Topic 13

Organization of the development of decisions by the head based on a systematic analysis of the current situation

1. Basic concepts and definitions of decision making theory …………… 2

2. Factors that determine the effectiveness of decisions …………… .. ………… 9

3. Concepts, principles and paradigms for developing solutions… .. ………… .. 16

4. Model of a problem situation ………………………………………… .. 25

Literature …………………………………………………………………… .. 33

Saint Petersburg - 2012

Basic concepts and definitions of decision theory

Further, we will use the following basic concepts: management, decision maker, problem or task (management), solution, goal (management, activity), operation (cybernetic), alternative, active resources, result, model, conditions (development of solutions).

Please note that these basic concepts should be taken only as terms, and not as strict definitions. There are at least two reasons for this.

First, for some categories of decision theory (DMT), there are simply no rigorous definitions. Secondly, any definition is always rather inert, and TPR is a dynamic, rapidly developing science that constantly revises its conceptual and methodological apparatus. Consequently, there is no need to learn by heart those words by means of which we will interpret the meaning of the basic concepts, but it is imperative to deeply penetrate the thoughts and images that stand behind these words, to be able to interpret them.

Control. As already noted, the solution to the problem facing the decision maker is possible only by directing and using active resources for the execution of specific tasks or works. Nothing is done by itself. People participating in the operation need to indicate where, when, what and with what help, what are the requirements for the quality of the tasks or work performed, what are the acceptable variations from the planned tasks and under what force majeure circumstances emergency measures should be taken, what are these measures, etc. All this is united by one concept - management. To manage is to direct someone or something towards the intended goal in order to achieve the desired result.

The main requirement for the quality of management is its continuity. The idea that everything will happen by itself is a mistake - this is a dangerous delusion! It is akin to the idea that you can leave the steering wheel for a long time while driving. Any business, like a car, without control can only move in one direction - down a slope. In addition to continuity, there are a number of other management requirements, for example, the requirement of a certain freedom ("backlash") in the actions of performers, the requirements of stability and flexibility (meaning that, if necessary, you can make adjustments to the previously planned plan with minimal losses), optimality and some others ...

Solution. Usually one and the same problem can be solved in different ways. However, the quality of the outcome of the operation, that is, the value of its results, depends not only on the quality of active resources and the conditions for their use, but also on the quality of the way these resources are used in these conditions. In this regard, in this course, the word "decision" will most often be interpreted as the best way to solve the problem facing the decision maker, as the most preferable way to achieve the goal set by the decision maker. Consequently, the meaning of the word "solution" in our case will be slightly different from the meaning that is attributed to it, for example, in mathematics, when they talk about solving a mathematical problem.

In mathematics, the correct solution to a correctly posed problem is always the same, regardless of how and under what conditions it solves this problem. The mathematical solution is always objective. In contrast, the solution to the problem is subjective, since different decision makers can choose different methods of solving the problem that they like. Moreover, the conditions for solving the problem leave a significant imprint on the choice of the decision maker: the same decision maker in different conditions may prefer, in the general case, a different way of eliminating the problem.

Target. A formalized description of the desired state, the achievement of which is identified in the minds of the decision maker with the solution of a problem or task. The goal is described in terms of the desired outcome.

Alternative. This is a conventional name for some of the possible (admissible in accordance with the laws of nature and the preferences of the decision maker) ways to achieve the goal. Each individual alternative differs from other ways of solving the problem in the sequence and methods of using active resources, that is, in a specific set of instructions to whom, what, where, with the help of what and when to do it. Active resources are all that can be used by a decision maker to solve a problem. The main active resources will always be considered people, time, finances (money) and consumables at the disposal of the decision maker.

Result. By the result we mean a special form of description of the most important characteristics of the outcome of the operation for decision makers. When researching an operation, the degree of preference (or, conversely, not preference) of its results is presented in the most appropriate scale for this: numerical, quantitative or qualitative. For example, let us consider “victory” and “defeat” as the outcomes of a financial transaction. In this case, it will be possible to measure the results of the operation, for example, either in the amounts of realized profits, purchased shares and other securities (quantitative scale), or in terms of the intensity of the outcome, for example, "great victory", "minor defeat", "significant defeat" (qualitative scale), or in terms of the order of the outcomes - first victory, second victory, third victory (numerical scale). The type of scale is selected depending on the purpose of measuring the results; this will be discussed in more detail later.

Model. The real world is complex and diverse. It takes a lot of creative effort and time to study or cognize it. At the same time, in order to develop solutions, it is often enough for the decision maker to know not everything in the object or phenomenon under study, but only the essential properties, features, patterns that are important for solving Problems. In order to save active resources, first of all, time, modeling was invented. This is a special approach to the study of reality, when the decision maker discards unnecessarily detailed details of the object or phenomenon under study, leaving only its most essential features. It is only necessary to demand and monitor so that such a simplification is not sweeping. It is important that according to the results and the study of the fragments of the appearance, properties and connections remaining after the simplification, it would be possible to draw the right conclusions for making decisions. Only then will simulation be truly useful. As a result, the decision maker replaces all real objects and phenomena essential for the development of solutions with simplified images that are compact, expressive and convenient for description, storage and other use. Such simplified images are called models. Thus, the model retains everything that is important that must be taken into account when developing solutions, however, the form of presentation of the model is chosen such that the process of developing a solution would be effective. It should be borne in mind that simulations are carried out for different purposes. Here is a list of the most common modeling goals:

§ study some element of reality - didactic and research models;

§ to work out some element of practical actions - training and game models;

§ to optimize any process, form or content of something - optimization models;

§ delegate authority to perform certain actions by other persons - preference models.

Each modeling goal can be associated with the most preferred form of building and presenting the model. For example, a model can be formed descriptively, that is, in words.

