Construction Of Membership Functions Research Articles

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.

Fuzzy decision-making model for solving the ISAO “risk triangle” in conditions of violation of air-craft separation norms.

Taking into account the prevailing influence of the human factor on the occurrence of the vast majority of aviation events and serious incidents, the leading role of such a component of the current ISAO flight safety concept as “the attitude of aviation personnel towards dangerous actions or conditions” has been determined, which well explains the mutual influence of other components of this paradigm. In turn, the components of this relationship are determined through indicators of the influence of the human factor on decision-making by frontline aviation operators, in particular air traffic controllers. This approach is logical, since, firstly, the professional activity of an air traffic controller is easy to imagine as a continu-ous chain of decisions; secondly, according to statistics, unwanted aviation events are the result of false decisions; thirdly, the vast majority of aviation security experts believe that the point is not that “front line” aviation operators do not make decisions at all, but that these decisions are untimely, incor-rect, ineffective, etc. In the context of this publication, such a component of decision making is considered as fuzzy risk as-sessment models, in particular violations of standard operating procedures, namely aircraft separation standards. Using the modifier “very” and the methodology of fuzzy mathematics, a scale (term set) of the linguistic variable “danger level” was formed. The dimension of the scale is larger than that recommended by ISAO, which allows for a more detailed analysis of the dangers of violations of separation standards. On the other hand, scale reduction does not cause difficulties in the conditions of using fuzzy operations of “concentration”, “stretching”, “merging”. Having adapted the well-known “Cooper-Harper scale” for research needs, a survey was conducted of professional air traffic controllers m = 70, employees of the Unified Air Traffic Control System of the Republic of Azerbaijan, who expressed their attitude to the dangers of violations of the separation norms of ACC, ARR aircraft S = 20 km in the form of a “point on the parameter scale”, which contributed to the use of the so-called “hint matrix” for constructing membership functions of the linguistic variable “hazard level” with smooth falling fronts. It has been established that all points of intersection of the membership functions of neighboring terms of the linguistic variable “hazard level” are greater than the “transition point” of L. Zadeh, therefore the distances between them, established on the continuum of the studied separation norm, “rather belong” to the corresponding linguistic assessment of the established scale. The reduction of this scale to the ISAO dimension contributed to the solution of the corresponding “risk triangle”.

Computation of Flow Coefficient via Non-deterministic Approach of Fuzzy Logic Called "SMRGT" Based on Meteorological Properties

In light of the current global climate changes, floods have emerged as a significant hydraulic and hydrological challenge on a global scale. The primary contributors to the expansion of impermeable areas and the intensification of flood flow are extensive urbanization, the proliferation of concrete edifices and the construction of asphalt thoroughfares. Anticipating the flow beforehand will be conducive to the successful execution of the task at hand. The objective is to reduce the likelihood of harm to individuals and damage to assets. By accurately determining the flow coefficient, which is a significant factor in flood flow, it is possible to mitigate existing issues to a significant degree. Numerous methodologies for modeling flow coefficients can be found in the extant literature. However, most of these methodologies rely on black-box techniques and are not easily generalizable. Hence, the present investigation has opted for a novel methodology; namely, the fuzzy SMRGT method that takes into account the physical characteristics of the phenomenon and is designed to assist individuals who encounter difficulties in selecting the appropriate quantity, structure and rationale of membership functions and fuzzy rules within a given fuzzy set. The data comprising annual precipitation, temperature and relative humidity measurements was acquired from the Regional Directorate of Meteorology. The model outcomes were juxtaposed with the actual observations. Statistical parameters, such as the coefficient of determination (R2 ), the root mean square error (RMSE), the Nash-Sutcliffe efficiency coefficient (NSE) and the mean absolute percentage error (MAPE), were used to evaluate the performance of the model. The statistical test results were: (RMSE: 0.096, NSE: 0.90, MAPE: 17.3, R2 :0.96). The findings suggest that the SMRGT model is highly effective in accurately forecasting the flow coefficient and represents a robust approach for constructing membership functions and fuzzy rules. KEYWORDS: Fuzzy logic, Uncertainty modeling, SMRGT, Flow coefficient, Precipitation, Mamdani fuzzy inference system.

