Lecture
The main component in fuzzy inference procedures is the fuzzy production rule base. At the same time, there are entire classes of applied problems in which the identification and construction of fuzzy production rules is impossible or is associated with serious conceptual difficulties. Such tasks include the tasks of pattern recognition, extrapolation and interpolation of functional dependencies, classification and prediction, non-linear and situational control, as well as data mining (Data Mining).
A common feature of such tasks is the existence of some kind of dependence or relationship connecting the input and output variables of the system model, presented in the form of the so-called “black box”. In this case, the identification and determination of this dependence in an explicit set-theoretic or analytical form is not possible either due to a lack of information on the simulated problem area or the difficulty of taking into account the variety of factors that affect the nature of this relationship.
For the constructive solution of such problems, a special mathematical apparatus has been developed, called the neural networks. The advantage of models based on neural networks is the ability to obtain new information about the problem area in the form of some forecast. At the same time, the construction and configuration of neural networks is carried out through their training on the basis of available and accessible information.
The disadvantage of neural networks is the presentation of knowledge about the problem area in a special form, which can significantly differ from the possible meaningful interpretation of existing relationships and relationships.
Fuzzy neural networks or hybrid networks, as conceived by their developers, are designed to combine the advantages of neural networks and fuzzy inference systems. On the one hand, they allow you to develop and present models of systems in the form of fuzzy production rules, which have the clarity and simplicity of a meaningful interpretation. On the other hand, neural network methods are used to build fuzzy production rules, which is a more convenient and less time-consuming process for system analysts. Recently, the apparatus of hybrid networks is universally recognized by specialists as one of the most promising for solving weakly or poorly structured problems of applied system analysis.
The most important application of fuzzy set theory is fuzzy logic controllers. Their functioning is somewhat different from that of conventional controllers; instead of differential equations, expert knowledge is used to describe the system. This knowledge can be expressed using linguistic variables, which are described by fuzzy sets.
If some processes of the control object do not lend themselves well to formalization and mathematical description, then in the existing control system, a phase regulator is used in parallel with the traditional regulator, i.e. fuzzy logic is used to replace and together with traditional control algorithms.
It has been experimentally shown that fuzzy control gives better results compared to those obtained with classical control algorithms. The obvious area for the implementation of fuzzy logic algorithms is all kinds of expert systems, including:
non-linear control and management in production (blast furnace, robot, dryer, etc.);
self-learning systems;
natural language text recognition systems;
planning and forecasting systems based on incomplete information;
financial analysis in the face of uncertainty;
database management;
improving management and coordination strategies, for example, complex industrial production.
Fuzzy numbers obtained as a result of “not entirely accurate measurements” are in many respects similar to distributions of probability theory, but compared with probabilistic methods, fuzzy logic methods can drastically reduce the amount of computation performed, which, in turn, leads to an increase in the speed of fuzzy systems.
The disadvantages of fuzzy systems are:
lack of a standard methodology for the design and calculation of fuzzy systems;
the impossibility of mathematical analysis of fuzzy systems by existing methods; the use of a fuzzy approach compared with the probabilistic does not lead to an increase in the accuracy of calculations;
increasing input variables increases computational complexity exponentially;
as a consequence of the previous paragraph, the rule base is increasing, which leads to its difficult perception.
When developing fuzzy systems, it is necessary to go through the following stages of design (after studying the basic concepts of fuzzy sets and systems):
Define the inputs and outputs of the created system.
Define membership functions with terms for each of the input and output variables.
Develop base rules for conclusions for the implemented fuzzy system.
To defazzify.
Set up and analyze the adequacy of the developed model for a real system.
Software implementation of a fuzzy controller on a specific microcontroller.
Based on the theory of fuzzy sets, methods for constructing computer fuzzy systems significantly expand the scope of computers. Recently, fuzzy control is one of the most active and productive areas of research in the application of the theory of fuzzy sets. Fuzzy methods help control the home and rolling mill, car and train, recognize speech and images, design robots with touch and vision. Fuzzy logic basically provides effective means of representing the uncertainties and inaccuracies of the real world. The presence of mathematical tools to reflect the fuzziness of the initial information allows you to build a model that is adequate to reality.
The prospect of this area of research lies in the advantages of the Theory of Fuzzy Sets when processing fuzzy data, which abounds in real business practice and the activities of enterprises of any industry in modern conditions.
Indeed, an important distinctive feature of the external environment of the enterprise is the presence of market uncertainty, since the company is affected by uncontrolled environmental factors. In the new conditions, when the external environment has become less favorable, and the competition has become more severe, the role of the scientific approach in solving the urgent tasks of managing the activities of any enterprise (company, bank) is growing sharply.
Radical transformations of the Russian economy have led to the fact that almost every enterprise has faced the problem of determining ways and means of adaptation to new operating conditions. In modern conditions, the enterprise must determine and forecast the parameters of the external environment, the range of products and services, prices, suppliers, markets, its long-term goals and strategy for their achievement.
