Multi-criteria Selection Problem Research Articles

Information System for the Selection of Hydropneumatic Capacitive Vessels

This article describes an algorithm for the automatic selection of hydropneumatic capacitive vessels used for household and industrial purposes. The suggested informational system makes it possible to reduce the working time spent on the selection of equipment and increase the relevance of the analyzed information. The article discusses a detailed description of the design of pneumohydroaccumulators, as well as provides examples of calculations of their main characteristics. The main task we needed to solve was a multi-criteria choice, and the article provides an overview of methods for solving this problem. In addition to these methods, we analyzed information systems that allow one to select suitable equipment among various alternatives. Based on the analysis of methods and similar software solutions, the authors suggested an information system and an algorithm for automatic selection of hydraulic accumulators by searching for options that meet the parameters specified by the system user. Also, the article discusses the process of purchasing capacitive equipment. There was demonstrated a logical model of the database structure storing the technical characteristics of the equipment which reflects objects of the information system and their connections. In this article we presented and argued the software for development of a specified information system. The development of the information system was based on the "1С platform: The enterprise". The task of selecting hydropneumatic capacitive vessels was solved by a request that can be interacted with through a report in the information system. This report allows the user to search for equipment by quantitative and qualitative characteristics: volume, operating pressure, vessel material, flange material, installation type (vertical or horizontal), availability of legs, cost, manufacturer or supplier. The report options allow users to search for equipment both in accordance with the specified parameters and with a deviation from them but only if the parameter is quantitative. The results of the report are ordered by relevance to the criteria specified by the user. The operation of the report query aggregating data was reflected in the flowchart. The article presents a situation where the user solves the selection problem by using capabilities of the report. The problem of multi-criteria selection was formulated in a way to demonstrate how a clear parameter of the report becomes fuzzy, and our solution of it allows you to find more alternative options with sorting by relevance helping you to identify the most suitable pneumohydroaccumulator. This software package was registered in the state registry of computer programs.

Resource-aware multi-criteria vehicle participation for federated learning in Internet of vehicles

Federated learning (FL), as a safe distributed training mode, provides strong support for the edge intelligence of the Internet of Vehicles (IoV) to realize efficient collaborative control and safe data sharing. However, due to the resource limitation and the instability of training environment in the complex IoV, ideal performance of FL cannot be achieved. Since considering the actual resource constraints and federated task requirements, the diversified device selection criteria make the resource-aware vehicle selection problem become a multi-criteria selection problem. To effectively support FL for IoV, the resource-aware multi-criteria vehicle selection problem was described as a many-objective optimization problem, and a resource-aware many-objective vehicle selection model (RA-MaOVSM) is proposed to optimize resource efficiency. The RA-MaOVSM considering heterogeneous resources (like computation resources, communication resources, energy resources and data resources) of on-board devices in IoV, and realizes the joint optimization of learning efficiency, energy cost and global performance. Additionally, a novel probability distribution combination game strategy is applied to many-objective evolutionary algorithm (MaOEA) for improving the model solving performance. Simulation results demonstrate that RA-MaOVSM can effectively optimize the IoV resources and FL model performance, and the designed algorithm exhibits good convergence and distribution, achieving a good balance among multiple device selection criteria.

Model-algorithmic support for socio-cyber- physical systems scheduling functioning

Goal. Development of model-algorithmic support for solving problems of socio-cyber-physical systems scheduling. Materials and methods. To achieve this goal, the authors used the methodology of the theory of structural dynamics proactive control of complex objects and the system-neocybernetic approach. Results. An approach (model and algorithm) is proposed, within the framework of which it is possible to approach the formalization and solution of multicriteria selection problems arising at various stages of the life cycle of complex organizational and technical complexes from a unified position. Such tasks, first of all, include the task of dynamic structural and functional synthesis of socio-cyber- physical systems schedules. Conclusion. The approach considered in the article is based on the concepts of system modeling and multi-criteria selection.

