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The subject of research in the article is decision-making support processes in the tasks of optimizing technological processes (TP) at the stages of their design or reengineering. The goal of the work is to improve the efficiency of technologies of automated design of TP due to the development of mathematical models of the tasks of selecting subsets of effective design solutions with intervally specified characteristics of options. The following tasks have been solved in the article: review and analysis of the current state of the problem of supporting decision-making in the tasks of optimization of TP at the stages of their design or reengineering; decomposition of the problem of making project decisions; formalization of the task of comparing intervals for selection of Pareto fronts using comparison indices based on the generalized Hukuhari difference; development of a mathematical model of the problem for the method based on Carlin's lemma; development of a mathematical model of the problem for the method based on Hermeyer's theorem; determination of the Pareto front in the task of optimization of TP by the method of pairwise comparisons. The following methods were used: system approach, theories of systems, theories of usefulness, theories of decision-making, system design, optimization and operations research. Results. The place and connections of the problem of determining the Pareto front in the problem of making project decisions are determined. A formalized interval comparison procedure for the selection of Pareto fronts using Hukuhari total difference comparison indices. Mathematical models of the problem of selection of Pareto fronts using methods based on Carlin's lemma and Hermeyer's theorem have been developed for the case of interval publication with the value of local criteria. An example of the formation of the Pareto front in the problem of optimization of the technological process by the method of pairwise comparison according to the indicators of the duration of the technological cycle, reliability and specified costs is given. Conclusions. The proposed mathematical models expand the methodological bases of the automation of TP design processes. They make it possible to correctly reduce the set of alternative options for construction of TP for the final choice, taking into account the knowledge, experience of designers and factors that are difficult to formalize. The practical use of mathematical models will allow to increase the degree of automation of design or control processes, to reduce the time of decision-making in conditions of incomplete certainty of input data and to guarantee their quality by selecting them only from a subset of effective ones.

The subject of research in the article is the process of ranking objects in the lists of recommender systems. The goal of the work is to increase the efficiency of recommender systems by improving the method of determining preferences between objects in lists using the theory of multi-criteria decision-making. The following tasks are solved in the article: review and analysis of the current state of the problem of identifying advantages between objects and their ranking in the lists of recommender systems; analysis of filtering methods used in recommendation systems; decomposition of the decision support problem for selection of objects; development of a combined method for ranking objects in the lists of recommender systems, combining the procedures for selecting a subset of Pareto-optimal objects, structural-parametric synthesis of a scalar multi-criteria estimation model, and evaluating the entire set of selected objects. The following methods are used: mathematical modeling, systems theory, utility theory, decision theory, optimization and operations research. Results. Based on the results of the analysis of the modern methodology for ranking objects in the lists of recommendation systems, the possibility of increasing their efficiency has been established. To take into account factors difficult to formalize, the knowledge and experience of users, it is proposed to implement the determination of preferences between objects using the theory of multi-criteria decision making. The problem of forming lists of recommendation systems is decomposed into the tasks of selecting a subset of Pareto-optimal objects, structural-parametric synthesis of a scalar multi-criteria estimation model, and evaluating a set of selected objects. A combined method for ranking options has been developed that combines the procedures of ordinalistic and cardinalistic ordering technologies and allows one to correctly reduce the subsets of objects included in the lists of recommendations. Conclusions. The developed method for determining preferences expands the methodological foundations for automating the development and operation of recommendation systems, other multi-criteria decision support systems, allows for the correct reduction of the set of non-dominated objects for the final choice, taking into account factors that are difficult to formalize, knowledge and user experience. The practical use of the obtained results due to more economical method of forming lists when adding new objects will allow to decrease the time and capacity complexity of the procedures for providing recommendations, and due to taking into account of set of weighted local indexes and allocation of set of non-dominated objects - to increase quality of given recommendations.

The subject of research in the article is the process of supporting decision-making in the tasks of optimizing closed logistics networks at the stage of reengineering. The goal of the work is to improve the efficiency of technologies for the automated design of closed logistics networks due to the improvement of mathematical models of multi-criteria problems of reengineering their topological structures. The following tasks are solved in the article: review and analysis of the current state of the problem of supporting decision-making in the tasks of optimizing logistics networks at the stage of their reengineering; decomposition of the problem of optimization of logistics networks at the main stages of their life cycles; selection of a logical scheme of the reengineering process of the logistics network as a territorially distributed object; development of a mathematical model of the general problem of multi-criteria optimization of logistics networks according to indicators of economy, efficiency, reliability and survivability; selection of models for scalar multi-criteria evaluation of reengineering options, taking into account factors that are difficult to formalize, knowledge and experience of the decision-maker. The following methods are used: system approach, theories of systems, theories of usefulness, theories of decision-making, system design, optimization and operations research. Results. Decomposition of the reengineering problem was carried out on the following tasks: determination of the purpose of reengineering and the principles of network reconstruction; network structure optimization; optimization of the topology of network elements; selection of functioning technology; determination of parameters of elements and vehicles; assessment and selection of the best network construction option. The general mathematical model of the multi-criteria task of reengineering the topological structures of centralized three-level logistics networks based on the indicators of costs, cargo delivery time, reliability and survivability has been improved. Universal functions of general utility and utility of local criteria are proposed to obtain scalar estimates for multiple indicators. Exclusion of part of local criteria and restrictions from the general model allows obtaining models of practically all interesting problems of optimization of logistics networks. Conclusions. The developed complex of mathematical models expands the methodological principles of automating the processes of designing logistics networks, allows for the correct reduction of a set of effective options for their construction for the final choice, taking into account factors that are difficult to formalize, the knowledge and experience of designers. The practical use of the proposed complex of mathematical models will reduce the time and capacity complexity of project decision-making support technologies, and due to the use of the proposed options selection procedures, increase their quality based on a number of functional and cost indicators.

