Petr DostálEconomy & Management – Decision Making 

Soft computing  Fuzzy logic  Genetic algorithms  Neural networks  Chaos Theory  Operational research  
Personal About me Curriculum vitae CV in Czech Contact details Publications My books Classic methods Fuzzy logic Neural network Genetic algorithms Hybrid methods Chaos theory Other Teaching BUT Brno, Czechia MUNI Brno, Czechia TBU Zlin, Czechia EPI Kunovice, Czechia NTU Nottingham, UK ASU Cairo, Egypt DOM Chicago, USA UCH Chicago, USA PhD students Foreign students Cooperation Consulting Photogallery Other About Soft computing My hobbies History Links 
Research papersList of all publicationsClassic methodsPrediction of the Heat Supply Daily DiagramThe paper deals with the suggestion of the method of calculation of Heat Supply Daily Diagram (HSDD) prediction for the control of district heat system. The method of superposition of models was designed with partial use of BoxJenkins model. This method is based on the probabilistic theory and mathematical statistics. The method of correction of heat demand, which is influenced by lay out of working shifts and sudden weather changes, was proposed. The aim of the prediction is to improve the quality of the control of the district heating system. Fuel and energy is saved, which contributes to economy and ecology. Dostál 1998 ISBN 8021410949 Some Knowledge of Prediction Methods This article is concerned with the importance of prediction and with various applications of prediction, and warns of the danger of forming erroneous predictions and the necessity of prediction correction. The various types and methods of prediction are described. The BoxJenkins prediction methodology, employing the autoregressive integrated moving average model, is discussed in greater detail. The article also classifies various time series and deals with the possibilities for the prediction of time series. Concrete applications of the prediction of time series are demonstrated in various fields, and the advantages and disadvantages of the BoxJenkins methodology are described. In conclusion other possibilities for prediction, outlining and other variants are mentioned for the purposes of possible further investigation. Dostál 1998 ISBN 8021412224 Forecast Model of Heat Demand The paper deals with the utilization of time series prediction for control of technological process in real time. An improvement of technological process control level can be achieved by time series analysis in order to prediction of their future behaviour. We can find an application of this prediction also by the control in the Centralized Heat Supply System (CHSS), especially for the control of hot water piping heat output. Due to the large operational costs involved, efficient operation control of the production sources and production units in a district heating system is desirable. Knowledge of heat demand is the base for input data for operation preparation of CHSS. Term “heat demand” is instantaneous required heat output or instantaneous consumed heat output by consumers. The course of heat demand can be demonstrated by means of heat demand diagrams. Most important is daily diagram of heat demand (DDHD), which demonstrates the course of requisite heat output during the day. This diagram is most important for technical and economic consideration. Therefore forecast of this diagram course is significant for shortterm and longterm planning of heat production. In this paper we propose the forecast model of DDHD based on the BoxJenkins methodology. The model is based on the assumption that the course of DDHD can be described sufficiently well as a function of the outdoor temperature and the weather independent component (social components). Time of the day affects the social components. The time dependence of the load reflects the existence of a daily heat demand pattern, which may vary for different week days and seasons. Forecast of social component is realized by means of BoxJenkins methodology. The complete forecast algorithm with inclusion of outdoor temperature is described. Finally is presented some computational results and conclusions. Dostál, Chramcov, Balátě 2009 ISSN 19974116 Prediction of time series via ARIMA model The paper deals with the use of BoxJenkins methodology represented by autoregressive  integrated  moving average model ARIMA (p, d, q). The searched data is the record of historical time series of bobsleigh rides per day. The time series represents the tendency and seasonality with 3 day periodicity. Dostál 2017 Fuzzy logicDecision Making in Economy and Management by Means of Fuzzy Logic with the Support of Classical MethodsThe article deals with the decision making in the field of economy and management. The tool for decision making is the fuzzy logic theory together with classical method represented by two dimensional partial differential equations of second order. The solution is focused on the judgmental forecasting of competitive environment in the branch of hotels. At first the theory is mentioned, then the way of building up a model and finally the case study of competitive environment of hotels in specified territory is mentioned. Dostál 2010 Computing in Economic and Finance  London Fuzzy Logic Investment Support on the Financial Market This paper discusses the use of fuzzy logic and modeling as a decision making support for longterm investment decisions on financial markets. A simple model is proposed to calculate recommendations for the investors. This research required thorough analysis of historical data that lead to discovery of interesting dependencies between the Dow Jones index, currency pairs, oil price and the VIX volatility index. The fuzzy model uses several input variables that are used to simplify the complex conditions on the financial markets. The purpose of the model is