Lexical method for solving a multicriteria problem of selecting a SIEM for building a situational center for cybersecurity

The author considers the creation of a Cybersecurity Situation Center (CSC), its tasks and composition, and also provides the main technological tools that should be included in an effective CSC. Particular attention is paid to the information security incident management system (SIEM), which is key to the CSC, and its purpose and main tasks that it should solve are considered. The authors analyzes the peculiarities of solving the problem of rational selection of a SIEM. The groups of indicators characterizing the degree of fulfillment of the requirements for a SIEM are allocated and their examples are given. The use of fuzzy set theory for processing expert information on qualitative indicators characterizing a SIEM is proposed. The features related to making a rational decision on the choice of a SIEM are analyzed. Groups of indicators that can help in assessing the degree of compliance of a SIEM with the requirements are allocated, and examples of these indicators are given. In order to process expert information on the qualitative indicators of a SIEM, the use of fuzzy set theory is proposed. A formal statement of the problem of selecting a SIEM is presented and the main stages of its solution are proposed, including the preparation of initial data, the choice of a method for solving the multi-criteria problem of rational selection of a SIEM and the development of an algorithm. It is proposed to use the method of normalization of quantitative indicators of a SIEM and the method of pairwise comparisons based on rank estimates to process its qualitative indicators. The use of the Saaty scale with 9 point values to obtain membership functions for the qualitative characteristics of a SIEM based on expert evaluation is considered. An algorithm for constructing membership functions of SIEM characteristics for each fuzzy term is developed. Methods for solving multi-criteria problems are described and the use of the lexical method is proposed to solve the problem of rational selection of a SIEM in the course of building a Cybersecurity Situation Center. An algorithm for its implementation has been created and implemented, and to demonstrate its effectiveness, an example of its use for the rational selection of a SIEM is given. In addition, recommendations for the practical use of the obtained results are given.

Stability of classification performance on an adaptive neuro fuzzy inference system for disease complication prediction

It is crucial to detect disease complications caused by metabolic syndromes early. High cholesterol, high glucose, and high blood pressure are indicators of metabolic syndrome. The aim of this study is to use adaptive neuro fuzzy inference system (ANFIS) to predict potential complications and compare its performance to other classifiers, namely random forest (RF), C4.5, and naïve Bayesian classification (NBC) algorithms. Fuzzy subtractive clustering is used to construct membership functions and fuzzy rules throughout the clustering process. This study analyzed 148 different data sets. Cholesterol, random glucose, systolic, and diastolic blood pressure are all included in the data collection. This learning process was conducted using a hybrid algorithm. The consequent parameters are adjusted forward using the leastsquare approach, while the premise parameters are adjusted backward using the gradient-descent process. The performance of a system is determined by the following indicators: accuracy, sensitivity, specification, precision, area under the curve (AUC), and root mean squared error (RMSE). The results of the training prove that ANFIS is an "excellent classification" classifier. ANFIS has proven to have very good stability across the six performance parameters. The adaptive properties used in ANFIS training and the implementation of fuzzy subtractive clustering strongly support this stability.