The subject of research in the article is the topological structures of closed logistics networks. The purpose of the work is to create a mathematical model and methods for solving problems of optimization of topological structures of centralized logistics networks in the process of reengineering, taking into account many topological and functional constraints. The article solves the following tasks: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; formalization of the problem of system optimization of logistics networks as territorially distributed objects; development of a mathematical model of the problem of optimization of centralized three-level topological structures of logistics networks at the stage of reengineering; development of a method for solving the problem of optimization of centralized three-level topological structures of logistics networks at the reengineering stage; estimation of time complexity of the method of optimization of centralized three-level topological structures of logistics networks. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; the problem of system optimization of logistics networks as territorially distributed objects has been formalized; developed a mathematical model of the problem of reengineering three-level topological structures of logistics networks in terms of cost and efficiency for the case of combined production and processing points; methods of directed search of variants of construction of a logistic network which use procedures of coordinate optimization and modeling of evolution on the basis of genetic algorithm are developed; estimates of the accuracy and time complexity of optimization methods of centralized three-level topological structures of logistics networks are obtained. Conclusions: Based on the results of the study of methods for solving the problem, an approximation of their accuracy and time complexity was performed. In practice, this will allow you to choose a more efficient method for solving large-scale practical problems, based on the required accuracy, available computing and time resources. The method based on the coordinate optimization procedure has a significantly higher accuracy, but it is more complex from a computational point of view. The accuracy of the evolutionary method based on a genetic algorithm can be increased by increasing the number of iterations. The practical use of the proposed mathematical model and methods of reengineering the topological structures of centralized closed logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of transport activities of companies.

The subject of research in the article is the process of ranking options in project decision support systems. The goal of the work is to create a method for ranking options to improve the efficiency of decision support systems by coordinating the interaction between automatic and interactive procedures of computer-aided design systems. The following tasks are solved in the article: review and analysis of the current state of the problem of ranking options in design decision support systems; decomposition of the problem of project decision support; development of a combined method of ranking options, which combines the procedures of technologies of ordinalistic and cardinalistic ordering; development of a method of minimax selection of options from a set of effective for the procedure of expert evaluation. The following methods are used: systems theory, utility theory, optimization and operations research. Results. As a result of the analysis of the modern methodology of decision support, the existence of the problem of correct reduction of subsets of effective design options for ranking, taking into account factors that are difficult to formalize, knowledge and experience of the decision maker (DM), has been established. The decomposition of the problem of supporting the making of design decisions into the tasks of determining the goal of designing an object, forming a universal set of design decisions, identifying sets of admissible and effective decisions, ranking and choosing the best design option for decision makers has been performed. A combined method for ranking options has been developed, which combines the procedures of ordinalistic and cardinalistic ordering technologies and allows you to correctly reduce subsets of effective design solutions for ranking decision makers. A method of minimax selection of options from a set of effective ones for the expert evaluation procedure of decision makers has been developed, which allows improving the quality of the assessment. Conclusions. The developed method expands the methodological foundations of automation of processes for supporting multi-criteria design decisions, allows for the correct reduction of the set of effective alternatives for the final choice, taking into account factors that are difficult to formalize, knowledge and experience of decision makers. The practical use of the results obtained due to the proposed procedure for determining the set of effective solutions will reduce the time and capacitive complexity of decision support, and due to the use of the maximin procedure for selecting options in the synthesis of the estimation model – to improve the quality of design solutions.