to evaluate the current market situation, compare current situation to similar situations in the past and to provide investment recommendations for longterm investing Dostál, Brož 2011 ISSN 19974116 Energy Time Series  Fuzzy Logic Prediction The article describes the design of the calculation method of heat supply diagram prediction by means of fuzzy logic. Other methods such as BoxJenkins methodology and the use of artificial neural networks are mentioned here for the purpose of comparing their prediction abilities in energy time series. The use of fuzzy logic seems very successful in the prediction of energy time series. Dostál, Žák 2003 ISBN 8021424117 Fuzzy Logic and Financial Time Series The article presents the possible prediction of time series by means of fuzzy logic. The prediction errors MAPE and the estimation of trends serve as the evaluation of used method. The obtained results show possible applicability to prediction of financial time series and their information efficiency during the process of decision making on the stock market. Dostál, Žák 2004 ISBN 807314025X The Use of Fuzzy Logic at Support of Manager Decision Making The article deals with the use of fuzzy logic at support of manager decision making. The brief description of fuzzy logic and the process of calculation are mentioned. The use is demonstrated on the three examples such as mortgage loan, stock trading and direct mailing. The scheme of models, rule blocks, attributes and their membership functions are mentioned. The use of fuzzy logic is the advantage especially at decision making processes where the description by algorithms is very difficult and criteria are multiplied. Dostál 2005 ISBN 8021429534 The Use of Fuzzy Logic in Pedagogy of Gifted Students This article suggests the methodology of selection of gifted students or pupils to segregated educational forms by means of fuzzy logic. The contribution specifies the term of a gifted student, the most used methods of selection, introduces the principle of fuzzy logic, describes the creation of fuzzy logic model and demonstrates the way of its use. Dostál, Machu 2005 ISBN 8021430125 The Visualization of Sensitivity Analysis of EVA by Means of Neurofuzzy Logics The article suggests the methodology of sensitivity analysis of indices EVA by the use of neurofuzzy logic model. The article presents the principle of neurofuzzy logics, defines the decomposition of indices EVA, set up the method of creation of model, makes the evaluation of accuracy of model and presents the way of the use of model. Dostál, Pavelková, Knápková 2005 ISBN 8021430125 The Use of Fuzzy Logic at Support of Direct Mailing The article deals with the use of fuzzy logic at support of direct mailing. The brief description of fuzzy logic, the process of calculation, the scheme of models, rule blocks, attributes and their membership functions are mentioned. The use of fuzzy logic is the advantage especially at support of direct mailing where the evaluation is very complicated. Dostál 2006 ISBN 8073140845 Risk Management and Fuzzy Logic The article deals with the use of fuzzy logic at support of risk management. The brief description of fuzzy logic, the process of calculation, the scheme of model, the inputs and output, their membership functions and rule block are mentioned. The use is demonstrated on the example of risk management – the risk of payment of debt by client. The application of fuzzy logic is the advantage especially at risk management where the description by algorithms is very difficult and criteria are multiplied. The wrong decisions can cause the bankruptcy of the firm. The significance of the use of fuzzy logic in the process of decision making is increasing now. The support of decision making does not remove the responsibility of the manager of his decision, but it can provide valuable information and thus to improve the quality of decision making in the process of risk management. The fuzzy logic besides artificial neural networks and genetic algorithms belong to relative strong methods as a tool for the support of decision making. Dostál 2006 ISBN 8073184001 Stock Market Fuzzy Decision Making There are different methods used as supports for decisionmaking processes. Nowadays the new theories of soft computing are used for these purposes. The article deals with the application of the decision making on the stock market where fuzzy logic model serves as a support for decision making of investors. Dostál, Kratochvíl 2011 ISBN 9788090807941 Fuzzy Logic and Risk Evaluation Artificial intelligence has had successful applications in economics, and finance. There are different methods used as supports for decisionmaking processes. Nowadays the new theories of soft computing are used for these purposes. The case of use is presented on the evaluation of risk by means of fuzzy logic. Dostál 2012 CEF 2012 Fuzzy logic decision support for longterm investing in the financial market This paper discusses the use of fuzzy logic and modeling as a decision making support for longterm investment decisions in financial markets. A simple model is proposed to calculate recommendations for investors. This research required thorough analysis of historical data that lead to discovery of interesting dependencies between the Dow Jones index, currency pairs, oil price and the VIX volatility index. The fuzzy model uses several input variables that are used to simplify the complex conditions in the financial markets. The purpose of the model is to evaluate the current market situation, compare the current situation to similar situations in the past and to provide investment recommendations for longterm investing. Dostál, Brož 2012 ISSN 21945357 Forecasting of Time Series with Fuzzy Logic There are different methods used as supports for forecasting. Nowadays the new theories of