Trends in the development of digital subscription services in international markets

Companies are trying to harness the potential of the current stage of development of the digital industry and make it cost-effective, which requires not only technological innovation but also the transformation of many existing business models. Based on an analysis of examples of digital subscription companies, this article provides additional explanations, including definitions and constituent characteristics of digital subscription business models. The aim of the article was to identify trends in the development of digital subscription services by analysing the number of active subscribers and the impact of COVID-19 on this indicator. Autoregression and analysis methods were used in the study, and the implementation of the selected models was carried out using the Python-3 programming language. The article describes a theoretical basis that determine the feasibility of using the subscription model for the company under non-deterministic critical conditions. The main approaches to forecasting the company’s performance indicators are identified. The type of data to be forecasted is determined, and the necessity of using autoregressive models for further analysis is declared. Factors associated with the COVID-2019 incidence that should be considered as exogenous variables were identified. The multicriteria selection problem was constructed by restricting the family of autoregressive models and determining the criteria for forecasting and data preparation time, forecast accuracy, and the possibility of considering external factors in determining the algorithm efficiency. It is found that moving average autoregression is the most effective. Given the further application of this algorithm to predict the number of subscribers, the expediency of implementing a subscription strategy for the company under non-deterministic critical conditions is declared. It is possible to effectively apply the selected mathematical model to predict the performance of a subscription company. The practical significance of the work lies in the possibility of creating certain benchmarks for the development of the market and a business strategy for product promotion, which will be based on an understanding of the potential benefits and threats of the market for digital subscription products and services

Quantitative Methods of Selecting a Tool for Project Management in the Financial Sector

The relevance of the study is due to the difficulties inherent in the selection of tools designed for effective project management in the financial sector, as well as the increasing competition in the financial services market. Within the framework of this article, the features of the choice of a project management tool in the financial sector based on the use of quantitative methods that make the decision-making process significantly more meaningful and effective are disclosed.The aim of the study is to develop elements of a methodology for quantitative analysis of alternative tools, including recommendations on the choice of alternatives and criteria for their analysis, as well as the complex use of various methods to justify the final choice of an instrument.The research materials and methods reflected in the methodology of quantitative analysis of alternative project management tools in the financial sphere, and implemented in the course of the research, are based on supplementing the results obtained through the use of the classical basic level method – the method of geometric averages by methods of advanced level decision theory – the method of eigenvalues and vectors, as well as the ideal point method. In order to comprehensively analyze the project implementation support systems on the market and their instrumental capabilities, a twostage methodology is proposed in the research process, including both qualitative and quantitative assessment of available alternatives. The formalized assessment of the functionality of the pre-selected tools made it possible to justify the choice of the most preferred alternative. Particular attention is paid to the issues of attracting additional information to reduce uncertainty in the considered choice situation. Results. The main result of the conducted research was the scheme of substantiation of the optimal choice of a tool includes the construction of a variety of alternatives – tools of domestic and foreign development, the construction of a variety of criteria and the attraction of additional information to form a hierarchy of criteria, as well as a consistent quantitative assessment of each selected alternative according to all the criteria under consideration. The constructed set of alternatives includes the tools of Jira Software, Asana, Bitrix24, Megaplan, GanttPro, YouGile and Planfix. The set of criteria is limited to the six most significant criteria: “Convenience of communication within the framework of the tool”; “Price of the tool”; “Level of complexity of the tool”; “Integration with external services”; “Functionality of the tool”; “Convenience and simplicity of the tool interface”. The presented system of criteria takes into account the main functional and instrumental characteristics necessary for systems to support the implementation of projects in the financial sector at the level of small and medium-sized businesses.Conclusion. The content of the article can be useful for improving decision-making processes during technological renewal and digitalization of projects in the financial sphere of small and medium-sized businesses in the context of the implementation of import substitution programs, the development of optimal choice mechanisms under several criteria. The described structure of the applied problem of multi-criteria selection can be used to update the content of such professionally significant academic disciplines for higher economic school as “Decision Theory” and “Instrumental methods in Economics”.

