprise. Conclusions. The proposed object-spatial approach to multi-criteria decision analysis makes it possible to explicitly take into account the spatial heterogeneity of geographic data, which is the result of the influence of geographic objects on the properties of the territory. The developed technology can be used to solve a wide range of problems related to determining the most rational placement of various capital construction and infrastructure facilities.

Fuzzy multi-agent assistance system for elderly care based on user engagement

An intelligent system intended to provide assistance to an elderly user in their home is presented. This multi-agent system is designed to monitor the interaction between the user and other agents, and regulate itself based on the estimated level of mental engagement of the user in order to contribute to help them maintain adequate levels of awareness and interaction with their home environment. The agents are devices programmed to preserve the security, comfort and health of the user, who is also conceptualized as one of the agents in the system. The user engagement level is estimated through fuzzy inference, that is, by means of a set of fuzzy membership functions and rules applied over the interaction of the user with different categories of agents. The system incorporates several dozen agents and is tested using two different datasets of real interactions between users and devices in their home environments. A uniform parameter configuration yielded very positive results for diverse scenarios and subsequently the parameters of the system were automatically optimized to show that improved performance, in the form of a more efficient system regulation and increased certainty in adjustment estimation, is obtained.

Soft-sensing of effluent total phosphorus using adaptive recurrent fuzzy neural network with Gustafson-Kessel clustering

To address the issue of soft-sensing of effluent total phosphorus in wastewater treatment processes (WWTPs), a soft-sensing system based on an adaptive recursive fuzzy neural network with Gustafson-Kessel (GK) clustering and hierarchical adaptive second-order optimization algorithm (HAS) is proposed in this paper. In GK-ARFNN, first, the GK clustering algorithm was utilized to cluster the input–output dataset. Thus, the establishment of the initial fuzzy rule base and the determination of the parameter value of the fuzzy set membership function was realized. Then, the recursive layer was added into FNN to improve the dynamic mapping ability of the system. Finally, the HAS algorithm was developed based on the improved Levenberg-Marquardt (LM) optimization algorithm, and all the free parameters of the GK-ARFNN were adjusted online using HAS to improve the generalization capability and prediction accuracy of the soft-sensing system. In addition, the convergence of the proposed GK-ARFNN algorithm was also analyzed in this paper, which can ensure the effectiveness of the solutions to modelling issues for practical industrial processes. The simulation results demonstrate that the GK-ARFNN-based soft-sensing system introduced in this paper achieved satisfactory accuracy in the prediction of effluent total phosphorus in WWTPs. The source codes of GK-ARFNN and some competitors can be downloaded from https://github.com/hyitzhb/GK-ARFNN.

The distributivity of extended uninorms over extended overlap functions on the membership functions of type-2 fuzzy sets

This paper mainly investigates the distributivity of an extended uninorm over an extended overlap function when the uninorm is continuous in (0,1)2. It first studies the distributivity of the extended representable uninorms over the extended overlap functions. Then, it presents the distributivity of the extended uninorms over the extended overlap functions when the uninorms belong to one of the usual classes Ucos,min, Ucos,max.

Real-time deep learning-based market demand forecasting and monitoring

• Develop a CNN algorithm consists of two parts of feature extraction and classification in one model which makes it a unique and practical model in the area. • Develop a model to find the highest effective features for the market demand prediction • Training the CNN hyper parameters using a heuristic model based on PSO . • Considering the very complexity of the market demand in the new competitive environment using a novel fuzzy-based PSO • Use the fuzzy membership concept with aid of PSO to change its parameters dynamically rather than considering constant values. Abstract The concept of market demand forecasting is a very precious and significant problem in the industry without which the generator companies would not be able to give a suitable offer and may experience big losses. This research introduces a novel deep learning based on convolutional neural networks (CNN) to learn the market behavior in details. The model comprises a weight update mechanism in the backpropagation process of CNN to enhance its performance. Moreover, a fuzzy particle swarm optimization (FPSO) based algorithm is used to enhance the CNN performance and find the most accurate predictions. The proposed FPSO would utilize the fuzzy set theory and membership function to update the weighting coefficients . To validate this proposal, real market demand data are used as the benchmark and the results are discussed in the paper. The simulation results prove the suitable performance of the proposed CNN-FPSO model.

RECOGNIZING LEAN SIX SIGMA SOFTWARE PROJECT MANAGER BY FUZZY METHODOLOGY IN SOFTWARE INDUSTRY

The main objective of this research is to design a structure for Identifying Lean Six Sigma Software Manager among software professionals by Fuzzy Sets. Researchers investigated that the software management of six sigma software projects and software management’s dedication are important for the deterrence of failure of them. Because the problem of identification of lean six sigma manager has several and differing conditions, this is MCDM (Multiple criteria Decision Making) software problem. Geometric structure of trapezoidal interval FAHP (Fuzzy Analytical Hierarchy Process) technology. This is several times used techniques, is applied for software company manager identification, membership functions of fuzzy sets. It provides additional degrees of freedom that make it possible to directly model uncertainties. There is no study about the selection of lean six sigma software manager in suitable literature. Software Company is one of the most important sectors for jobs all over the world. Some software companies are contacted and studied their software processes carefully. In Lean Six Sigma Software manager identification process, there are multiple criteria to consider and many candidates. In order to put those software development criteria in numerical presentation and ranking, Fuzzy Analytical Hierarchy Process (FAHP) is a widely used Multi Criteria Decision Making (MCDM) tool. In this article, the planned criteria are Software Project Development Team Leadership-PC1, Software Project Development Sectoral Expertise-PC2, Personal and Software Project Development Environmental Analysis Capability- PC3,Software Training andEducation-PC4. Key Words: Software Manager Selection; Fuzzy Analytical Hierarchy Process; Lean six sigma; Multi criteria Decision Making ; Software Development Processes