The uncertainty present in the tasks of managing the activities of any enterprise (company, bank) is characterized by the blurring of the opinions and assessments of experts, the incompleteness and vagueness of information about the main parameters and conditions of the analyzed problem, the need to take into account the degree of attitude of the decision-maker to risk. Thus, the uncertainty leading to a significant increase in the complexity of the tasks of managing the activities of the enterprise is generated by many factors. The combination of these factors in practice creates a wide range of different types of uncertainty.
Thus, all of the above allows us to conclude that uncertainty is a distinctive feature of various tasks of enterprise management, as well as a risk factor in making management decisions, therefore, it must be taken into account for a more adequate reflection of reality. Obviously, in this situation it is advisable to use formal methods and modern information technologies.
But the possibilities of solving various problems of managing the activity of the enterprise, due to their natural uncertainty, are limited within the framework of methods suitable for use under conditions of certainty or the assumption of the random nature of variables with a well-known distribution law, that in conditions of ambiguously defined and qualitative parameters inherent in the market, gives in most cases an inadequate solution. The use of methods of mathematical statistics is hampered by the fact that management decisions have to be made in conditions of uncertainty, lack of resources, time and information, and almost every financial and economic situation is unique in nature, therefore it is not possible to justify a certain distribution law with the necessary level of reliability.
Briefly list the distinctive advantages of fuzzy-systems compared to others:
The use of fuzzy systems
As for the domestic market of commercial systems based on fuzzy logic, its formation began in mid-1995. The following packages most popular with customers:
The main consumers of fuzzy logic in the market in post-Soviet countries are bankers and financiers, as well as experts in the field of political and economic analysis. They use CubiCalc to create models of various economic, political, stock market situations. As for the easy-to-learn FuziCalc package, it took its place on the computers of large bankers and emergency specialists - that is, those for whom the speed of settlements in the conditions of incompleteness and inaccuracy of the input information is more important. However, it is safe to say that the era of the heyday of the application of fuzzy logic in the domestic market is still ahead.
Today, elements of fuzzy logic can be found in dozens of industrial products - from control systems for electric trains and combat helicopters to vacuum cleaners and washing machines. Advertising campaigns of many companies (mainly Japanese) present successes in using fuzzy logic as a special competitive advantage. Without the use of fuzzy logic, modern situational centers of Western leaders are unthinkable in which key political decisions are made and various crisis situations are modeled. One of the most impressive examples of the large-scale application of fuzzy logic was the comprehensive modeling of the UK Health and Welfare System (NHS), the first time to accurately assess and optimize social spending.
Not bypassed the means of fuzzy logic and software systems serving a large business. The first, of course, were the financiers, whose tasks require the daily adoption of the right decisions in difficult conditions of an unforeseen market. The first year of using the Fuji Bank system brought the bank an average of $ 770,000 per month (and this is only officially declared profit!).
Following the financiers, worried about the successes of the Japanese and the loss of strategic initiative, the US industrial giants became interested in cognitive fuzzy schemes. This is evidenced by the site https://intellect.icu. Motorola, General Electric, Otis Elevator, Pacific Gas & Electric, Ford and others in the early 90s began to invest in the development of products using fuzzy logic. With solid financial “support”, firms specializing in fuzzy logic got the opportunity to adapt their designs to a wide range of applications. "Elite Weapons" entered the mass market.
Among the leaders of the new market stands out the American company Hyper Logic, founded in 1987 by Fred Watkins (Fred Watkins). At first, the company specialized in neural networks, but soon it completely concentrated on fuzzy logic. Recently, the second version of the CubiCalc package of HyperLogic, which is one of the most powerful expert systems based on fuzzy logic, has entered the market. The package contains an interactive shell for developing fuzzy expert systems and control systems, as well as a run-time module that allows you to design user-created systems as separate programs.
In addition to Hyper Logic, companies such as IntelligenceWare, InfraLogic, Aptronix can be called among the "patriarchs" of fuzzy logic. In total, more than 100 packages are presented on the world market, which in one form or another use fuzzy logic. Three dozen DBMSs have a fuzzy search function. Own programs based on fuzzy logic were announced by such giants as IBM, Oracle and others.
Based on the principles of fuzzy logic, one of the Russian software products is also built - the well-known package "Business Forecast". The purpose of this package is to assess the risks and potential profitability of various business plans, investment projects and simply ideas for developing a business. "Leading" the user according to the scenario of his plan, the program asks a series of questions that allow both accurate quantitative answers and approximate qualitative estimates - such as "unlikely", "high risk" and others. Summarizing all the information received in the form of a single business project scheme, the program not only makes a final verdict on the riskiness of the project and expected profits, but also indicates critical points and weaknesses in the author’s intention. Business Forecast differs from similar foreign packages in simplicity, cheapness and, of course, in a Russian-language interface.
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Computational Intelligence
Terms: Computational Intelligence