MODELING OF INFORMATION SECURITY SYSTEMS BASED ON MULTICRITERIA OPTIMIZATION ALGORITHMS

The system of ensuring the information security of an object is considered as a multicriteria task of choice. The possibility of applying multicriteria optimization methods to the design of an infocommunication facility protection system is analyzed. Formalized procedures for solving a multi-criteria selection problem are presented; algorithms for calculating and justifying the choice are shown.

Problems of optimization and choice of options for the creation and application of complex organizational and technical complexes

Goal. Development of a generalized approach to formalization and solution of various classes of multicriteria selection problems for subsequent use of the results obtained in the creation and use of appropriate support systems and management decision-making. Materials and methods. To achieve this goal, the authors of the article used the methodology and methodological foundations for solving the class of problems under consideration, which were developed at the present time in the interdisciplinary branch of system knowledge. Results. An approach is proposed in which it is possible to approach the formalization and solution of multi-criteria selection problems arising at various stages of the life cycle of complex organizational and technical complexes from a unified position. Such tasks, first of all, include the tasks of group selection, vector optimization, cascade (hierarchical) selection, coordination and game selection. An example of solving the optimization problem is given, illustrating the advantages of the proposed approach. Conclusion. The approach considered in the article is based on the concepts of system modeling and selection with multi-consideration in conditions of uncertainty of environmental impact, based on the theory of mathematical structures by N. Burbaki.

Narrowing the Pareto set on the basis of fuzzy information about the ratio of ODA preferences

A multi-criteria choice model is considered, which includes a set of possible options, a numerical vector criterion and a fuzzy binary preference relation of the decision-maker person (DPR). The task of multi-criteria selection is to choose one or more "best" options from the Pareto set, that is, to narrow this set taking into account the information about the preference ratio of the DPR. Narrowing is carried out according to the axiomatic approach. The paper considers the algorithm for narrowing the Pareto set based on an arbitrary finite set of "quanta" of fuzzy information about the preference ratio of the DPR. Accordingly, an algorithm is proposed that allows, on the basis of an arbitrary set of clear information, to construct an estimate from above for an unknown set of options to be chosen, that is, to narrow the Pareto set. The purpose of this paper is to extend this algorithm to the case of a fuzzy preference relation, where the DPR assigns different degrees of certainty to its reasoning. In the fuzzy case under consideration, the set of options to be chosen and the top estimate constructed for it are also fuzzy. In the first section of the article, the statement of the problem of multi-criteria selection is presented and the basic axioms are formulated. The second chapter is devoted to the description of the reduction of this task to the geometric problem of constructing a fuzzy double cone. In the third section, a generalization of the algorithm is given, which makes it possible to construct the generators of a fuzzy double cone. Based on these constituents, a new vector criterion is constructed, the Pareto set with respect to which is the desired narrowing of the original Pareto set. An illustrative example is considered in the fourth chapter.

CONSTRUCTION OF MULTI-CRITERIA SOLUTIONS TO SELECTION PROBLEMS

An approach to solving the problems of multi-criteria selection with the determination of suitable applicants based on the values of a number of criteria is considered. Known approaches to the solution of these problems do not always allow determining reasonable solutions with full consideration of the features of the selected criteria and their evaluation conditions. Comparison of evaluations by criteria often takes place from subjective positions without proper justification, which affects both the results of the selection and the possibilities of their practical application. Known multi-criteria selection procedures use fixed measurement scales to compare values, which in practical situations may not correspond to real ratios of indicators. Another significant shortcoming of these procedures is ignoring the presence of non-linear dependencies between evaluations by criteria and attributes of decisions made in different ranges of their values. The above indicates the possibility of obtaining inadequate evaluations of decisions with corresponding negative consequences. The paper proposes an approach to the construction of solutions to multi-criteria selection problems based on the definition of applicants by ordering them according to the degree of approximation to the option with the best ratios of evaluations according to the selected performance criteria based on iterative concessions according to the specified criteria. Applicants are compared on the basis of the ratios of assessments according to the agreed criteria, the definition of which is provided by a set of mathematical models that reproduce the dependence of the values of individual criteria on the attributes of the applicant decisions. The formation of a sequence of candidates for solutions is based on the results of comparisons according to individual criteria, which allows to determine alternative solutions and evaluate their effectiveness with the construction of a Pareto subset. An example is considered that reproduces the processes of choosing alternative options for building a virtual data processing system based on the characteristics of virtual machines from providers of cloud processing technologies. The obtained research results indicate the possibility of using the proposed approach as part of decision-making support subsystems to solve the problems of operational management of dynamic service and production processes.

