Multicriteria Choice Problem Research Articles

A model for forecasting the volume of the entertainment services market under non-determinative conditions

The subject matter of the article is the theoretical-methodical and applied principles of modelling and forecasting indicators of the market volume of entertainment services. The goal of the work is to find a mechanism that will allow determining the volume of subscribers, taking into account exogenous variables, especially during socially unstable situations, such as a pandemic, war, cataclysms, etc. The following tasks are solved in the article: formation of criteria for companies for which the created mechanism is planned to be applied; review of basic autoregression models; determination of factors that should serve as an external influence when predicting the number of subscribers; creation of a multi-criteria choice problem; conducting experiments according to the proposed methodology to test the proposed hypotheses and systematize the obtained results. The following methods are used: analytical and inductive methods for forming factors of external influence and description of target companies; expert evaluation method for determining the most influential external indicators; experimental method, statistical methods of processing time series and methods of multi-criteria evaluation to determine the most effective autoregression model. The following results were obtained: the factors of external influence were formed: As external variables, it was decided to choose: the dynamics of the incidence of coronavirus, the rate of change in the global gross domestic product, the change in the S&P500 index, and the news from the world's largest news agencies converted into numerical form; a set of criteria for comparing models was created, saving forecasting time, accuracy, the possibility of taking into account external influence and the specificity of taking it into account; it was determined that the most accurate model is autoregression of the moving average, which at the same time is the most effective model given the created problem of multi-criteria selection; the similarity of the obtained results of experiments with global and domestic research is established. Conclusions: the use of analytical and inductive methods in combination with an experimental approach made it possible to obtain an effective (with an accuracy of more than 95%) mechanism for forecasting the market volume of companies that operate in the film industry and have a signature pricing model. The obtained result will allow players with a smaller market volume not to lose their audience due to the instability of the external environment, and, accordingly, will stimulate the development of the industry in general.

A stochastic method for exploiting outranking relations in multicriteria choice problems

A stochastic method for exploiting outranking relations in multicriteria choice problems

Mathematical models of a multi-criteria problem of reengineering topological structures of ecological monitoring networks

The article deals with the theoretical aspects of the problem of reengineering the topological structures of terrestrial ecological monitoring networks. As a result of the analysis of the current state of the problem, it was revealed the need to changethe network of monitoring points, to increaserequirements for the efficiency and accuracy of observations, as well as to do the more advanced technologies for collecting,processing, storing and transmitting information. All this is possible due to reengineering of existing monitoring networks. This requires the improvement of network system optimization technologies and their software in terms oftaking into account the features of the reengineering problem, as well as the mathematical models and methods used for this. To solve the problem of reengineering of terrestrial monitoring networks, an aggregative-decomposition approach is proposed. The approach is divided into a set of tasks considering their interconnections in terms of input and output data. This made it possible to define a set of tasks that form the basis of reengineering procedures. To increase the efficiency of technologies for computer-aided design and reengineering of networks, a set of mathematical models is proposed that covers the main stages of their life cycles. The article discusses: a systemological model of iterative technology for obtaining design solutions; analytical models for evaluating the properties of network reengineering options in terms of efficiency, reliability, survivability and costs; models for identifyingeffective options for network reengineering based on Karlin and Germeier theorems; a model for evaluating the local properties of options in the form of a utility function of local criteria; model of scalar multicriteria estimation of network reengineering options based on utility theory. The utility function makes it possible to implement both linear and non-linear (including Z-andS-shaped) dependencies on their values. For the practical implementation of modelsof multicriteria problems of reengineering of topological structures of networks, it is proposed to use the method of generation of effective design solutions in parallel with the generation and the method of comparator parametric synthesis of the scalar multicriteria estimation function. The performance and efficiencyof the proposed mathematical models and methods are demonstrated by examples of solving the problems of subset selection of Pareto-optimal options for building networks and parametric synthesis of the scalar multicriteria estimation function. The application in practice of the proposed set of models and methods will increase the degree of automation of network reengineering processes, reduce the time for solving the problem of multi-criteria choice due to the reduction in the time complexity of the analysis procedures, and increase the stability of the decisions made by compromising their choice only from a subset of effective ones.