Application of Intelligent and Digital Technologies to the Tasks of Wind Energy

The article considers the relevance and issues of wind turbine modeling, the principles of wind energy conversion (WEC) system operation, working areas and regulation. The influence of soft computing technologies on the different aspects of wind power systems, particularly in the fields of operation and maintenance, is considered. This article discusses the recent research, development and trends in soft computing techniques for wind-energy-conversion systems. For reliable analysis, the interaction of the wind-generator operation with the atmospheric boundary layer is considered. The authors give a detailed description of the approaches for the study and numerical modeling of the atmospheric boundary layer (ABL) in the vicinity of a wind farm. The study of the atmospheric boundary layer in the vicinity of the Ulyanovsk wind farm on the basis of cluster analysis of meteorological data is performed. Ten localizations of ABL homogeneous properties are identified. The subject of the study is the application of the results of cluster analysis to set linguistic variables in fuzzy inference algorithms as well as to adjust the initial conditions in the digital model of a wind generator. The results of cluster analysis made it possible to reasonably construct membership functions for the wind speed value in the fuzzy control algorithm to limit the output power of wind turbines. A simulation of the operation of a three-bladed horizontal type wind turbine for the conditions of one of the resulting clusters is performed, and the main regularities of the flow around the wind turbine are revealed. The results obtained are a valuable source for assessing the mutual influence of wind farms and the environment as well as wind farm site development.

Constructing membership function systems using the middle hedge operator

Here, we present an operator-dependent, analytic membership function family that is derived from two soft inequalities by using the so-called middle hedge operator. This operator is defined over a pair of a strictly increasing and a strictly decreasing parametric membership functions that represent two soft inequalities. The middle hedge operator can also be treated as a membership function of an interval on a bounded or unbounded domain. Owing to its construction, the values of this membership function at the end points of the interval, which it represents, are equal to a given parameter value. This parameter may be interpreted as an intersection parameter. That is, if a fuzzy partition of a bounded or unbounded interval is created by using middle hedge operators with a fixed value of the intersection parameter, then each two successive membership functions in the fuzzy partition intersect at the same level. Here, we demonstrate that this new membership function family is very flexible and it can be readily used for constructing a membership function system in a fuzzy control system.

Оценка способов энергообеспечения полуострова Ямал на основе нечеткого многокритериального анализа

Provision of useful energy is the most important condition for realising the potential of underdeveloped regions. For new development areas, including the Yamal Peninsula, there are various energy alternatives. Based on well-known basic approaches, the article presents a procedure for formalising the analysis of alternatives mostly using qualitative initial data. At the pre-project stage, only limited and fuzzy information (predominantly in the form of expert opinions) is accessible. To achieve the set goal, six criteria for export assessment were selected and further processed using fuzzy multicriteria decision-making models based on fuzzy multicriteria analysis of alternatives in order to formalise logical reasoning with vague or imprecise statements. Due to insufficient measurements for constructing fuzzy sets, linguistic estimates of intuitive or logical pairwise comparisons were formalised using the Bellman–Zadeh model, the Saaty scale and the construction of membership functions. The fuzzy set was obtained by finding the eigenvector and the largest eigenvalue for the pairwise comparison matrix. Implementation of the maximin criterion along with the concession matrix allowed us to distinguish between alternatives when obtaining the same or similar estimates. As a result, the study showed the priority of diversification of primary energy source to provide useful energy to consumers in Yamal. According to the model, the most preferable source is atomic energy. In second place are gas turbine technologies, which are significantly ahead of wind energy sources. Diesel generators are considered the least favourable. Thus, the results of fuzzy modelling correspond with the explanatory factors of choice. The fuzzy set method with the transformation of linguistic estimates into quantitative ones can also be included in the apparatus of multicriteria selection with respect to combined options. The research findings can be used to prepare comprehensive strategies and schemes for location of industries and the energy infrastructure in remote Arctic territories.