The hybrid mathematical model for the evaluation and selection of iron ore raw materials in the context of the European Green Deal

The actual scientific research on the development of the hybrid mathematical model for evaluating and selecting iron ore raw materials in the context of the EU Green Deal is carried out. The necessity of developing decision support systems within the framework of the EU Green Deal concept is substantiated, in order to increase the degree of validity of decision-making in the evaluation space, regarding the green course and achieving the goals of the green agreement. For the first time, a systematic theoretical-multiple model of the problem of evaluation and selection of iron ore raw materials, according to the proposed factors of chemical composition, cost, and environmental policy of the manufacturer. The problem of multi-criteria selection of alternatives based on the imaginary alternative of the "satisfaction point" of the decision-makers (DM) requirements using the information model of criteria for evaluating the properties of the object of study on the chemical composition of iron ore raw materials. For the first time, a hybrid mathematical model of multi-criteria evaluation of iron ore raw materials with target needs was developed: quality of chemical composition of iron ore raw materials; the cost of iron ore; environmental policy and environmental impact in the extraction and/or enrichment of iron ore raw materials. The results of a study on a real example of evaluation and selection of iron ore concentrate for six alternatives implemented by Metinvest (Ukraine) were tested. The general step-by-step algorithm of the evaluation concept is described, which can be quickly implemented in the software product for the application. The developed model will be a useful tool for various programs of state support/business assistance in the procurement of iron ore raw materials by reasonably choosing a supplier using targeted needs in the context of synchronization with the EU Green Deal initiative. Raw material extraction and subsequent transport logistics are especially important for the engineering industry, the electrical engineering industry, and the automotive industry, with strong potential for the aeronautics and aerospace industry.

Pharmaceutical 3PL supplier selection using interval-valued intuitionistic fuzzy TOPSIS

Third party logistics (3PL) supplier selection problem is a multi-criteria selection problem that is frequently discussed in the literature. Medicine is a fundamental element for human health and drug transportation must be carried out on time and under conditions that will ensure that the drug does not lose its physical properties. Therefore, the pharmaceutical industry is one of the foremost and most important sectors in 3PL. In this multi-criteria problem where the evaluation criteria are linguistic rather than numerical, vagueness and impreciseness in evaluations can only be handled with the help of fuzzy sets. With the help of intuitionistic fuzzy sets, one of the new extensions of fuzzy sets, the vagueness and impreciseness here will be discussed and the 3PL supplier selection problem will be tried to be solved with the TOPSIS method, which is one of the most used MCDM methods in the literature. The use of Interval-Valued Intuitionistic Fuzzy sets will add more flexibility and accuracy to the assessment. Thus, the Interval-Valued Intuitionistic Fuzzy TOPSIS method is used to solve the 3PL supplier selection problem and the robustness of the decisions taken is tested with a sensitivity analysis.

A METHODICAL APPROACH TO THE SELECTION OF COMPOSITION AND PLACEMENT OF ON-BOARD EQUIPMENT IN THE MODERNIZATION OF MILITARY AIRCRAFT

The main provisions of solving the problem of multi-criteria selection of the composition and placement of the option of on-board equipment during the modernization of military aircraft are considered.