Анализ больших данных в задачах многокритериального выбора

The problem of multi-criteria choice with non-uniform scales of criteria is considered. A model of a multicriteria choice problem is described, the main elements of which are sets of alternatives and quality criteria, as well as algorithms that allow ranking alternatives without prior reduction of the criteria scales to homogeneous ones. Algorithms for constructing aggregated ranking of alternatives are based on the construction of preference matrices by criteria containing information on the degree of superiority of one alternative over another. Propositions are proved that allow ranking alternatives with assessments according to two quality criteria. Algorithms for indexing alternatives are proposed that allow ranking alternatives for an arbitrary number of criteria. The best aggregated ranking is determined by the total distance to the rankings of alternatives by criteria. All algorithms have polynomial computational complexity, which makes it possible to work with large arrays of initial information. A software system for ranking alternatives in problems with big data has been developed. The initial information is stored in Excel tables, which makes it easy to take into account the limitations on the criteria scales. The operation of the software system is demonstrated by the example of choosing the best version of a drone for purchase in order to observe the terrain, shoot it and transmit information to the operator.

Digital technology of centralized procurement organization

The article is devoted to the development of models framework for digital transformation of processes in corporate and public procurement systems. In particular, the solution of the problem of multicriteria choice in economic systems described by the three-part graph "producer — resource — consumer" is considered. A mathematical model for the optimal distribution of a homogeneous resource from suppliers to consumers in a centralized procurement system is proposed. This model is reduced to a transport problem with intermediate points. Optimization is aimed at achieving maximum compliance in terms of the totality of technical and commercial characteristics of a homogeneous resource. To set the requirements for these characteristics on the part of the consumer, it is proposed to use fuzzy variables. This provides the consumer with a flexible mechanism for describing resource requirements based on his preferences. An operator of aggregation of local correspondences concerning a set of characteristics is proposed in the form of a discrete Choquet integral with a fuzzy measure. Using the example of production equipment, it is shown how it is possible to formalize the parameters of the model, and then to optimize and automate the process of distributing equipment by solving a transport problem with intermediate points in such a way, that the maximum correspondence in its characteristics is achieved. The developed models and algorithms can be used to create information services on electronic trading platforms, including the of public procurement.

Optimization of Multi-Criterial Selection Algorithm with a Dynamically Filled Large Set of Alternatives

We consider the problem of the correct ranking of a dynamically replenished large set of alternatives in multicriteria choice problems that use in the solution the previously obtained modified method for analyzing hierarchies, based on the operation of additive convolution of local priorities not on the obtained set of characteristics of paired comparison matrices (as in the classical method), but on a set of pairs the relative weights of the coordinates of the eigenvectors being compared with each other for each criterion and the subsequent operation of additive convolution according to the criteria and alternatives in each pair. In this version, the algorithm ensures that previously achieved preferences are preserved when adding new alternatives and, thereby, makes it possible to optimize when processing large volumes of dynamically changing data, which significantly expands the applicability of the popular algorithm.

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

The Edgeworth-Pareto principle in the case of IT2F preference relation

The multicriteria choice problem is considered, which includes a set of feasible alternatives, a vector criterion defined on this set and a fuzzy preference relation of the decision maker. It is assumed that this relation is an interval type-2 fuzzy relation. For this problem, a set of nondominated alternatives is introduced, certain axioms of reasonable behavior of a decision maker in the decision-making process are formulated, and the Edgeworth-Pareto principle is established, according to which the best choice should be made only within the Pareto set.

Система поддержки принятия решений для выбора оптимального постквантового механизма инкапсуляции ключей. Часть 1. Алгоритм принятия решений

The purpose of this study is to develop a decision support system that will allow, for the given conditions of using the cryptosystem, to choose the most appropriate implementation of the post-quantum key encapsulation mechanism. In the first part of the series of articles, the problem of choosing the optimal implementation of the post-quantum key encapsulation mechanism is presented as a multi-criteria choice problem. Decision-making methods that are best applicable to the problem under consideration have been determined. An algorithm for solving the problem has been developed. A web application has been designed that implements the functionality of a decision support system.

