.4.1 The use of fuzzy sets for the analysis of investment projects

As mentioned above, the use of fuzzy logic in solving various issues in the field of finance and the economic sector has found wide application. In a scientific paper [18], an analysis of an investment project based on the use of a fuzzy set is considered.

Figure 2.8 shows a triangular membership function. This type of membership function is the most commonly used in the practice of analyzing investment projects. The triangular number A is set using three parameters: the minimum value (a), modal (b), and maximum (c), which correspond to pessimistic, basic, and optimistic scenarios

.

The triangular form of the membership function using mathematics can be described as , where, for any membership function takes values , and .

Basic operations on fuzzy sets:

- addition . where , ;

- multiplication . where , ;

- division. , where , ,if positive, and , , if negative [40].

In this example, the following indicators are used: an investment project involves implementation within three years; the size of the initial investment is determined; the estimated discount rate may range from ten to twenty percent per annum; the planned range of net cash flows has been determined; the residual value of the project is zero. In this example, a risk analysis using a fuzzy set is considered. Based on the data obtained, a conclusion is drawn about the average degree of risk of this investment project.

2.4.2 Fuzzy logic for assessing the risks of the current activities of the enterprise

Consider the example of the use of fuzzy sets for questions, the assessment of the external risk of the enterprise [41]. This specific example describes the monitoring and risk assessment of the operating activities of an enterprise.

As the enterprise under study, the plant was used in the territory of which the harmful substance is stored. It is well known that this substance has a negative effect on the human body. Even if this enterprise has a life safety system, but it does not always reflect complete and accurate information. For example, if a leak of a harmful substance occurred directly from the tank, then this type of risk can be described as an external risk.

It was decided to use the fuzzy logic method. In this example, the following were taken as input variables: the reliability of the life safety system and the consequences of the leakage of harmful substances.

Figure 2.9 presents a fuzzy inference system for risk assessment. When analyzing the situation, the following parameters were taken: the consequences of risk leakage amounted to 65 points out of 100, which corresponds to the fourth category; the reliability of the security system was 75 points out of 100, which falls into the class of high reliability of the system.

In this example, the Mamdani fuzzy inference algorithm was used. A number of rules were identified for the analysis. As a result, an output risk score of 43 points was obtained. Based on the risk assessment of the current activities of the enterprise, the result corresponds to an average degree of risk, that is, moderate risk [41, 42].

Consider the existing advantages and disadvantages of the fuzzy set method. The main advantages of using the fuzzy set method: application in the analysis of qualitative variables; the ability to operate with fuzzy input data; the ability to operate with linguistic criteria; the probability of quickly simulating complex dynamic systems with the ability to compare them with a given degree of accuracy; overcoming the shortcomings and limitations of existing methods for assessing project risks.

Fuzzy control is effective when technological processes are too complicated for analysis using quantitative methods or when the initial information is interpreted inaccurately, indefinitely. Systems using fuzzy logic can solve the problems of decision making, pattern recognition, data classification and many others.

However, like any method, this method has its drawbacks: subjectivity in the choice of membership functions and the formation of fuzzy input rules; lack of awareness of the method; the need for special software, as well as employees who know how to work with it.

Figure 2.10 shows block diagram of fuzzy logic. Where are three examples presented: general case, specific example and GUI editor.

But despite its shortcomings, it is worth noting the widespread use of fuzzy logic has found wide application in a number of major international companies. In Kazakhstan, these methods of fuzzy logic are not yet applied in practice. However, they have a great prospect. In particular, for those organizations and companies that have many years of experience and, accordingly, have accumulated statistical information to obtain objective estimates [43, 44].

The theory of fuzzy sets in financial management can be applied to: analysis of the risk of bankruptcy of an enterprise; risk assessment of an investment project; when building an optimal portfolio of securities and businesses; in assessing the investment attractiveness of stocks and bonds, and so on [18].