Preference incorporation in MOEA/D using an outranking approach with imprecise model parameters

Multi-objective Optimization Evolutionary Algorithms (MOEAs) face numerous challenges when they are used to solve Many-objective Optimization Problems (MaOPs). Decomposition-based strategies, such as MOEA/D, divide an MaOP into multiple single-optimization sub-problems, achieving better diversity and a better approximation of the Pareto front, and dealing with some of the challenges of MaOPs. However, these approaches still require one to solve a multi-criteria selection problem that will allow a Decision-Maker (DM) to choose the final solution. Incorporating preferences may provide results that are closer to the region of interest of a DM. Most of the proposals to integrate preferences in decomposition-based MOEAs prefer progressive articulation over the “a priori” incorporation of preferences. Progressive articulation methods can hardly work without comparable and transitive preferences, and they can significantly increase the cognitive effort required of a DM. On the other hand, the “a priori” strategies do not demand transitive judgements from the DM but require a direct parameter elicitation that usually is subject to imprecision. Outranking approaches have properties that allow them to suitably handle non-transitive preferences, veto conditions, and incomparability, which are typical characteristics of many real DMs. This paper explores how to incorporate DM preferences into MOEA/D using the “a priori” incorporation of preferences, based on interval outranking relations, to handle imprecision when preference parameters are elicited. Several experiments make it possible to analyze the proposal's performance on benchmark problems and to compare the results with the classic MOEA/D without preference incorporation and with a recent, state-of-the-art preference-based decomposition algorithm. In many instances, our results are closer to the Region of Interest, particularly when the number of objectives increases.

ВИКОРИСТАННЯ ТЕОРІЇ НЕЧІТКИХ МНОЖИН ТА БАГАТОКРИТЕРІЙНОГО ВИБОРУ АЛЬТЕРНАТИВ ДЛЯ ОПИСУ ДІЯЛЬНОСТІ ПІДПРИЄМСТВА В УМОВАХ НЕВИЗНАЧЕНОСТІ

The task of decision-making in conditions of uncertainty is the choice of a rational decision, formed under the influence of certain and uncertain factors, which are quantitatively and qualitatively described by the features. Methods of decision-making on fuzzy models allow you to easily and objectively evaluate alternatives by individual criteria. The analysis of scientific works and the practice of evaluating the company's activities indicate an insufficient level of its analytical and mathematical support, as well as the need for more detailed consideration of multicriteria choice of alternatives to describe the company's activities and decision-making in uncertainty. Thus, the article presents various classifications of uncertainty of the enterprise, their characteristics and sources. The classification of methods of research of activity of the enterprise in the conditions of uncertainty is developed. Key concepts and definitions of fuzzy set theory are considered. The use of fuzzy set theory and multi-criteria choice of alternatives for describing the activities of the enterprise and decision-making in conditions of uncertainty is specified. The paper considers a multi-criteria choice of alternatives based on the intersection of fuzzy sets, based on the fuzzy advantage relationship, using the fuzzy input rule, based on additive convolution. The ranking of alternatives on the set of linguistic vector estimates is also revealed. The advantages and disadvantages of using different multi-criteria choices of alternatives and fuzzy logic in general are highlighted. The main problem of multi-criteria selection using fuzzy models is the presentation of information about the relationship between the criteria and ways to calculate their integrated estimates. Methods based on different approaches give different results. Each approach has its limitations and features, and the user must get an idea of them. Before applying one or another method of decision making. The heuristic approach provides the widest opportunities for presenting information. Analysis of fuzzy decision-making methods allows us to formulate requirements for further development in this area.

Development of mathematical models and optimization of operation modes of the oil heating station of main oil pipelines under conditions of fuzzy initial information