FUZZY-LOGICAL EXPERT SYSTEM FOR ASSESSING THE FINANCIAL SECURITY OF ENTERPRISES

The purpose of this study is to build a fuzzy expert system for assessing the financial component of the economic security of telecommunications enterprises. The methodological basis of the research is founded on scientific works of domestic and foreign scientists and leading experts in the field of financial analysis and modeling of economic processes, as well as statistical and financial reporting data that are publicly available. To construct an integral indicator of the financial security of an enterprise, a fuzzy conclusion is used. Three financial indicators are used as input variables. The first indicator X1 is the Current Ratio (CR). The second indicator X2 is Equity Ratio (ER). The third indicator is Return on Assets (ROA). The output variable is defined as an indicator of the financial security of an enterprise Y123 (FS). Both the input variables and the output variable are converted to fuzziness by constructing membership functions. The type and parameters of the affiliation function are justified, and the bell-shaped affiliation function is chosen to describe the uncertainty of values that fall under the normal distribution. The quantity of fuzzy sets at every input is considered as z=3 and the quantity of input variables is considered as ω=3. To achieve completeness of the model, the quantity of logic rules is considered as r=33=9. To calculate a degree of market concentration, Mamdani fuzzy conclusion is applied. Defuzzification is engaged to calculate the value of the output variable Y123(FS) for an indicator that determines the degree of financial security of an enterprise and, as a result, the degree of its economic security. To assess the level of the financial security indicator of an enterprise, a fuzzy expert system is constructed. The fuzzy expert system allows you to use various indicators thanks to the fuzzy logic methodology, which takes into account the fuzziness of input variables and output variables as much as possible. For the three telecommunications companies whose core business is wireline communication, ratios are calculated based on financial reports. Financial coefficients are used to determine the integral indicator of financial security of enterprises. This indicator can be characterized by both numerical values and linguistic terms.

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

НЕЧЕТКОЕ УПРАВЛЕНИЕ ИНФОРМАЦИЕЙ И СОБЫТИЯМИ БЕЗОПАСНОСТИ: ОСОБЕННОСТИ ПОСТРОЕНИЯ ФУНКЦИЙ ПРИНАДЛЕЖНОСТИ

The object of the study is methodological approaches to solving the problems of constructing membership functions in the application to decision-making procedures (decision support) for the fuzzy management of information and security events of modern cyber-physical systems. These methodological approaches (methods) allow taking into account the vagueness of the observed and controlled parameters of the protection of complex controlled technical systems. At the same time, the comparative analysis of the approaches under consideration is focused on the most applicable methods for specific tasks - the method of constructing membership functions based on the analysis of probability density functions and the method using a simple probabilistic scheme. Based on the method that uses the analysis of probability density functions, a mechanism for determining the values of membership functions for the problem of making decisions about the relevance of a particular computer attack to a fuzzy set of dangerous attacks (a set of attacks of a high level of danger) is proposed. This mechanism does not have a great mathematical and computational complexity, but it allows us to take into account the fuzziness of the observed and controlled security parameters, which will increase the reliability of monitoring information and security events within the framework of fuzzy security management of systems of this class

The New Fuzzy Analytical Hierarchy Process with Interval Type-2 Trapezoidal Fuzzy Sets and Its Application

The degree of type-1 fuzzy sets membership function cannot express the linguistic variable of a complex problem. The type-2 fuzzy sets as a problem solver such that more fuzziness for constructing membership functions can be handled. Recently, many multi-criteria decision making (MCDM) methods have been expanded using type-2 fuzzy sets. Analytical Hierarchy Process (AHP) is one of the well-known MCDM that can take into account multiple and conflicting criteria at the same time. Our goal is to develop an interval type-2 trapezoidal fuzzy AHP through the new proposed ranking i.e. the modified total integral value. Based on the illustrative examples for trapezoidal type-2 fuzzy sets, the new proposed ranking has a well-performance in ranking. Furthermore, we apply the new trapezoidal type-2 fuzzy AHP to a supplier selection problem. Based on the results of the application, the new fuzzy AHP has the same ranking results as the existing fuzzy AHP.