The subject of research in the article is the network of closed logistics. The goal of the work is the creation of mathematical models and methods for solving problems of optimizing transportation routes in closed-loop logistics systems, taking into account many topological and functional limitations. The following tasks are solved in the article: the development of a systemological model for the problem of optimizing transportation routes in a closed logistics system; development of a mathematical model of the problem of structural and topological optimization of a three-level centralized network of closed micro-logistics routes for global transportation; development of a mathematical model for the optimization of ring transportation routes in a closed logistics system for local transportation; development of methods for optimizing ring transport routes in a closed logistics system. The following methods are used: methods of system theory, graph theory, methods of the theory of utility, optimization and research of operations. The following results were obtained: the decomposition of the problem of optimizing transportation routes in closed-loop logistics systems at the macro and micro levels was performed; a systemological model of the problem has been developed, which reflects the whole complex of tasks that are solved at various stages of the life cycle of logistics systems. To improve the efficiency of closed-loop logistics systems, a joint solution to the problems of network optimization for the transportation of direct product flows and return flows has been proposed. A mathematical model of the problem of structural and topological optimization of a three-level centralized network of closed micro-logistics routes for global transportation has been developed. To solve such problems, methods using directed enumeration of options are recognized effective; a mathematical model of the optimization problem of the network of closed micro-logistics routes for local transportation with the simultaneous transportation of the contents of the forward and reverse flows was developed; To solve the problem of optimizing closed-loop micro-logistics route networks at the local transportation level while simultaneously transporting the contents of the forward and reverse flows, modifications of the Clark-Wright methods are proposed, as well as a method based on coordinate-wise optimization and insertion schemes; experimental studies of the proposed modifications of the methods made it possible to obtain estimates of their temporal complexity. Conclusions: Practical use of the proposed mathematical models and modifications of methods for optimizing closed-loop logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of implementing transport companies. The obtained estimates of the time complexity of the optimization methods will make it possible to predict the costs of computing and time resources in their practical use for solving optimization problems of closed-loop logistics networks.

The subject matter of the article is the problem of multicriteria estimation of the properties of technological systems (TS) in the process of their structural-parametric optimization. The goal of the study is to increase the efficiency of procedures for multicriteria estimation of TS properties at the stages of their design and reengineering using the technology of comparative parametric identification of the preferences of a decision maker. The objectives are: to increase the adequacy of the additive-multiplicative model of multifactor estimation of variants of building a TS based on the Kolmogorov-Gabor polynomial; to develop an efficient method of parametric synthesis of additive-multiplicative models of multifactor estimating and selecting variants of building a TS based on a decision maker’s preferences; to carry out the analysis and give recommendations on the practical use of the suggested method of parametric synthesis of models of multicriteria TS estimation. The methods used are: system analysis, decision theory, identification theory, multicriteria optimization methods. The following results are obtained: to increase the adequacy of the models of TS multifactor estimation, it is suggested to use the utility function of partial criteria that makes it possible to realize not only linear, convex or concave, but also S (Z)-like dependencies on their values. To solve the problem of parametric synthesis of models of multicriteria TS estimation, the method of comparative identification of a decision maker’s preferences is improved on the basis of the procedures for calculating the Chebyshev point and the residual vector. The experimental study of the efficiency of the suggested variant of the method is carried out. Conclusions. The application of the suggested function in additive-multiplicative models of TS multi-factor estimation does not change the methods for selecting their parameters. The suggested improvement of the method of comparative identification of a decision maker’s preferences on the basis of the procedures for calculating the Chebyshev point and the residual vector for the parametric synthesis of models of TS multicriteria estimation enables covering all practically important situations of selection described by binary relations of equivalence, strict, and nonstrict preferences. The experimental study of the method confirms the increase in the efficiency of the procedures of parametric synthesis of models built on its basis in comparison with the method of group accounting of arguments on the basis of genetic algorithms. Practical application of the results obtained in the support systems for making multicriteria design and management decisions will improve their accuracy and, on this basis, increase the functional and cost efficiency of modern TS.

The subject of the research in the article is the process of evaluating the properties of technological systems at the stages of their design and reengineering. The goal – to improve the efficiency of procedures for multi-criteria evaluation of options for constructing technological systems using the apparatus of fuzzy sets. Objectives: to search for new or modification of known functions of belonging to fuzzy sets "the best variant of building a technological system" by particular criteria in the direction of reducing the complexity of procedures for calculating their values; perform a comparative analysis of the temporal complexity and accuracy of approximation of the preferences of the decision maker with the help of monotonic membership functions; give recommendations on the practical use of monotonous membership functions in decision support systems. Common scientific methods are used, such as: decision making, utility theory, fuzzy sets and identification. The following results are obtained. The article presents the model of preferences of the decision-maker developed by the authors for evaluating individual properties of technological systems using the membership function of fuzzy sets, which allows to realize both linear and nonlinear (convex, concave, S-shaped and Z-shaped) criteria. The carried out experimental research has revealed its advantages in terms of accuracy and time complexity in comparison with the functions of Gauss, Harrington, logistic function, gluing of power functions and their modifications. Methods are proposed that reduce the time complexity of procedures for calculating the values of membership functions. Conclusions. As a result of the analysis of known membership functions for fuzzy sets, it has been established that they do not adequately reflect the preferences of the decision-maker for the characteristics of systems close to extreme values and have a relatively high computational complexity. The proposed membership function and its calculation method make it possible to increase the adequacy of multifactorial estimation models and significantly reduce the time complexity of procedures for calculating its values. Practical use of the proposed membership function in the support systems for the adoption of design and management solutions will make it possible to obtain solutions of the problems of multifactor estimation and choice of a much larger dimension or with less expenditure of computing resources practically without loss of accuracy.