The relevance of the study is substantiated by the fact that when managing the processes of oil transportation through main pipelines, it becomes necessary to determine and select the optimal operating modes of the oil pipeline units, taking into account the fuzziness of some part of the initial information. In this regard, solving the problem of multi-criteria selection of effective operating modes for an oil heating station for a hot oil pipeline system, which is often described in a fuzzy environment, based on the apparatus of fuzzy set theories, is an urgent scientific and practical problem. A method for the synthesis of models in the conditions of fuzzy output parameters of the object has been developed, with the help of which fuzzy models of the investigated oil heating station of the main oil pipeline have been built. Based on the modification and combination of various optimality principles, mathematical formulations of the problem of multi-criteria selection of effective operating modes for an oil heating station in a fuzzy environment are obtained. By modifying and adapting the principles of guaranteed results and equality in a fuzzy environment, a heuristic method has been developed for solving the formulated problem of selecting object's operation modes using the initial fuzzy information. The proposed heuristic method for multi-criteria selection in a fuzzy environment is based on the use of the experience and knowledge of the decision-maker. The proposed approach is implemented in the formulation and solution of the problem of multi-criteria selection of operating modes of the oil heating station in Atyrau of the Uzen-Atyrau-Samara main oil pipeline. As a result of the application of the proposed method, an improvement in the degree of fulfillment of a fuzzy restriction on environmental impact was achieved by 2 %, as well as the optimal values of the operating parameters of the object were improved: the temperature was reduced by 1.85 % (5.67 K), pressure – by 0.04 % (kPa) and fuel consumption – by 2.9 % (0.0002 kg/s). The obtained results have confirmed the effectiveness of the proposed approach to solving the assigned tasks.

MULTI-CRITERIONAL CHOICE OF AN ALTERNATIVE UNDER THE RULES OF FUZZY PRODUCTS WITH SOME RELIABILITY DEGREE

One of the main problems of decision-making tasks is the need to take into account subjective expert assessments, the complete consistency of which is rare, and the choice of the best alternative. The complexity of the connections between the many-sided aspects of the decision-making situation and the lack of an accurate forecast of the consequences leads to the fact that when assessing and choosing alternatives, it is possible, and often necessary, to use and process qualitatively fuzzy estimates. In decision-making situations, when at least one of the elements (outcomes, criteria, preferences, expert opinions, etc.) is described qualitatively, indistinctly, there are problems of multi-criteria decision-making with fuzzy initial information.
 Let’s consider the solution to the problem of multi-criteria choice based on the rules of fuzzy conditional inference, which have the form of fuzzy statements, the conditions and conclusions of which, along with expert assessments of the criteria, are presented in the form of interval fuzzy numbers of the second type (IT2FN). The convolution of private implications in each statement is made according to Lukasiewicz's rule. To reduce the type and defuzzify the resulting IT2FN, the Karrnik-Mendel algorithm was used to construct the minimum and maximum centroids of nested fuzzy sets of the first type, which give an estimate of the utility interval for each alternative. To refine the obtained utility estimates, under conditions of incomplete definiteness of statements, using the generalized Bayesian inference mechanism, adjusted estimates of the utility intervals of alternatives are constructed. By comparing these intervals, a larger interval is determined and the corresponding alternative is taken as a solution to the problem under consideration.
 The application of the proposed approach to solving the problem of multicriteria selection of the most corroded section of a gas pipeline with ambiguous expert opinions is shown. To date, specific practical and theoretical results have been obtained for decision-making problems with fuzzy initial information

Towards proper consumer choices - MCDM based product selection

Everyday situations each day more often require us to solve sometimes even complex decisional problems. Such conditions may include the problem of choice when purchasing services, products or devices. The ever-increasing assortment of products and services makes it more and more time-consuming for customers to choose the most suitable product for them. Following their intuition or considering only some selection criteria may result in an unsatisfactory choice. Decision making in multi-criteria selection problems needs the consideration of many factors, which are often conflicting.For this purpose, more people reach for multi-criteria decision methods (MCDM). These methods provide an easy way of solving a given problem under certain circumstances. With the increasing popularity of those methods, more are developed each day. This paper presents an approach based on four MCDM methods applied to solve the problem of choosing the most favourable CPU model available on the market regarding price and performance, among other criteria. For this purpose, COMET, TOPSIS, VIKOR and PROMETHEE II methods were performed. Later, a comparative analysis of the rankings obtained using the applied methods was conducted. Rankings provided by used methods were compared using correlation coefficients. The research showed that choosing a specific method is relevant for the results and that real-life problems can be successfully solved using multi-criteria decision methods.The obtained results confirm the suitability of MCDM methods as a decision support tool for consumers’ product selection. Applications based on MCDM allowing customers to perform multi-criteria analysis of a set of products could contribute to increased consumer satisfaction and growth of popularity and competitiveness of online stores providing them.