Such models are called verbal. Elements of reality and the connections between them can also be represented using symbols or signs. These are semiotic models. In addition, from childhood, everyone is familiar with physical copies of objects and objects - toys. And everyone in childhood played games: war, school, some kind of profession, that is, he simulated behavior in reality. Each of us once painted something, expressing our thoughts about what we saw or heard. These graphic images are drawings, diagrams, maps of the area, etc. - also models, that is, - simplified images of reality.

Each of the listed models has its own, quite definite set of properties. Verbal models have a high information capacity (remember at least the greatest work of Leo Tolstoy "War and Peace"), but they are difficult to use to transform information or solve computational and analytical problems. Semiotic models, depending on the specific form of using certain signs and symbols - schemes, graphs, logic diagrams, mathematical equations and inequalities - are good, for example, for information and optimization problems, for their representation by means of computing technology. Game models (political, economic, social and business games) occupy a special place. With the help of game models, it is convenient to investigate the mechanisms of behavioral uncertainty. When developing management decisions in economics, the verbal and graphic forms of models are most often used. Mathematical and game models are used to increase the validity and evidence of decisions.

On the basis of a systematic analysis of the order of work of the head of the enterprise (firm) in the development of solutions, a graphical model of the management process has been developed. This model is shown in Figure 1.1.

Conditions developing solutions. Each problem is always associated with a specific situation, situation and a very specific set of conditions. The problem is always solved within the framework of the status quo. Analyzing this or that way of achieving the goal, the decision maker should clearly understand the patterns that connect the course and outcome of the operation with the decisions made. The set of ideas about these patterns, of course, is perceived by the decision maker in a simplified, model form. Some of the regularities can be recorded in a strictly formal form. For example, Newton's laws in mechanics describe in mathematical form the relationships in the "mass-force-acceleration" chain.

Figure 1.1. Graphical model of the control process

In TPR, the model of regularities in the chain Decision-outcome called the "mechanism of the situation." At the same time, it is believed that the model simplification of the links in the specified chain in no way means their rejection.

It means that of the whole variety of connections and patterns, the model includes only those that are of predominant importance, that is, those that make the most significant contribution to the formation of the result. For example, when estimating time t falling of a body in the Earth's atmosphere from a height h it is necessary to take into account, strictly speaking, the influence of both the weight and the shape of the falling body, and disturbances of the atmosphere (wind), however, in a significant range of altitudes h it can be considered that only the height as the leading factor determines the "mechanism of the situation". In this case, the relationship between h and t will be simplistically unambiguous, namely: h = 0.5 g t 2.

In TPR, only two types of model connections in the “mechanism of the situation” are considered: unambiguous and ambiguous.

Unambiguous connections give rise to a stable and well-defined relationship between the solution being implemented and the outcome from its implementation. And as soon as a method of action is set, the outcome and the results associated with it immediately become quite definite (as in our example with an estimate of the time of falling from a given height). Such "situation mechanisms", in which the expected outcome occurs almost always, and the probability of other (unexpected for the decision maker) outcomes is negligible, we will call non-risky situations, deterministic mechanisms of the situation or conditions of certainty.

Such connections between the method and the outcome of the operation (risky situations, or uncertainty conditions), within the framework of which, with repeated reproduction of the same alternative, the appearance of different outcomes is possible. At the same time, the degree of possibility of the appearance of certain outcomes and results is quite comparable (that is, some outcomes cannot be considered extremely small in comparison with others).

The most expressive model of the "situation mechanism" with a multivalued connection between the alternative and the outcome is random mechanism occurrence of insured events. Even if the same insurer insures several identical objects, two outcomes are possible: "the occurrence of an insured event" or "non-occurrence of an insured event". And if we associate the number of insurance objects with the occurrence of an insured event, then the result is several possible values ​​of the paid insured amount of insurance objects. This is a typical mechanism of stochastic (random) uncertainty, and interaction with competitors is behavioral.

But there are also more difficult situations. For example, there may be no data on the probabilities of certain outcomes, although it is known that random factors are the main factors in the operation. Or it may turn out that there is no data on possible alternatives for the behavior of other subjects involved in the decision-maker's operation, although it is known that these persons will take some action to achieve the goals. Finally, the nature of the phenomena and events occurring in the operation may simply be unclear or unknown. The "mechanisms" of all such situations will be classified as naturally undefined. The list of concepts used in the TPR is not limited to this presentation. As the material is presented in the appropriate places, important concepts will be introduced there, such as a problem situation, an effective solution, an expert, a criterion, preferences, the best solution, etc.

3.3. The structure of intelligent decision support systems

3.4. Generalized structure of the expert system

Lecture 4. Classification of applied intelligent systems

4.1. Classification of expert systems

4.2. Examples of applied intelligent systems

Lecture 5. Basic concepts and definitions of decision theory

5.1. Roles of people in decision making

5.2. Alternatives

5.3. Criteria

5.4. The main stages of the decision-making process

5.5. Mathematical methods of decision theory

Lecture 6. Decision making using statistical hypothesis testing

6.1. Statistical decisions

6.2. The main tasks of statistical decisions

6.3. Statistical hypothesis testing

6.4. Solution errors

6.5. Decision rule for hypothesis testing

Lecture 7. Bayesian and sequential decision-making procedures.