soft computing are used for these purposes. The applications on stock market have specific features in comparison with others. The processes are focused on private corporate attempts at money making; therefore the details of applications, successful or not, are not published very often. The fuzzy logic helps in decentralization of decisionmaking processes to be standardized, reproduced, and documented. Dostál 2013 ISSN 21945357 Fuzzy Clustering in Real Estates There are different methods used as supports for decisionmaking processes. Fuzzy logic has had successful applications in business. In this article the fuzzy clustering method is used in the field of real estates. The fundamental of fuzzy logic clustering is mentioned. The case of use is presented on real estate’s clustering by means of fuzzy logic. Dostál 2013 ISBN 9788070808634, ISSN 23361662 Application of Fuzzy Logic in Identification of Gifted Pupils TFuzzy logic has successful applications in many areas. In this article the fuzzy theory is used for evaluating the identification criteria of gifted students in the ordinary school class. Students were identified with the nomination method applying by the class teacher who evaluates all students in nine criteria (in 3 general areas: learning L, thinking T and creativity C) which has 5 terms. The fuzzy logic allows to clear evaluation of larger number of data without compensation of variables. Its advantage comes from using of vague variables and settings of weights of importance in used identification method. Dostál, Machů 2015 ISSN 23366141 Fuzzy Clustering in Education of Gifted Pupils The article deals with the application of the Fuzzy Clustering in education and also the identification of gifted students by the individualizing system of Mastery Learning. In Mastery Learning we group the students according their type and level of giftedness and increase student´s motivation and learning effectivity hereby. For dividing students into groups several evaluation tests are used. Fuzzy clustering brings the possibility how to evaluate partial outcomes (criteria) with different conditions and relevance. The article describes application of Fuzzy Clustering in concrete case study, which aim was to find the most efficient group – group of gifted students. Dostál, Machů 2015 ISBN: 9780986041952 Multicriteria Evaluation of Gifted Students The article deals with the multicriteria evaluation of gifted students. Students were evaluated with nine criteria: level of learning quality, logic thinking, creativity in spoken and written expressions, broad vocabulary application, text comprehension, knowledge of school subject, reading, speaking, activity and motivation. The research problem is how to evaluate these multicriteria into one final outcome. The fuzzy logic was used for evaluation of gifted students. The advantage of fuzzy logic comes from using of vague variables and settings of weights of importance in used evaluation process. Dostál, Machů, Škapa 2016 ISBN: 9780986041969 Risk Investment and Fuzzy Interface System The aim of the article is the presentation of the use of fuzzy interface system for the risk investment evaluation. The fuzzy logic theory has had successful applications in risk analysis. The processes are focused on private corporate to avoid high risk business, therefore the details of applications, successful or not, are not published very often. The created fuzzy interface model helps in decentralization of decisionmaking processes to be standardized, reproduced, and documented. The risk evaluation plays very important roles especially in business because it helps to reduce costs. Dostál, Rukovanský, Doskočil 2017 ISBN: 9780986041976 Neural networksNeural Networks and the SharesThis article is concerned with the prediction of share prices by means of the neural networks. The first part presents the possibility of using filtration for calculation of prediction. The second part evaluates the relation of the prediction accuracy to the period of sampling. The third part deals with the problem of the application of fuzzy logic in the process of decision making. Dostál 2000 ISBN 8021416688 Prediction of the Heat Supply Daily Diagram via Artificial Neural Network The paper deals with the possibility of utilization of Heat Supply Daily Diagram (HSDD) forecast for the control of District Heating System (DHS), especially for the control of hotwater piping heat output. We focus on involvement of external meteorological influences on the shape of HSDD, such as air temperature, wind velocity and air pressure. Inclusion of these weather influences results in improvement of HSDD forecast. This article presents the utilization of the artificial neural network models for prediction of HSDD. Dostál, Chramcov, Balátě 2002 ISBN 3980808920 Cluster Analyses and Neural Network The cluster analysis represents a group of methods whose aim is to classify the investigated objects into clusters. There have been suggested many new algorithms recently. This article deals with the use of an advanced method of neural network represented by Kohonen selforganizing maps for cluster analysis and describes its basis. The software Matlab 7.1 was used to present the applications of this method. We mention its possible use in economics and two case studies are discussed as well. Dostál, Pokorný 2008 ISBN 9788070806920 Price Judgement via Artificial Neural Network The article presents the possible use of artificial neural network as a means for price judgement. The problem is demonstrated on the case of the price estimation of real property and a car. The advantage of the price judgement via artificial neural network consists in the tasks where there are a lot of criteria and cases. One need not embrace such a quantity of information and make the right sense. It means for example, the