The example of evaluating the effectiveness of the management system of la-bor protection of the enterprise with the method of multicriteria selection of alternatives based on a fuzzy advantage ratio

The management system of labor protection (MSLP) is an effective tool, which allows the business entity to provide the proper level of labor protection on the enterprises, that corresponds to the requirements of safe and healthy conditions of work for employees. The approaches of construction and functioning of MSLP are improving based on international experience. In 2018 the Cabinet of Ministers of Ukraine has approved “The concept of reforming the management system of labor protection in Ukraine”, which basing on a risk-oriented approach determines the principles, directions and tasks of building a system of labor safety and health in Ukraine and aims to create the national system of production risks prevention and to ensure safe and healthy working conditions for employees. This article deals with the use of the method of multicriteria choice of alternatives based on fuzzy advantage ratio in the process of evaluating the effectiveness of the labor protection management system of enterprises, that allows more objectively identify threats to efficiency of MSLP of the specific business entity. There are some examples of usages of this method to solve issues related to ensuring the economic security of economic entities. Based on those scientific works authors tried to evaluate the effectiveness of functioning of MSLP. The solution of this problem was carried out on the example of a specific chemical enterprise. The department of Life Safety of the National Forestry University of Ukraine has carried out significant work to identify threats to efficiency of MSLP, related to the activities of the labor protection service, which in this article are considered as a set of acceptable alternatives and could be the threat for MSLP efficiency. Also, there were identified some criteria for selecting among the identified threats (acceptable alternatives): the threat occurs infrequently and irregularly; the appearance of threats from time to time; threat occurs frequently and regularly (recurrence of the threat) over a period of time. In the course of the work, the most significant threats were found. That is, the problem of rational choice of alternatives from a certain set X was solved, for which some fuzzy advantage ratio is given g1, g2, g3 with the function μgj : X × X → (0, 1). To solve the problem of multicriteria selection described above, was select an effective method of convolution of the vector criterion into a scalar. The results show that the most significant threats to efficiency of MSLP of the enterprise that was analyzed is an excess of the frequency of injuries at the enterprise over the frequency in the industry and a gross violation of occupational safety rules, accidents. The results obtained indicate that an accident has occurred or may occur at the assessed enterprise. The use of the method of multi-criteria selection of alternatives on the basis of a fuzzy ratio of advantages in the process of evaluating the effectiveness of the management system of labor protection of the enterprise allows more objectively identify shortcomings of MSLP, that potentially lead to undesirable consequences and, accordingly, take the necessary measures in time to normalize the situation.

Use of fuzzy areas of preference in tasks of multi – criteria evaluation of freight air transport

This paper shows how, based on the theory of fuzzy sets, the problem of multi-criteria selection of cargo planes is solved. It is proposed to determine fuzzy preference intervals on the scales of aircraft efficiency criteria. At the same time it is allowed to intersect such intervals taking into account the limitations on the maximum and minimum degree of belonging of criterion values. For combinations of fuzzy intervals, Decision Maker makes its judgments on a fuzzy preference scale. The resulting aircraft efficiency model is checked for coverage of all points of the criterion space with a level of preference not lower than the specified one. This model can be used to estimate any number of cargo aircraft in automatic mode. Both clear and fuzzy criterion values can be submitted to the model input, and then the method allows to build the functions of aircraft belonging to all areas of preference. The software implementation of this model can be used to make decisions about the purchase, manufacture, repair of certain types of aircraft and to determine which types of aircraft should be decommissioned.

The search for optimal deviations of criterial values which allow to achieve the desired results for a fixed alternative in solving multi-criteria selection problem

The search for optimal deviations of criterial values which allow to achieve the desired results for a fixed alternative in solving multi-criteria selection problem