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 ...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.展开更多
It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multip...It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise.The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.展开更多
In the decision-making tasks for ranking the alternatives and choosing the best ones,procedures on the digraphs are often used.A digraph of the aggregated relation on a set of alternatives for information of experts o...In the decision-making tasks for ranking the alternatives and choosing the best ones,procedures on the digraphs are often used.A digraph of the aggregated relation on a set of alternatives for information of experts or criteria is preconstructed.If the digraph does not contain any cycles,then the Demukron algorithm for partitioning the digraph into levels can be used to order the alternatives by preference.This algorithm cannot be applied if there are clusters consisting of equivalent alternatives.In the paper the algorithm for partitioning an arbitrary digraph of into preference levels is proposed.In contrast to the standard procedure,the digraph of the aggregated relation admits the presence of cycles,and,consequently,of equivalent vertexes-alternatives.The vertexes in any cycle of digraph belong to one level of preference.展开更多
The problem of decision-making when evaluating alternatives according to several quality criteria is considered. Information is used about the pairwise comparison of alternatives by criteria: how many times one alte...The problem of decision-making when evaluating alternatives according to several quality criteria is considered. Information is used about the pairwise comparison of alternatives by criteria: how many times one alternative is preferable to the other. The criteriamay have nonuniform scales. The method to form preferences matrices for representing numerical estimates of alternatives in attitude scales is proposed. The properties ofthe constructed relation are investigated. The algorithms for constructing the relationwith the minimum distance from the preferences by criteria are developed. An algorithm for constructing an aggregated relation based on the summation of preferencesby criteria is developed. Aggregate relation depends on the method of specifying thedistance between the matrices of preferences. The proposed algorithms for constructing an aggregated relation can use coefficients of importance of criteria. The methodcan be applied in collective choice problems when assigning estimates to alternativesby experts. A comparison of the proposed algorithms with each other and with knowndecision-making methods is carried out. The software system of multi-criteria choiceis developed. The task of choosing start-up projects for the purpose of investing by aventure fund has been solved.展开更多
文摘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.
基金financially supported by the Russian Foundation for Basic Research,Project No.17-08-00530.
文摘It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise.The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.
文摘In the decision-making tasks for ranking the alternatives and choosing the best ones,procedures on the digraphs are often used.A digraph of the aggregated relation on a set of alternatives for information of experts or criteria is preconstructed.If the digraph does not contain any cycles,then the Demukron algorithm for partitioning the digraph into levels can be used to order the alternatives by preference.This algorithm cannot be applied if there are clusters consisting of equivalent alternatives.In the paper the algorithm for partitioning an arbitrary digraph of into preference levels is proposed.In contrast to the standard procedure,the digraph of the aggregated relation admits the presence of cycles,and,consequently,of equivalent vertexes-alternatives.The vertexes in any cycle of digraph belong to one level of preference.
文摘The problem of decision-making when evaluating alternatives according to several quality criteria is considered. Information is used about the pairwise comparison of alternatives by criteria: how many times one alternative is preferable to the other. The criteriamay have nonuniform scales. The method to form preferences matrices for representing numerical estimates of alternatives in attitude scales is proposed. The properties ofthe constructed relation are investigated. The algorithms for constructing the relationwith the minimum distance from the preferences by criteria are developed. An algorithm for constructing an aggregated relation based on the summation of preferencesby criteria is developed. Aggregate relation depends on the method of specifying thedistance between the matrices of preferences. The proposed algorithms for constructing an aggregated relation can use coefficients of importance of criteria. The methodcan be applied in collective choice problems when assigning estimates to alternativesby experts. A comparison of the proposed algorithms with each other and with knowndecision-making methods is carried out. The software system of multi-criteria choiceis developed. The task of choosing start-up projects for the purpose of investing by aventure fund has been solved.
