Investment projects are the basic activities of a company, and what follows, each company must make difficult investment decisions. These decisions are usually burdened with risk which must be assessed and then accepted or managed based on the individual risk tolerance. However, risk quantification is one of the most difficult tasks in managing investment projects. An increase in the variability of products, raw materials, and energy prices, together with the growing pressure on competitiveness and cost reduction, have been observed in recent years. These factors introduce an element of uncertainty in the values of economic parameters used to prepare financial analyses in a company and hence make the overall process more complex. The fundamental issue in the problem of assessing the profitability and risk of investment projects is not only to develop appropriate indicators defining the profitability and risk, but also to improve methods for gathering and processing data, together with a formal description of uncertainty appearing in the calculation of efficiency. An adequate description of uncertainty has a decisive influence on the estimation of the investment projects profitability and risk. It conditions the effective practical application of methods for the quantification of the investment projects profitability and risk. For many years, stochastic calculus was the only (appropriate) way to describe and deal with uncertainty mathematically. In fact, it still remains the tool the most commonly used in practice and prevails in the literature concerning the risk of business activity. However, the last decades have shown that the number and complexity of dependencies both inside and outside a company makes it difficult to use the probability theory to represent uncertainty. Because of this, the description of decision-making problems increasingly often uses alterna fuzzy sets (possibility distributions).
- Spis treści
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1. Introduction 7
2. Efficiency and risk of investment projects 10
2.1. Efficiency of investment projects 10
2.2. Risk of investment projects 14
2.3. Risk assessment methods of investment projects 15
2.3.1. Descriptive method 16
2.3.2. Expert evaluation method 16
2.3.3. Sensitivity analysis 16
2.3.4. Efficiency correction methods 17
2.3.5. Method of marginal payback period 17
2.3.6. Analog (discrete) method 18
2.3.7. Operational methods 18
2.3.8. Scenario analysis 18
2.3.9. Statistical and probabilistic methods 18
2.3.10. Method of the loss expected value 19
2.3.11. Analysis of decision trees 19
2.3.12. Methods of computer simulation 19
2.4. Measures of investment projects risks 20
2.5. Hybrid data in the risk assessment of investment projects 21
3. Chosen problems of fuzzy set theory and Dempster–Shafer theory of evidence 25
3.1. Definition of fuzzy sets 25
3.2. Operations on fuzzy sets 25
3.2.1. Set intersection operation 26
3.2.2. Disjunction operation 28
3.2.3. Fuzzy relations 29
3.2.4. Fuzzy implication 34
3.3. Definition of a fuzzy number 38
3.4. Arithmetic operations on fuzzy numbers 41
3.5. Possibility and credibility distributions, fuzzy variables 44
3.6. Fuzzy and interval regression 46
3.7. Simulation of fuzzy systems 49
3.8. Dempster–Shafer (D–S) theory of evidence 49
3.9. Fuzzy random variables 52
4. New methods of processing hybrid correlated data 54
4.1. Using simulation of fuzzy systems for execution of arithmetic operations on interactive fuzzy numbers 54
4.2. Using non-linear programming for execution of arithmetic operations on interactive fuzzy numbers 56
4.3. Hybrid propagation method 57
4.4. Methods of data processing – numerical examples 58
4.4.1. Description of the example problem 58
4.4.2. Data and results of calculations 61
4.4.3. A summary of the results of calculations 68
4.5. Calculation of net present value – different approaches 69
4.5.1. Description of the problem of the calculation of net present value 69
4.5.2. Data and results of calculations 70
4.6. A summary of the results of calculations 75
5. Multi-criteria decision making methods 77
5.1. Multi-criteria decision making methods in the investment projects evaluation 77
5.2. Fundamentals of multi-criteria decision making methods approach 79
5.3. Analytic hierarchy process method 79
5.3.1. Defining the unstructured problem 80
5.3.2. Hierarchical decomposition of the decision 80
5.3.3. Pairwise comparisons 81
5.3.4. Pairwise matrix evaluation 83
5.3.5. Additive weighted aggregation of priorities 88
5.3.6. Evaluation of rating inconsistency 88
5.4. Fuzzy analytical hierarchy process 89
5.4.1. Fuzzy extent analysis 90
5.4.2. Fuzzy analytical hierarchy process – numerical example 92
5.5. Technique for order of preference by similarity to ideal solution method 97
5.5.1. Technique for order of preference by similarity to ideal solution method for real and interval data 98
5.5.2. Fuzzy technique for order of preference by similarity to ideal solution 101
5.5.3. Fuzzy technique for order of preference by similarity to ideal solution – numerical example 104
6. Rule-based systems in multi-criterion evaluation 108
6.1. Fuzzy reasoning principles 108
6.2. Mamdani’s fuzzy inference method 114
6.3. Fuzzy reasoning with Takagi–Sugeno models 123
6.4. Fuzzy reasoning on relational models 130
6.5. Modified evidential reasoning approach 133
7. Multi-criterion evaluation of projects of the metallurgic enterprises using selected methods 152
7.1. Projects evaluation using fuzzy analytic hierarchy process 154
7.2. Evaluation of chosen projects using fuzzy technique for order of preference by similarity to ideal solution 155
7.3. Evaluation of chosen projects using Mamdani’s fuzzy inference method 157
7.4. Evaluation of chosen projects using Takagi–Sugeno model 162
7.5. Evaluation of chosen projects using modified evidential reasoning approach 164
7.6. Summary of evaluation of projects using different method 168
8. Summary and concluding remarks 169
References 173