METHODICAL APPROACHES TO CONSTRUCTION OF FUNCTIONS OF FUZZY MATHEMATICAL MODELS

The paper generalizes scientific and methodological approaches to the development of economic and mathematical models based on the theory of fuzzy logic and linguistic variable. Forecasting and decision support using fuzzy mathematical models allows to summarize and concentrate expert information, to predict the course of processes in various fields, taking into account quantitative and qualitative factors. In comparison with known expert methods, the theory of fuzzy logic has a number of advantages, the main of which are the automation of calculations through the use of mathematical packages, such as Matlab, Scilab; the ability to learn models, use quantitative and qualitative properties of the object of modeling, obtain solutions for various related problems on the basis of one knowledge base filled with expert, analytical and experimental information, and others. It is substantiated that the construction of membership functions is one of the main stages in the construction of fuzzy mathematical models. The main ways in which you can build membership functions depending on the method of obtaining information are considered. Two methods are used to construct membership functions: the involvement of many experts and the involvement of one expert. The method of constructing membership functions involves fassification of fuzzy estimates of influencing factors. The phase of fasification involves the choice of fuzzy terms for the linguistic assessment of the influencing factors given on the corresponding universal sets. The most common membership functions are generalized, which include triangular, trapezoidal, Gaussian, sigmoid. An example of an expert questionnaire is given, which should be used when building a mathematical model based on information from a group of experts. An example of constructing membership functions for a conditional linguistic variable is given. Calculating the eigenvector of a matrix of pairwise comparisons significantly increases the complexity of using a mathematical model. Therefore, we propose to use consistent pairwise comparisons. Despite the fact that in mathematical packages the construction of membership functions is automated, the primary choice of form and characteristics should be carried out by calculation methods considered in the work.

FUZZY-LOGICAL APPROACH TO CONSTRUCTING AN INTEGRAL INDICATOR IN A LEVEL ESTIMATION MODEL SIGNIFICANT MARKET ADVANTAGE

The purpose of this research is to construct fuzzy expert system to estimate an integral degree of market concentration by fuzzy-logical approach. The methodological basis of the study consists of scientific works of domestic and foreign scientists and leading specialists, statistical and analytical materials of state authorities. Fuzzy Inference is introduced for the integrated indicator construction. Two indicators are chosen as input variables. The first indicator, CR, is a level of concentration ratio. The second indicator, HHI, is the Herfindahl-Hirschman index. Output variable, MC indicator, means a degree of market concentration. Both input and output variables are transformed to fuzziness through the construction of membership function. The function type and parameters are substantiated and “bell”-shaped membership function to describe uncertainty of the values falling under normal distribution is chosen. The quantity of fuzzy sets at every input is considered z=3 and the quantity of input variables is considered ω=2. To achieve completeness of the model, the quantity of logic rules is considered r=3²=9. To calculate a degree of market concentration, Mamdani fuzzy conclusion is applied. Defuzzification is engaged to calculate value of the output variable which is MC indicator to mean a degree of market concentration and therefore readiness to implement the innovation strategy for enterprises active in innovation. To estimate a degree of market concentration, the fuzzy expert system given allows for engagement of different indicators due to fuzzy logic methodology which considers fuzziness of the input and output variables. The construction of an integral indicator for assessing the state of economic competition in order to establish the feasibility of identifying operators and providers with a significant market advantage will improve the assessment of the state of economic competition in the market in the telecommunications services market in Ukraine.

Generating Clustering-Based Interval Fuzzy Type-2 Triangular and Trapezoidal Membership Functions: A Structured Literature Review

Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption. Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function which mainly focused on producing Gaussian membership function. The other two important membership functions, triangular and trapezoidal, are constructed using the grid partitioning method. However, the method suffers a drawback of not being able to represent actual data composition in the underlying dataset. Some research proposed triangular and trapezoidal membership functions construction using readily formed Fuzzy Type-1 membership functions, which means it remains unclear how the membership functions are heuristically constructed using fuzzy C-Means outputs. The triangular and trapezoidal membership functions are important because previous works have shown that they may produce superior performance than Gaussian membership function in some applications. Therefore, this paper presents a structured literature review on generating triangular and trapezoidal Interval Fuzzy Type-2 membership functions using fuzzy C-Means. Initially, 110 related manuscripts were collected from Web of Science, Scopus, and Google Scholar. These manuscripts went through the identification, screening, eligibility, and inclusion processes, and as a result, 21 manuscripts were reviewed and discussed in this paper. To ensure that the review also covers the important components of fuzzy logic, this paper also reviews and discusses another 49 manuscripts on fuzzy calculation and operation. Furthermore, this paper also discusses the contributions of the conducted review to the body of knowledge, future research directions and challenges, with the aim to motivate the future works of constructing the methods to generate Interval Fuzzy Type-2 triangular and trapezoidal membership functions using fuzzy C-Means. The methods imply flexibility in choosing membership function type, hence increasing the effectiveness of fuzzy applications through leveraging the advantages that each of the three membership function types could provide.

ПОБУДОВА НЕЧІТКОЇ ЕКСПЕРТНОЇ СИСТЕМИ ДЛЯ ОЦІНЮВАННЯ РІВНЯ СУТТЄВОЇ РИНКОВОЇ ПЕРЕВАГИ

Identifying operators with significant market power as an element of state regulation in the field of telecommunications solves one of the key tasks for the national regulator – identifying business entities that may be subject to tariff regulation to limit monopoly power. Unlike existing methods, especially when a telecommunications operator operates simultaneously in several service markets, this method provides a comprehensive analysis of the state and degree of power of the operator – the share that a monopolist can simultaneously hold. The developed algorithm for comprehensive analysis of the telecommunications market of operators in the markets of telecommunications services forms an important component of analytical tools for collecting, processing and calculating at the level of the national regulatory body. The methodological basis of the study, consisted of scientific works of domestic and foreign scientists and leading specialists, statistical and analytical materials of state authorities. Fuzzy Inference is introduced for the integrated indicator construction. Two indicators are chosen as input variables. The first indicator CR is a level of concentration ratio. The second indicator HHI is a Herfindahl-Hirschman index. Output variable is defined as MC indicator which means a degree of market concentration. Both input variables and the output one are transformed to fuzziness through the construction of membership function. The function type and parameters are substantiated and “bell”-shaped membership function to describe uncertainty of the values falling under normal distribution is chosen. The quantity of fuzzy sets at every input is considered as z = 3 and the quantity of input variables is considered as ω = 2. To achieve completeness of the model, the quantity of logic rules is considered as r = 3² = 9. To calculate a degree of market concentration, Mamdani fuzzy conclusion is applied. Defuzzification is engaged to calculate value of the output variable which is MC ‒ indicator to mean a degree of market concentration and therefore readiness to implement the innovation strategy for enterprises active in innovation.

Intelligent system of identification of local area network state

This article considers the problem of diagnosing local area network, as well as the task of structural determination is the creation and easy adjustment of the model object by building the knowledge base of available expert information. The algorithm of formalization of knowledge in designing intelligent systems is reviewed and proposed. The article considers the theory of fuzzy sets and fuzzy logic. The concept of the theory of fuzzy sets and fuzzy logic are formalized in the form of fuzzy and linguistic variables, and the vagueness of certain operations in the overall decision-making process is synthesized in the form of fuzzy algorithms. For the effective solution of tasks of type analysis and hypothetical sources of network problems in a local area network, a method of constructing membership functions based on analytical processing of the results of expert surveys is used.

Multi-level Qualitative Reasoning Logic

Qualitative reasoning is a very efficient method that people often use to solve problems. Recently, the literature about qualitative reasoning as a causal analysis and decision-making tool has been emerging. However, the existing qualitative reasoning methods are mainly used for the modeling of imprecise problems. There are not many studies on formalization tools of qualitative “inference”. This paper proposes a logical system for qualitative reasoning (QRL). The main research contents include: the grammar and semantic structure of QRL are given; the meaning of formula logic truth value in QRL and its assignment rules are discussed; and the reliability and completeness of QRL are proved. Compared with fuzzy logic, probability logic and other uncertain reasoning methods, the advantage of QRL method is that it can use axiomatic reasoning method, and does not need to construct membership functions and collect a large number of samples.