7.1. Bayesian decision making

7.1.1. Bayesian procedure for testing a simple hypothesis

7.1.2. Bayesian procedures in the classification problem

7.2. Decision making with sequential Wald procedure

Lecture 8. Decision making by the method of discriminant analysis

8.1. Classification when class distributions are fully defined

8.1.1. Model of two normal distributions with a common covariance matrix (Fisher's model)

8.1.2. Model of two normal distributions with different covariance matrices

8.1.3. Multiple Normal Distribution Model with Common Covariance Matrix

8.2. Classification in the presence of training samples

8.2.1. Substitution Algorithm in Fisher's Model

8.2.3. Classification rules

8.3. Decision rule error

Lecture 9. Tree classifiers

9.1. Purpose of tree classifiers

9.1. Classification tree structure

9.3. Computational problems of tree-like classifiers

9.3.1. Determining the quality of prediction

9.3.2. Selecting partitions

9.3.3. Determining the rule to stop splitting

Lecture 10. Decision trees

9.1. Decision tree characteristics

9.2. Building a decision tree

Lecture 11. Forecasting methods

11.1. Time series analysis

11.1.1. Time series model

11.1.2. Trend, seasonal and cyclical components

11.1.3. Time series decomposition

11.1.4. Exponential smoothing

11.2. Causal forecasting methods

11.3. Qualitative forecasting methods

Lecture 12. The main task of linear programming

12.1. Mathematical model of the basic linear programming problem

12.2. Linear Programming Problem with Inequality Constraints

12.3. Examples of linear programming problems

12.3.1. Transport task

12.3.2. Assignment problem

Lecture 13. Simplex method for solving linear programming problem

13.1. Characteristics of the simplex method

13.2. Tabular Algorithm for Replacing Basic Variables

13.3. Finding a Support Solution for the Basic Linear Programming Problem

13.4. Finding the Optimal Solution to the Basic Linear Programming Problem

Lecture 14. Multi-criteria decision-making methods with objective models

14.1. Combining criteria

14.2. Main criterion method

14.3. The method of successive concessions

14.4. Target Programming Method

14.5. Method using the principle of guaranteed results

14.6. Equal Least Relative Deviation Method

14.7. STEM procedure for finding satisfactory criteria values

Lecture 15. Choice of Pareto-optimal solutions

15.1. Basic definitions

15.2. Graphic interpretation

15.3. Formulation of the problem

Lecture 16. Evaluation of multicriteria alternatives using utility theory

16.1. Utility theory

16.2. Decision making based on expected utility value

16.3. Multicriteria Utility Theory (MAUT)

Lecture 17. Comparison of alternatives by the method of analytical hierarchy

17.1. The main stages of the analytical hierarchy method

17.2. Decomposition of the task

17.3. Pairwise comparison of criteria and alternatives

17.4. Properties of an ideal comparison matrix

Lecture 18. Priorities for criteria and alternatives and the choice of the best alternative in the method of analysis of hierarchies

18.1. Calculation of the intrinsic characteristics of an inversely symmetric matrix

18.2. Calculating the value of priorities

18.3. Determining the best alternative

18.4. Consistency check

18.5. An example of applying the method of analyzing hierarchies

Lecture 19. Evaluation of multicriteria alternatives by ELECTRE methods

19.1. Stages of an approach aimed at developing indices of pairwise comparison of alternatives

19.2. Properties of Binary Relations

19.3. ELECTRE I method

19.4. ELECTRE II method

19.5. ELECTRE III method

Lecture 20. Basic concepts and mathematical model of game methods of substantiating decisions

20.1. Basic concepts of game theory

20.2. Mathematical model of the game

20.3. The lower and upper price of the game. The minimax principle

Lecture 21. Methods for solving games

21.1. Solving the game in pure strategies

21.2. Solution of the game in mixed strategies

21.3. Simplifying games

21.4. 2x2 game solution

21.5. Graphical method for solving (2x2) games

Lecture 22. Games 2 x p

Lecture 23. Solution of games mx 2 and mxn

23.1. Solution of games t x 2

23.2. Solution of games mxn

Lecture 24. Criteria for making decisions in conditions of risk and uncertainty

24.1. Basic concepts. Mathematical model

24.3. Maximin Wald test

24.4. Savage's Minimax Risk Criterion

24.5. Hurwitz pessimism-optimism criterion

Literature

Evolutionary algorithms are used in control tasks, for example, in the task of planning a route for a mobile robot. The goal of any navigation system is to reach the destination with the rational use of resources, without collisions with other objects. Often, the path of the robot is planned in advance in offline mode (the necessary information is entered in advance, the data and knowledge do not change in the session of solving the problem, the reaction time is long). Evolutionary algorithms combine offline planning and real-time planning (online planning). Offline planning looks for a path close to the optimal one, while online planning takes into account possible collisions due to the detection of unknown objects and replaces part of the original plan with another route. Evolutionary algorithms are applied to the construction of conflict-free aircraft routes and to resolve air conflicts.

Automatic theorem proving is used in the control of moving objects to build fully autonomous systems. An example is the control system of the mobile integral robot STRIPS - a self-propelled vehicle that moves according to commands generated in the control device. A typical task solved by STRIPS is the task of moving a part from a certain point in the workspace using a robot gripper into a container.

An intelligent system based on fuzzy rules guides a cargo ship between islands without human intervention. One Portuguese company in the pulp and paper industry has implemented fuzzy autoclave control. To record the management strategy, 25 fuzzy rules were used, which significantly reduced variations in product quality and energy costs and raw materials consumption. Examples of fuzzy control over the production of products at the technological operation "metallization" of precision resistors and models of control of a robot-manipulator in the "eye-hand" system are described.

Fuzzy rules have been successfully used in the design of an aircraft with high-tech wings of improved aerodynamics. In 1990, several billion US dollars worth of fuzzy household appliances were sold by Japanese manufacturers.

Lecture 5. Basic concepts and definitions of decision theory

Under decision making the process of human activity aimed at choosing the best course of action is understood. Models describing human behavior are widely used in operations research. Under operations research understand the application of mathematical, quantitative methods to justify decisions in all areas of purposeful human activity.