Digital economy in assessing the investment attractiveness of innovative enterprises based on the results of their own scientific and technical research in the field of petrochemical chemistry

The concept of the digital economy greatly simplifies the solution of multi-criteria choice problems in an innovative environment, in particular, when an economic assessment of the investment attractiveness of a number of enterprise projects with a set of varied in a wide range of technical indicators and commercialization indicators is necessary. Based on the example of small innovative enterprises based on the results of their own scientific and technical research in the field of petrochemical chemistry, a model for the formation of investment portfolios is compiled, taking into account the impact of costs on an improved set of product technical characteristics and the relevance of the level of these characteristics by the investor. The choice of projects from the field of petrochemical chemistry is due to the high importance of this sector both in the economy of individual regions, as the most flexible and at the same time self-sufficient economic system, for example, the Republic of Tatarstan, and at the national and global level. The presence of own scientific developments of the co-author of the article in the field of petrochemical and chemical cluster provides a close relationship of the economic component of innovative projects with variation of all possible technical and technological characteristics of an innovative product in a wide range, depending on investors’ requirements. In addition to traditional applications, the complex of transparent high-strength polymers and polymers with non-stick properties, based on the principles and mechanisms of anionic (co) polymerization of cyclic carbonates with isocyanate-containing compounds under conditions of anionic initiation, gained interest in space technologies, technologies of nano-sized particles and liquid crystals, which requires the search for new methods of synthesis and digital on-line interrelation of the changing costs of the project with its economic efficiency.

FORMS FOR CALCULATION OF UNIVERSAL COEFFICIENTS WHEN ADOPTING MULTIPLE CRITICAL DECISIONS

The problem of multi-criteria choice is a key element in making complex decisions. A number of methods have been proposed that suggest that decisions made with their use are the most rational. Their main element is the linear convolution of particular criteria, and the difference is in those or other heuristic or expert methods for specifying the numerical coefficients of the relative importance of the criteria. Previously, the author developed an approach that allows the use of pre-calculated universal tables of numerical coefficients of importance of particular criteria when forming a linear convolution. It significantly reduces both the laboriousness of the decision-making process and the inevitable subjectivity that arises during the heuristic selection or expert assignment of coefficients of importance. At the same time, the Monte-Carlo method was used for the calculation, which, in event of with a large number of criteria, created significant computational difficulties due to the lack of accuracy of the random number generator and the avalanche-like increase in the amount of computation. In this article, we managed to derive exact formulas for calculating universal importance coefficients. They are based on the so-called numerological approach, summarizing the patterns that emerged in the analysis of a number of tables of universal coefficients calculated by the statistical method. The formulas obtained allowed, in particular, the use of universal coefficients of importance of criteria in problems with any number of criteria, even without special software, which will contribute to the expansion of the scale of application of scientifically-based methods for making decisions.

Factors with Impact in the Assessment and Choice of Tourist Destinations

The preference disaggregation approach to the problem of multicriteria choice is to uncover the inherent model of choice that brings a decision unit to a conclusion in terms of an overall preference on the alternatives. In the context, the actual market shares of a class of competing products (alternatives) constitute a concise global variable originated in and reflecting the cumulative preferences of the consumer body, which affects the pattern of the market. This paper presents a systematic method to analyse the preference information cumulated in the actual market shares of competing products in terms of the criteria involved in the process of choice. The aim of this study is to present an entirely new approach to the problem of multicriteria choice and an application to analyse the market of tourist agency destination offer. In the paper outlines the market share analysis methodology for building an additive utility model in situations concerning attributes on which preferences behave monotonically. When contemporary information and communication technologies are included into the processes of choosing then electronic word-of-mouth (e-WOM) communication appears, while specific marketing messages are being created and transferred. The paper ends with some concluding remarks.

Two-step procedure for multi-criteria choice of generating-capacity structure in remote areas

The paper dwells upon the problem of multi-criteria choice of ways to develop generating capacities to supply power to remote consumers. We herein propose a two-step multi-criteria analysis method: choosing promising power-generation technology first, and then specifying the generating-capacity structure. The paper describes the structure of the proposed multi-criteria methods: the interval TOPSIS method for Step 1; for Step 2, an upgraded analytic hierarchy process based on identifying the structure of the decision maker’s preferences. We demonstrate the use of this method with evidence from the Penzhinsky District, Kamchatka Krai. Thermal power plants, hydroelectric power plants, diesel power plants, as well as solar and wind power are analyzed as power sources. Step 1 includes: analyzing the potential power-supply loads in a specific area; formulating alternative power-generation technology; formulating goals and criteria; criterion-based evaluation of alternative options using objective and subjective models; multi-criteria evaluation of alternatives; analyzing the sensitivity of results and the selection of promising technology. Step 2 includes: formulating goals and criteria on the basis of the selected power-generation technologies; formulating the available alternatives; criterion-based evaluation of alternatives; multi-criteria evaluation and final decision-making.

