As a result of studying this section, the student must: know
- • the methods underlying decision theory;
- • the systems of axioms on which measurement theory is based;
- • the attributes, indicators and criteria for describing and assessing the state and forecasting the development of socio-economic systems;
- • scales for measuring the characteristics of objects;
- • various ways of modeling a problem situation;
- • the general statement of the decision-making problem;
- • the mathematical model of the decision-making problem;
- • the construction of a system of preferences;
- • choice functions;
- • properties of criteria — completeness, non-redundancy, measurability;
- • the concept of an indifference map and the aggregate criterion of a multi-criteria decision-making problem;
- • solutions dominated in the Pareto sense;
- • Pareto optimality;
- • the axiom;
- • the Pareto—Edgeworth set and the Pareto front;
- • the angle of preference; be able to
- • point out the differences and interrelation of the methodological foundations of scientific disciplines;
- • correctly choose the type of scale for measuring the properties of the object, phenomenon or process under study;
- • formulate and correctly choose ways of modeling a problem situation;
- • formulate criteria for selecting alternative solutions;
- • carry out the formation of a set of alternatives and decision-making criteria in a multi-criteria decision-making problem;
- • formulate the general statement of the decision-making problem for many criteria;
- • determine the values of the parameters of decision-making problems;
- • identify classes of equivalence or indifference on the set of alternatives;
- • construct preference relations, specify a utility function;
- • construct a choice function;
- • construct Pareto dominance relations;
- • check the conditions for the existence of additive utility functions;
- • find Pareto-dominated alternatives in real situations;
- • construct the Pareto—Edgeworth set and the Pareto front;
- • apply the «cost—effectiveness» method;
- • find the most efficient numerical algorithms for finding the Pareto—Edgeworth set;
- • assess the practical meaning of the Pareto—Edgeworth set and the Pareto front in decision-making;
master
- • skills in determining admissible transformations for various types of measurement scales;
- • ways of choosing methods of modeling a problem situation;
- • methods for analyzing decision-making problems with many criteria when developing specific economic and organizational-managerial models;
- • methods for forming and describing decision-making problems;
- • skills in forming and describing the mathematical model of a decision-making problem in a specific situation;
- • ways of constructing utility and risk functions for decision-making problems under conditions of probabilistic uncertainty;
- • methods for constructing preference curves for additive utility functions;
- • skills in applying the angle of preference and the cone of preference in real problems with two criteria;
- • ways of finding sections of the boundary of the solution region that make up the Pareto—Edgeworth set in practical problems.
Key words
Decision theory; systems analysis; attribute; indicator; criterion; scale; problem situation; decision-making problem; set of admissible solutions; criterion space; multi-criteria problem; preferences; binary relation; choice function, decision rule; stochastic dominance; risk function; lexicographic preference relation; aggregate criterion; indifference curves; utility function; local rate of substitution; indifference map, additive utility function; optimality criteria; discrete set of alternatives; Pareto—Edgeworth set; Pareto front; angle of preference.
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