By operation, we mean a system of actions united by a single plan and aimed at achieving a specific goal. An operation is always a managed event. The choice of some parameters that characterize the way of its organization depends on us. Any definite choice of parameters depending on us will be called a solution. The decision-making itself goes beyond the research of operations and falls within the competence of the person in charge (or a group of persons) who have been given the final choice.

5.1. Roles of people in decision making

In the decision-making process, people can play different roles. We will call the person who actually chooses the best course of action, decision maker(Decision maker). Another role that a person can play in the decision-making process is the role of a leader or member of an active group - a group

people with common interests and trying to influence the selection process and its result.

In the decision-making process, a person can act as an expert, i.e. a professional in a particular field, to whom they turn for assessments or recommendations. Sometimes he takes part in preparing complex decisions. decision-making consultant... Its role is to organize the decision-making process: helping decision makers in the correct formulation of the problem, identifying the positions of active groups, organizing work with experts.

A special place is occupied by a person (a group of persons) who owns mathematical methods and uses them to analyze an operation. This face ( operation researcher,research analyst) itself does not make decisions, but only helps in this

5.2. Alternatives

Action options are usually called alternatives. ... To formulate the decision-making problem, it is necessary to have at least two alternatives.

The alternatives are independent and dependent. Independent are those alternatives, any actions with which (removal from consideration, selection as the best) do not affect the quality of other alternatives. With dependent alternatives, the assessments of some of them affect the quality of others. There are various types of dependency alternatives. The simplest is group dependence: if it is decided to consider at least one alternative from the group, then the entire group must be considered.

Using the concept of an alternative, quite often the decision-making process is defined as an informed choice of the best alternative from a variety of alternatives.

5.3. Criteria

Solution options are characterized by different indicators of their attractiveness to decision makers. These indicators are called criteria. Criteria for evaluating alternatives Are indicators of their attractiveness to participants in the selection process.

In most tasks, it has quite a few criteria for evaluating solution options. These criteria can be independent and dependent.

Suppose that two compared alternatives have different scores for the first group of criteria and the same for the second group. In decision-making theory, it is customary to consider the criteria as dependent if the decision maker's preferences when comparing alternatives change depending on the estimates for the second group of criteria.

The complexity of decision-making tasks is also affected by the number of criteria. With a small number of criteria (two to three), the task of comparing alternatives is quite simple, the qualities by criteria can be compared. With a large number of criteria, the task becomes more complicated due to the difficulties of comparison.

The specific type of criterion that should be used in the numerical assessment of the effectiveness of a particular operation depends on the specifics of the operation under consideration, as well as on the research task.

Many operations are performed in conditions that contain an element of randomness. In these cases, not just a characteristic of the outcome of the operation, but its average value (mathematical expectation) is chosen as an assessment criterion. For example, if the task is to get the maximum profit, then the average profit is taken as a criterion. In other cases, when the task is to implement a well-defined event, the probability of this event is taken as a criterion.

5.4. The main stages of the decision-making process

The decision-making process consists of a sequence of stages, namely:

identification of the problem,

defining goals and criteria for choosing a solution,

determination of solution options (alternatives),

analysis and comparison of alternatives,

choosing the best alternative

organization of control.

Let's consider the content of some of the listed stages.

Formulation (identification) of the problem - this is the definition of the essence of the problem

(Figure 5.1). It is necessary to identify the problem itself, not the symptoms of its manifestation.

Figure 5.1. Problem formulation stage

It is very important to clearly define the goals of choosing a solution and the criteria for their assessment. It is desirable that the criteria for assessing the decisions made could be quantified, although this is not always possible. Let us consider as an example the problem of choosing a gas pipeline route in the north of Siberia. The task was characterized by a small number of alternatives (two to three), a large number of criteria (six to ten). It was necessary to choose one, the best alternative. The list of criteria included: the cost of building the pipeline; construction time; pipeline reliability; the likelihood of accidents; consequences of accidents; impact on the environment; safety for the population, etc.

The successful solution of the problem largely depends on the developed alternatives. Comparison and analysis of alternatives is carried out using mathematical methods. To apply quantitative methods, it is required to build a mathematical model of the phenomenon. When building a model, it is necessary to establish quantitative relationships between the conditions of the operation, the parameters of the solution and the outcome of the operation - criteria or indicators of effectiveness.

Model selection. If the problem is formulated correctly, it becomes possible to choose a ready-made model. If there is no ready-made model, it becomes necessary to create such a model (Fig. 5.2).

Model bank

Rice. 5.2. Model selection

There are mathematical models that describe well various situations that require certain decisions. Let us single out the following three classes: deterministic, stochastic and game models.

When developing deterministic models, one proceeds from the premise that the main factors characterizing the situation are defined and known. Here, optimization tasks of some value are usually posed (for example, cost minimization).

Stochastic (probabilistic, statistical) models are used in cases where some factors are of an uncertain, random nature.

Taking into account the presence of opponents or allies with their own interests, it is necessary to use game-theoretic models.

Finding a solution(fig. 5.3.). Finding a solution requires specific data, the collection and preparation of which usually requires significant efforts. If data is already available, it often needs to be converted to a form that matches the selected model.

Preparation

Rice. 5.3. Finding a solution

Verification of the solution. The resulting solution should be verified for acceptability using appropriate tests. An unsatisfactory solution means that the chosen model does not accurately reflect the nature of the problem being studied. In this case, it must either be improved or replaced by a more suitable model.

Organization of control. If the found solution turned out to be acceptable, then it is necessary to organize control over the correct use of the model. The main task of such control is to ensure compliance with the constraints assumed by the model, the quality of the input data and the resulting solution.