Ultimate Possibilities of Pareto Set Reduction Based on Quanta of Fuzzy Information

The multicriteria choice problem with a fuzzy preference relation is considered. This problem involves a set of feasible alternatives, a numerical vector criterion, and a fuzzy preference relation of a decision- maker (DM). The concepts of fuzzy vector space, a polyhedral fuzzy set, and the distance between convex fuzzy sets and cones are used. To reduce the Pareto set, ultimate possibilities of using information about the fuzzy preference relation in the form of its quanta are studied. For a sufficiently wide class of choice problems, it is proved that an originally unknown fuzzy set of nondominated elements can be arbitrarily accurately approximated using a finite set of fuzzy information quanta.

An algorithm for pairwise comparison of alternatives in multi-criteria problems

Difficult decisions and problems arise in almost all areas of human activities. In most tasks, the choice of the best alternatives is produced on the basis of task of numeral estimations of alternatives on the criteria of quality. The article considers the problem of multi-criteria choice with nonuniform scales of criteria. Algorithm for pairwise comparison of alternatives, based on the construction of the criteria preference matrices, containing information on the degree of superiority of one alternative over another, is offered. Transitivity of aggregated relation, built for two criteria, is proved. The results, obtained using the method of additive convolution and the proposed algorithm, are compared.

METHOD OF UNIVERSAL COEFFICIENTS FOR THE MULTI-CRITERIAL DECISION MAKING

The problem of multi-criteria choice is a key element in making complex decisions and it has not lost its relevance for more than half a century. A number of approaches and methods suggest that the decisions made with their use are most rational. An overview of the most common methods and their applications is presented. The main element of most of these methods is the linear convolution of particular criteria, and their difference consists in one or another heuristic or expert way of specifying the numerical coefficients of the importance of the criteria. Author developed an approach that allows the pre-calculated universal tables of numerical coefficients of the importance of particular criteria to be used in the formation of a linear convolution, which significantly reduces both the complexity of the decision-making process and the inevitable subjectivism arising from heuristic selection or expert assignment of its coefficients. In the paper, an analogous approach is developed for an equally theoretically and practically important convolution of criteria, which in different publications is called differently: minimax, guarantee, Hermieier convolution. This allowed us to propose a new general method for making decisions and comparing multicriteria alternatives (the MUC method), based on the joint use of both types of bundles. Its application was demonstrated on two practically important tasks - the rating evaluation of universities and the analysis of various design concepts of high-altitude unmanned aero vehicles.

Method of converting a set of possible solutions in the theory of decision-making

The problem of multi-criteria choice is considered in the paper, which are first reduced to single-criterion and then to the linear programming problem. For the effective solution of the problem provides a method of converting a set of possible solutions (the corresponding domain of admissible solutions) by eliminating from consideration deliberately unpromising alternatives with the opportunity to further their directional search. Numerical results of algorithm work are given in the presence of three to five criteria

A Combined Approach to Reducing the Pareto Set Using Linear or Multiplicative Scalarization

In this paper, the multicriteria choice problem, including the decision maker’s (DM) binary preference relation, is considered. Two combined two-stage approaches are proposed. According to these approaches, first, we have to reveal some information on the DM’s preference relation and then apply scalarization methods based on linear or multiplicative functions. The justification of both the combined two-stage approaches is given.

Pareto set reduction based on an axiomatic approach with application of some metrics

A multicriteria choice problem involving a decision-maker’s binary preference relation is considered. Several two-stage methods are proposed for its solution. First, the Pareto set is reduced by applying an axiomatic approach. Then the problem is scalarized on the resulting set by using the Chebyshev or Euclidean metric. The methods proposed are substantiated with the help of well-known and new techniques for characterizing weakly efficient and proper efficient points. Illustrative examples are given.

Decision chains in analyzing multicriteria choice problems

This article provides a comparative analysis of chains of alternatives that emerge in solving multicriteria choice problems by methods of the criteria importance theory and the even swap method and brings to light the essential difference between these chains.