Power quality comprehensive evaluation method based on fuzzy mathematics and cloud theory

In the comprehensive evaluation of power quality, there exist problems such as the boundary of evaluation index classification and weight distribution which is too subjective or objective. Based on the theory of fuzzy mathematics and cloud, the power quality comprehensive evaluation method was proposed to solve the two problems. This method improves the traditional fuzzy comprehensive evaluation method through variable weight theory and cloud theory, which are fixed weight calculation and membership function construction. Firstly, the superposition variable weight construction method of excitation type in variable weight theory is selected to calculate the weight vector. Secondly, the normal cloud model in cloud theory is used to construct the membership function to comprehensively evaluate power quality. Compared with the traditional fuzzy comprehensive evaluation method, the improved fuzzy comprehensive evaluation method solves the influence of the actual situation of evaluation factors on the index weight and avoids the influence of subjective factors in the membership function construction process of the traditional fuzzy comprehensive evaluation method, making the evaluation results more reasonable and credible. Finally, a practical example is given to prove that the model is more accurate and reasonable.

RESEARCH OF THE BANKRUPTCY PREDICTION RELIABILITY IN CASE TO INTRODUCE A NEW CATEGORY OF THE COMPANIES FINANCIAL POSITION

The motivation for this research was the result obtained earlier by the authors in the field of developing industry models for predicting bankruptcy with high prognostic ability. The article examines the prediction reliability of the financial position of companies in the case of introducing an additional category of financial position that reflects the position between financial solvency and insolvency (bankruptcy). The authors hypothesize that the reliability of models decreases if the requirements for their accuracy increase due to the introduction of an additional category of financial position. Hypothesis testing is performed using a non-entropic approach. This approach should reduce the measure of uncertainty in terms of the uncharacteristic nature of some of the identified features of financial position relative to the initial categories. At the same time, features of financial position are defined as ranges of specific weight of balance sheet items that have positive or negative information importance. Information importance is determined based on the methods of system-cognitive analysis, implemented automatically in the EIDOS X++ system, as well as by reproducing information models using MS Excel tools. Normalization of the informational importance values of features and their interpolation allowed us to obtain functions similar to the membership functions in the theory of fuzzy sets. When constructing membership functions relative to ranges of significant balance sheet items ("Fixed assets", "Inventory", "Accounts Receivable", "Short-Term financial investments", "Retained earnings (uncovered loss)", "Accounts payable"), ranges with zero or insignificant values of characteristic functions corresponding to the initial categories of financial position are identified. This actually meant a high level of uncertainty in the prediction. The authors propose to introduce additional linguistic variables and their corresponding fuzzy sets, whose carriers are the relative scales of the above balance items, this will reduce uncertainty. A total of 5 such fuzzy sets were identified, where the researchers used the concept of "gray zone" as a linguistic variable, which was actually used as a new category of financial position. All calculations are shown on the example of fixed assets. The prognostic ability of models based on an optimized sample, where the category of the position of companies that have at least 3 out of 5 features of the "gray zone" has been replaced, is reduced, as expected, but only slightly. And in the case of reproducing algorithms of system-cognitive analysis using MS Excel tools, there is even an increase in the prognostic ability of one of the models. In fact, the hypothesis that the reliability of models decreases if the requirements for their accuracy increase was not confirmed. From an economic point of view, the theoretical significance of the obtained result is that with the help of a non-entropic approach it was possible to show the need to introduce a new category of financial position. From a mathematical point of view, the theoretical significance lies in the fact that membership functions for linguistic variables are obtained based on real data on the financial position of almost two hundred Russian companies, these reduction functions can be used by specialists in the field of fuzzy set theory in the future. The results obtained are applicable at least for the construction industry, but can also be replicated relative to other sectors of the economy when forming the corresponding samples.