5.5. Mathematical methods of decision theory

The use of certain mathematical methods is due to the nature of the problems being solved. In the science of decision making, there are three types of problems: well-structured, semi-structured and unstructured problems. Well structured, or quantitatively formulated problems - those in which significant dependencies can be numerically expressed. Weakly structured, or mixed problems - those that contain both qualitative and quantitative elements, with the qualitative, little-known and uncertain aspects of the problems prevailing. Typical operations research problems are well structured. In multicriteria decision-making problems, part of the information required for a complete and unambiguous decision is missing. Such problems are semi-structured.

There are problems in which only a list of basic parameters is known, but quantitative relationships between them cannot be established. In such cases, the structure, understood as a set of relationships between parameters, is not defined, and the problem is called unstructured.

To solve well-structured problems, methods of linear and dynamic programming, game methods of justifying decisions, methods of the theory of statistical decisions, methods of mathematical statistics and probability theory, methods of queuing theory, methods of statistical modeling, are used. To solve semi-structured and unstructured problems, various methods for evaluating multi-criteria alternatives are used (expert methods, hierarchy analysis method, utility theory, risk theory, etc.), artificial intelligence methods that allow us to model human behavior when solving certain problems.

Decision theory

Decision theory- an area of ​​research involving the concepts and methods of mathematics, statistics, economics, management and psychology in order to study the patterns of people's choice of ways to solve various kinds of problems, as well as ways to find the most profitable possible solutions.

Decision making is a process of rational or irrational choice of alternatives with the goal of achieving a conscious result. Distinguish normative theory which describes a rational decision-making process and descriptive theory describing the practice of decision making.

The process of selecting alternatives

The rational choice of alternatives consists of the following stages:

1. Situational analysis;
2. Problem identification and goal setting;
3. Search for the necessary information;
4. Formation of alternatives;
5. Formation of criteria for evaluating alternatives;
6. Conducting an assessment;
7. Choosing the best alternative;
8. Implementation (execution);
9. Development of criteria (indicators) for monitoring;
10. Execution monitoring;
11. Evaluation of the result.

The irrational choice of alternatives includes all the same components, but in such a "compressed" form that tracing the cause-and-effect relationships becomes impossible.

Ergodicity problem

In order to make "strong" statistically reliable predictions for the future, you need to get a sample of future data. Since this is not possible, many experts assume that samples from past and current, for example, market indicators, are equivalent to a sample from the future. In other words, if you take this point of view, it turns out that the predicted indicators are just statistical shadows of past and current market signals. This approach reduces the analyst's job to figuring out how market participants receive and process market signals. Without the stability of the series, it is impossible to draw well-grounded conclusions. But this does not mean at all that the series should be stable in everything. For example, it can have stable variances and completely non-stationary averages - in this case, we will draw conclusions only about the variance, in the opposite case, only about the mean. Resilience can be more exotic in nature. The search for stability in the series is one of the tasks of statistics.

If decision makers believe that the process is not stationary (stable), and therefore ergodic, and even if they believe that the probability distribution functions of investment expectations can still be calculated, then these functions are “subject to sudden (that is unpredictable) changes ”and the system is essentially unpredictable.

Decision making under uncertainty

Uncertainty conditions are considered to be situations when the results of the decisions made are unknown. Uncertainty is subdivided into stochastic (there is information about the probability distribution over a set of results), behavioral (there is information about the effect of participants' behavior on the results), natural (there is information only about possible results and there is no information about the relationship between decisions and results) and a priori (there is no information and on possible results). The problem of justifying decisions under conditions of all types of uncertainty, except for a priori, is reduced to narrowing the initial set of alternatives based on the information available to the decision-maker (DM). The quality of recommendations for making decisions under conditions of stochastic uncertainty increases when taking into account such characteristics of the decision maker's personality as the attitude to their gains and losses, the propensity to take risks. Justification of decisions under conditions of a priori uncertainty is possible by constructing adaptive control algorithms

Choice under Uncertainty

This area represents the core of decision theory.

The term "expected value" (now called mathematical expectation) has been around since the 17th century. Blaise Pascal used this in his famous bet, (see below), which is contained in his work "Thoughts on Religion and Other Subjects", published in. The idea of ​​expected value is that in the face of many actions, when each of them can give several possible results with different probabilities, a rational procedure should identify all possible outcomes, determine their values ​​(positive or negative, costs or benefits) and probabilities, then multiply the respective values ​​and probabilities and add to give the “expected value”. The action to be chosen should provide the highest expected value.

Alternatives to Probability Theory

A very controversial issue is whether it is possible to replace the use of probability in decision theory with other alternatives. Proponents of fuzzy logic, possibility theory, Dempster-Schafer's theory of evidence, and others support the point of view that probability is only one of many alternatives and point to many examples where non-standard alternatives have been used with obvious success. Probability theorists point out:

• Richard Trelkeld Cox's work on justifying the axioms of probability theory;
• the paradoxes of Bruno de Finetti as an illustration of the theoretical difficulties that can arise due to the rejection of the axioms of the theory of probability;
• perfect class theorems that show that all admissible decision rules are equivalent Bayesian decision rule with some prior distribution (possibly inappropriate) and some utility function. Thus, for any decision rule generated by improbability methods, there is either an equivalent Bayesian rule, or there is a Bayesian rule that is never worse, but (at least) sometimes better.

The validity of the probabilistic measure was questioned only once - by J. M. Keynes in his treatise "Probability" (1910). But the author himself in the 30s called this work "the worst and most naive" of his works. And in the 30s he became an active adherent of the Kolmogorov axiomatics - R. von Mises and never questioned it. The finiteness of probability and countable additivity are strong constraints, but the attempt to remove them without destroying the buildings of the whole theory was in vain. This was recognized in 1974 by one of the brightest critics of Kolmogorov's axioms, Bruno de Finetti.