Mixed Fuzzy-Logic and Game-Theoretical Approach to Justify Vehicle Models for Servicing the Public Bus Line

One of the main problems to be solved by the transport operators is the substantiation of the vehicle models servicing the transport lines. A gametheoretical approach is proposed in this paper to justify the bus model choice based on the passengers’ preferences and the structure of the passenger flows. To estimate the customers’ preferences, the membership functions for fuzzy sets of the optimal vehicle models were defined. The simulation experiment aiming to estimate the city fleet structure in terms of the vehicles’ capacity was conducted for the Talas city (Kazakhstan) based on the proposed approach with use of the corresponding software implementation of the developed mathematical models. As a result of the experimental studies, the impact of the passengers’ flow structure and the number of carriers on the rational structure of the city bus fleet was studied in the paper.

Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

From the last decade, modelling of Interval Type-2 (IT2) fuzzy controllers has become an exciting area of research in the field of control systems engineering. The input-output relationship of the fuzzy controller gives insights into the exact structure of the controller. From the literature, it is observed that IT2 fuzzy controllers handle plant uncertainty in a better way than their Type 1 (T1) counterparts due to the presence of additional Degree of Freedom (DoF) provided by the Footprint of Uncertainty (FoU) present in the membership functions of Interval Type-2 Fuzzy Sets (IT2FSs). Further, it is also noticed that controllers obtained with non-uniformly distributed fuzzy sets control the uncertain and nonlinear plants in a better way than their uniformly distributed counterparts. To take advantage of these two, in this study, the authors have made an attempt to unveil the exact input-output relationship of an Interval Type-2 Fuzzy PID (IT2FPID) controller, where the modelling is done using a particular type of FoU and non-uniformly distributed fuzzy sets. Apart from modelling, the properties of the newly derived controller are analysed. Moreover, to justify the theoretical development made in this manuscript, the applicability of the controller is shown through simulation, where an unstable chemical reactor plant with a large time delay is controlled. Finally, the effectiveness of the proposed controller is delineated by comparing its performance with that of some recently developed controllers.

A spherical fuzzy TOPSIS method for solving the physician selection problem

The membership functions of the intuitionistic fuzzy sets, Pythagorean fuzzy sets, neutrosophic sets and spherical fuzzy sets are based on three dimensions. The aim is to collect the expert’s judgments. Physicians serve patients in the physician selection problem. It is difficult to measure the service’s quality due to the variability in patients’ preferences. The patients physician preference criteria is differing and uncertainties. Thus, solving this problem with fuzzy method is more appropriate. In this study, we considered the physician selection as a multi-criteria decision-making problem. Solving this problem, we proposed a spherical fuzzy TOPSIS method. We used the five alternatives and eight criteria. The application was performed in the neurology clinics of Konya city state hospitals. In addition, we solved the same problem by the intuitionistic fuzzy TOPSIS method. We compared the solutions of two methods with each other. We found that the spherical fuzzy TOPSIS method is effective for solving the physician selection problem.

Properties of interval type-2 fuzzy sets in decision support systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

Interior Design Scheme Recommendation Method Based on Improved Collaborative Filtering Algorithm

The recommendation engine is similar to the function of the product recommender in our real life, which provides great convenience for people to choose the appropriate decoration scheme in the process of interior design and decoration. A home improvement website or company can design a suitable recommendation algorithm to provide home improvement program recommendation services for users with decoration needs. After understanding the user behavior of the home decoration website, this paper proposes an interior design scheme recommendation method based on an improved collaborative filtering algorithm. The method designs a collaborative filtering algorithm that combines multilayer hybrid similarity and trust mechanisms. Fuzzy set membership function is introduced to correct users’ rating similarity, and users’ interest vector is extracted to calculate users’ preference for different types of items. The algorithm dynamically fuses those two aspects to obtain the mixed similarity of users; meanwhile, the user’s hybrid similarity and trust are fused in an adaptive model. Then, the user neighbor data set generated based on the overall similarity of users is used as a training set, taking the item scores and features into consideration. On the one hand, the users and the projects are taken into account as well. The final prediction score is more accurate, and the recommendation effect is better. The experimental results show that this method can recommend interior design schemes with high performance, and its performance is better than other methods.

Методология построения нейронной нечеткой сети в области информационной безопасности

This paper proposes the use of hybrid models based on neural networks and fuzzy systems to build intelligent intrusion detection systems based on the theory of fuzzy rules. The presented system will be able to generate rules based on the results using fuzzy logic neurons. To avoid oversaturation and assist in determining the necessary network topology, training models based on extreme learning machine and regularization theory will be used to find the most significant neurons. In this paper, a type of SQL injection cyberattack is considered, which actively exploits errors in systems that communicate with the database via SQL commands, and for this reason is considered a kind of straightforward attack. The fuzzy neural network architecture used in detecting SQL injection attacks is a multi-component structure. The first two layers of the model are considered as a fuzzy inference system capable of extracting knowledge from data and transforming it into fuzzy rules. These rules help build automated systems for detecting SQL injection attacks. The third layer consists of a simple neuron that has an activation function called a leaky ReLU. The first layer consists of fuzzy neurons, the activation functions of which are Gaussian membership functions of fuzzy sets, defined in accordance with the partitioning of the input variables. The technique uses the concept of a simple linear regression model to solve the problem of choosing the best subsets of neurons. To perform model selection, the paper used the widely used least angular regression (LARS) algorithm.