Moreover, he actually showed the opposite - the rejection of countable additivity makes integration and differentiation operations impossible and, therefore, makes it impossible to use the apparatus of mathematical analysis in the theory of probability. Therefore, the task of rejecting countable additivity is not a task of reforming the theory of probability, it is a task of rejecting the use of methods of mathematical analysis in the study of the real world.

Attempts to abandon the finiteness of probabilities led to the construction of a probability theory with several probability spaces on each of which Kolmogorov's axioms were fulfilled, but the total probability was no longer supposed to be finite. But so far no meaningful results are known that could be obtained within the framework of this axiomatics, but not within the framework of Kolmogorov's axiomatics. Therefore, this generalization of Kolmogorov's axioms is still purely scholastic in nature.

S. Gafurov believed that the fundamental difference between Keynes's probability theory (and, consequently, mathematical statistics) from Kolmogorov's (von Mises, etc.) is that Keynes considers statistics from the point of view of decision theory for non-stationary series…. For Kolmogorov, Von Mises, Fischer, etc., statistics and probability are used for essentially stationary and ergodic (with correctly selected data) series - the physical world around us ...

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When studying the decision-making process, it is necessary to take into account two nuances. Firstly, making decisions is generally not as difficult as it seems, but making the right decision is really difficult. Secondly, decision-making is a psychological process, but, as you know, human behavior does not always lend itself to logic - sometimes it is controlled by feelings. For this reason, decisions can be both spontaneous and illogical, as well as logical and deliberate.

Below we will talk about a rational approach to decision making in all details, but you need to understand that a person is often influenced by all sorts of psychological factors, for example, personal values, experience or attitudes. Therefore, we begin by looking at the impact of psychological and behavioral factors on decision making. Thus, further we will focus on decisions of an intuitive, judgmental and rational nature.

Intuitive solutions

Intuitive decisions can be described as choices made based on feelings of correctness. The decision-maker does not analyze all the pros and cons, and often does not even assess the situation in detail. He just chooses. Interestingly, intuitive judgments are common. Moreover, many people depend on their intuition, tend to trust it in every way, because it helps to find the right solutions and effective ways out of difficult situations.

Despite this, when it comes to serious decisions where there are many choices, a person is faced with such a phenomenon as randomness. And if you look at the issue of choice from a position, the chances of making the right decision are very low. Hence the conclusion: you need to listen to intuition and even follow it, but the right choice is possible only when all the pros and cons of the situation are carefully analyzed.

Judgment based decisions

Judgmental decisions may seem intuitive at first glance. The reason for this is the non-obviousness of the logic. But in reality, such decisions are a product of knowledge and accumulated experience. People use knowledge of what happened in similar cases in the past to search for alternative choices in the present and predict their results in the future. Taking common sense as a basis, a person makes a decision that was previously successful. Judgment is the basis of the decision, and this is useful, because many life situations are often repeated. Therefore, what was useful then can bring it now.

Considering that a decision based on judgment is made in the mind of a person, it will always be fast and cost effective. However, common sense in its purest form is a very rare phenomenon, tk. everyone has their own needs, tasks, beliefs, etc. So judgments alone are not enough to make decisions in unique and complex situations where problems only seem obvious.

If the situation is new and the person has no experience yet, he cannot justify his choice logically. Judgments here can be bad, because There are a lot of factors that need to be considered, and the mind is not able to process them all at once due to its limited capabilities. Based on the fact that judgment is based on experience, too much orientation towards the latter can shift decisions to the sides familiar to a person from actions in the past. In such a situation, it is very easy not to notice good alternatives. But more importantly, a person who relies too much on judgments and experience may consciously or unconsciously avoid new things. And this, in turn, can cause big problems in the future, because the relevance of almost any information decreases over time.

It is never too easy to adapt to a new and even more difficult, because there is always the possibility of making the wrong decision. But in many situations, a person may well increase his chances of making the right choice - if only he tries to make a rational decision.

Rational solutions

Rational decisions differ in that they do not depend on past experience, but are justified through a process of objective analysis. It consists of several stages:

• Diagnosing the problem
• Identifying alternatives
• Assessment of alternatives
• Final choice
• Solution implementation

We will analyze each of the stages to make it clearer what and how to do.

Diagnosing the problem

We talked about this in detail in the last lesson, so here we will only give the most general information. Diagnosing a problem is the first step in solving any problem. But there are two ways to go in the diagnostic process.

In the first, the problem is the situation when it was not possible to achieve the goals. What the person expected to happen does not happen. In the second case, the problem is an opportunity. A person becomes aware of it when he realizes that something can be done to improve a particular situation.

It is difficult to define the problem completely because it is influenced by several factors at once. Experience shows that a successful problem definition is already 50% of its solution. Therefore, it is customary to pay great attention and a lot of time to diagnosing problem situations in the business sphere. In a sense, this process can be called independent, since it itself is subdivided into a number of its stages:

• Diagnosing (identifying and accepting that a problem has arisen)
• Understanding (it is necessary to understand the essence of the problem)
• Revealing the causes (analysis of external and internal information)
• Data filtering (discards anything irrelevant to get relevant information)

With regard to the relevant information, it should be noted that this is information that relates to the current problem, the persons involved in it, the goals of its resolution and the period during which they need to be achieved. With this data, you can proceed to the second stage of rational decision-making.

Formulation of criteria and limitations

When diagnosing a problem for making a decision, a person must understand what exactly he can do with it, i.e. how to solve. Decisions are often unrealistic, as resources for implementation can be limited, especially when it comes to one person. Also, the problem may be due to external reasons, which cannot be influenced.

At this stage, it is necessary to impartially define the constraints in which alternatives will be sought. This can save you a lot of time and find a workable solution. Restrictions always depend on the specific situation and the persons involved.

In addition to boundaries, it is important to establish criteria for evaluating alternatives. These are the so-called recommendations for assessing the decision to be made. They include everything that can help cut off unrealistic options and stay within the aforementioned boundaries.

Identifying alternatives

At the third stage, it is necessary to compose and formulate a set of alternatives that can solve the problem. It is recommended to record all options for action that can positively affect the result. But given that people rarely have the knowledge and resources to evaluate all the alternatives, the most serious options should be identified.

Alternatives are considered until one is found that satisfies all needs. For this, a wide range of options should be taken into account. Difficult problems need to be analyzed as deeply as possible in order to be able to develop multiple solutions at once.

Assessment of alternatives

Before choosing the final solution to the problem, you need to evaluate the whole variety of options, considering the pros and cons of each and predicting the possible consequences. Almost always, all options are associated with negative aspects, but at the same time, a compromise can be found in most situations.

To compare solutions, you need to have standards for assessing performance (which we talked about earlier). You need to focus on both quantitative and qualitative parameters. Sometimes, of course, it is not possible to compare the options in full, but the decision in any case must take a specific form, and it is better that it reflects the purpose for which the decision is made.

When assessing alternatives, use the scoring system effectively to understand which choice is best. It is also advisable to take into account and predict the development of events. The more points and the higher the likelihood of implementation of an option, the more this indicates the correctness of the choice.

Final choice

If all the previous stages were completed successfully, it will be quite simple to make a choice - you just have to decide on the option that suits you most. But if multiple factors matter, and if the data and analysis are purely subjective, it may be that none of the options will work. If this happens, experience and judgment are required. They will make it possible to form a more objective picture of the current situation and make progress in resolving it.

It is also important to say that the behavior of a person when making a decision should not be maximizing, but satisfying. Those. it is required to choose the most obvious and acceptable solution, even if it is not the best, than looking for an ephemeral ideal option, which may not exist at all.

Solution implementation

It is not enough just to determine the direction of action. It is much more important to implement a solution in order to solve a problem or get a benefit. The most successful are those solutions that are approved by all parties involved in resolving the issue. If there are several parties and there are disagreements, you should not waste time convincing people of your position and insisting on its correctness. It is much better to try to find a compromise that satisfies each and every one.

As a result of all the above actions, you need to get feedback. To do this, you should measure and evaluate the consequences of your choice or compare the results obtained with the predicted ones. Feedback should be understood as the flow of information about what happened before the decision was made and what happened after.

On this, the topic of making rational decisions can be considered closed. However, the question of decision-making methods is still open, since we have not said about the approaches to this process. They should not be correlated with the already considered classification, since they view this phenomenon in a different light.

Decision-making approaches

There are four pairs of decision-making approaches in total:

• Centralized and decentralized
• Group and individual
• Participation and non-participation
• Democratic and deliberative

Let's see what their features are.

Centralized and Decentralized Approaches

The centralized approach is based on the fact that the maximum number of decisions is made by some higher authority, for example, the board of directors in the company. And in a decentralized one, responsibility for making decisions extends to all levels, including the lowest. The amount and nature of decentralization in each case is determined separately.

Group and individual approaches

In a group approach to decision-making, several parties are involved, working together on the problem. An individual approach allows only a one-man choice. The first option is more expedient, since the collective decision is easier to implement. But the second option is more preferable if there is a time limit or the other party involved cannot participate in the decision making physically.

Participation and non-participation approaches

If you focus on a participatory approach, you need to get the opinion of all parties about the decision to be made. When a choice is made based on the views of stakeholders, the likelihood of success is increased. This approach should not be confused with the group approach. in it the decision is made collectively, and in the participatory approach there is only a survey - the final decision is made by the person in charge. When it comes to the non-participation approach, only one person collects information and analyzes alternatives, and then makes the choice himself.

Democratic and deliberative approaches

A democratic approach involves making decisions in the direction of the majority. It is not very effective for organizations because often divides people into two camps - "winners" and "losers", which can lead to conflict situations and failures in management and work. A deliberative approach, on the other hand, involves all parties in decision-making, which makes it possible to find a compromise that suits everyone.

A deliberative approach usually serves as a form of a group approach, but the focus is on finding out the points of view of as many stakeholders as possible (through meetings, interviews, meetings, etc.), and then making a choice.

Interestingly, in the practice of applying the group approach, the following was noticed:

• Groupthink is activated, in which the majority exerts social pressure on the minority, as a result of which individuals agree on what is beneficial to the masses, even if their interests are not taken into account in any way.
• The group approach serves as a breeding ground for the collision of personal opinions of the participants to a much greater extent than all other approaches.

At the same time, it should be borne in mind that the use of a group approach has a number of serious advantages:

• The group is more effective at solving problems with a broader view of the problem and its causes
• The group sees the prospects much wider, and therefore is able to find the best solution.
• Group enthusiasm (especially encouraged) is much stronger than individual
• The group is less prone to and distrust of new solutions

Guided by all of the above, we can conclude that if the problem being solved concerns several sides, it is most effective to make decisions collectively and taking into account the opinions of each. If the problem concerns one person, he can make decisions himself, but at the same time he is free to use any other approaches and means of finding solutions.

Everything that we managed to talk about is more recommendatory in nature than a system. However, this information is universal - it will help you make effective decisions in any simple or difficult situations. But you should always look back at the peculiarities of problem situations, the interests of the parties involved and other factors affecting decision-making. It is these factors that will be discussed below.

Factors influencing decision making

In fact, the scope of the topic of factors influencing the decision-making process is very large, therefore we will highlight only the subtleties that are most important in our opinion, which most directly affect the choice and its effectiveness.

First of all, these are personal factors. These include states and processes. Next are the situational factors: external and internal. The external environment is economic and political conditions, legal norms, sociocultural factors and technologies, natural and geographical factors. The business sector is also complemented by consumers, suppliers, competitors, infrastructure - all this matters. The internal environment is the goals and structure of the organization, corporate culture, organizational processes and available resources. When talking about the decision-making environment, it is equally important to mention risks, certainty and uncertainty, time and changes in the environment itself.

There are also uncertain factors (they differ in the source of uncertainty (environmental uncertainty or personal uncertainty), in nature (random or non-random)), informational and behavioral factors, as well as negative consequences and interconnectedness of decisions.

As you yourself can see, the topic of factors influencing decision-making is not only very interesting, but also broad. To better understand it, as well as in general in how people make decisions, you can (highly recommended for those who want to become an expert in this area), pay attention to the theory of decision making. She is able to provide answers to many questions.

Decision theory: fundamentals

Decision theory is a special area of ​​research that operates in mathematical, statistical, economic, psychological and managerial terms to study the patterns of people choosing ways to make decisions and solve problems and how to achieve their goals.

There is a normative theory describing the rational process of choice and a descriptive theory describing its practical aspects. From a rational point of view, decision-making consists of several stages:

• Problem analysis
• Problem identification and task definition
• Collection of information
• Identifying alternatives
• Determination of criteria for evaluating alternatives
• Defining indicators to monitor implementation of decisions
• Assessment of alternatives
• Choosing the best alternative
• Creating an action plan
• Implementation of the action plan
• Monitoring the implementation of the action plan
• Evaluation of results

You can go through these stages, depending on the specifics of the situation, in parallel, simultaneously or with a return to the passed stages. The passage of all stages must be rationally justified. Decision theory also says that you need to be able to statistically predict the development of events. But this requires a sample of future data. The impossibility of this indicates the need to apply statistics from past experience.

The core of decision making theory is a separate area - decision making under conditions of uncertainty, i.e. in such situations when the result of the choice is unknown. Uncertainty can be stochastic (when there is data on the probability distribution for a group of results), behavioral (when there is data on the impact of the behavior of the persons involved), natural (when there is data from probable results and there is no information about the relationship between decisions and results) and a priori ( when there is no data even on possible results).

What we call expectation today was formerly called expected value. Its essence is that given different behaviors, each of which can lead to several possible outcomes, a rational approach should identify all possible outcomes, establish their value and likelihood, and indicate, based on their totality, the total expected value. This reduces the negative effect of uncertainty on decision making.

Subjective probability theory subsequently emerged, significantly expanding the theory of expected value, and promoting the theory of real human behavioral decision-making at risks (we also recommend reading about the theory of prospects of Kahneman and Tversky).

With regard to the difference between risk and uncertainty, situations with an unknown outcome are described either through risk or through uncertainty. Choice in terms of risk means that the likely outcomes are known, but some of them are more favorable, and some are less favorable. And the choice under conditions of uncertainty is based on an unknown set of outcomes. Experienced business people always strive to follow the rule, i.e. lead uncertainty to risks. This can be achieved by collecting additional information about the problem and applying it.

According to decision theory, erroneous decisions are divided into first and second row errors. This is due to the fact that the results of the wrong choices are fundamentally different in terms of the fact that an unrealized favorable outcome influences the problem much less than a realized unfavorable one. But the division into errors of the first and second order is possible only when all risks are taken into account and analyzed.

If we touch on the theory of probability, which is most directly related to the theory of decision-making, we can say that replacing the use of probability with alternatives is quite problematic. Some experts argue that probability is just one of many alternatives. Others say that abandoning the theory of probability can create theoretical difficulties, etc.

It is easy to see that decision theory is fraught with a huge amount of useful information, the study of which will allow you to delve much deeper into behavioral psychology. In general, it defines the norms of behavior for the person making the decision. She sets up pointers to follow in order to avoid conflicts with her own preferences, judgments and principles.

But theory does not dictate human behavior at all. It only helps him, provides a methodology that allows him to make decisions that include elements of subjectivity. Interestingly, as the complexity of problems grows, a person's ability to informally process information based on their own judgments weakens. This is where decision theory comes into its own, offering advantages over any other analytical approach to problem solving. It includes many subjective aspects of problems, which is especially important when making decisions on an individual basis.

Let us repeat that we do not insist on mastering the theory of decision making. To a greater extent, it is necessary for specialists, for example, managers, psychologists, sociologists and professionals from other fields of science. However, studying this theory, even for the sake of interest, can raise the effectiveness of your decisions to a qualitatively new level. However, you probably noticed that the process of making rational decisions, which we described in the first block, is based on the foundations of decision theory. Therefore, one way or another, you will encounter it constantly.

So, we have already managed to study two important issues - we talked about problems, their types and methods of working with them and figured out how people make decisions, at the same time getting acquainted with the theory of decision making. But the solutions, as it should be assumed, can be more or less effective. Our task with you is to learn how to find and develop exactly effective solutions, and there are many practical methods for this.

In the third lesson, we will talk about the methods of finding new ideas and solutions: brainstorming, the technique of creative cooperation, the 635 method, the conference of ideas, the "Discussion-66" method, synectics and synectic conferences, the Delphi method, ideological engineering and others. You will have at your disposal a fairly solid arsenal of techniques for increasing personal efficiency in life, education and work.

Do you want to test your knowledge?

If you want to test your theoretical knowledge on the topic of the course and understand how it suits you, you can take our test. In each question, only 1 option can be correct. After you have selected one of the options, the system automatically proceeds to the next question.