minimization of unwanted omitted criterion or human fault, unacquaintance of problems, etc. Dostál 2004 ISBN 8021426764 Risk Management and Artificial Neural Network The article presents the possible use of artificial neural network as a means for risk management. The problem is demonstrated on the case of the set up of the rate of risk of a client. The advantage of the solution via artificial neural network consists in the tasks where there are a lot of criteria and cases. One need not embrace such a quantity of information and make the right sense. It means for example, the minimization of unwanted omitted criterion or human fault, nonacquaintance of problems, etc. The artificial neural network can help us in the field of risk management. The results of calculation can help us in the decision making process. The mentioned method supports the discovery of risk situation that can be caused by client, investment, loan, mortgage, etc. Thus the losses in case of wrong decision can be prevented. Dostál, Rais 2005 ISBN 8073182769 The Prediction of Sale Time Series by Artificial Neural Network The article presents one of the methods of prediction of time series with the support of MATLAB program when Neural Network Toolbox is used. There are mentioned the steps of calculation. The setup of parameters plays a key role for correct prediction. The method of calculation can be used for any time series. Dostál, Kratochvil 2012 ISBN 9788073142797 Genetic algorithmsGenetica and SharesThe article deals with applying the genetic algorithms to prediction of indexes and prices of shares and optimalization of portfolio. Dostál 2002 ISBN 8086510565 Energy Time Series  Genetic Algorithm Prediction There are manifold methods from different branches that are used for the predictions of time series. Except for the classical methods, it can be mentioned the use of BoxJenkins methodology, artificial neural networks, fuzzy logic, wavelet analyses and genetic algorithms. Dostál 2002 ISBN 807318074X Cluster Analysis and Genetic Algorithms The paper deals with the cluster analysis and genetic algorithms and describes their basis. The application of genetic algorithms is focused on a cluster analysis as an optimization task. The case studies present the way of solution of two and three dimensional cluster analysis in MATLAB program with use of the Genetic Algorithm and Direct Search Toolbox. The way of its possible use in business is mentioned as well. Dostál, Pokorný 2008 ISBN 9788072045822 Methods of Large Investment Unit Modelling The paper presents concrete results of large investment unit modelling using generic algorithms. The paper is, in a way, a sequel to authors' previous works based on traditional deterministic models. Dostál, Rais 2001 ISBN 8086510271 Production Schedule by Means of Genetic Algorithms This paper focuses on a concrete application of Genetic Algorithms to production schedule. It highlights the basic disadvantages of standard analytic models compared to the models based on the principle of Genetic Algorithms. Dostál, Rais 2003 ISBN 8073140179 The Solution of Logistical and Transport Problems by Means of Genetics Algorithms The article presents the possible use of genetic algorithms for the solution of logistics and transport problems. The logistics problem is demonstrated on the case of pickup places and collection centers. The transport problem is demonstrated on the case of traffic route. The process of optimalization is contribution to minimize the costs and maximize the profit. Dostál, Rais 2004 ISBN 807314025X The Solution of Cutting Plans by Means of Genetic Algorithms The article presents the possible use of genetic algorithms for the search of optimal cutting plans. The problem is demonstrated on the case of cutting plans for one, two or threedimensional materials. The process of optimization minimizes the scrap and thus it contributes to minimization the costs and maximization of the profit. Dostál, Rais 2004 ISBN 8021426764 Genetic Based DNA Algorithm to Solve Distribution Problem The artikle drala with genetic based DNA algorithm is proposed to deal with the distribution problem. DNA interons , Hot and Cold spots features are used to improve the performance of standard genetic algorithm. This modified algorithm can solve single or multiobjective problems. The distribution problem is one of the important economic problems. The correct solution of this problem saves time and cost. This proposed algorithm is implemented on a distribution problem. The results are compared with those yields from genetic algorithm and neural network. Dostál, Omar, Elwahed ISBN 9788021438934 Hybrid methodsSoft Computing and Stock MarketThe article deals with the possible methodology of processing of data and information for the search of buy and sale signals of share prices, currency ratio and commodities on the world markets. The methodology includes fundamental, psychological, technical (regression analysis, dynamic models, fuzzy logic, artificial neural networks, genetic algorithms, chaos analysis, hybrid models) analyses, simulation and other methods. The process of decision making and evaluation are also mentioned. Dostál 2003 ISBN 8021424117 Soft Computing and Control of District Heating System The article deals with the possible methodology of processing of data and information for the search of prediction of energy, heat, etc. consumption. The methodology includes regression analysis, dynamic models, fuzzy logic, artificial neural networks, genetic algorithms, chaos analysis, hybrid models, dynamical simulations and other methods. The process of decision making and evaluation are also mentioned. Dostál, Chramcov, Balátě 2003 ISBN 3980808947 Stock Market Decision Machine The article deals with the build up of the stock market decision making machine that can improve prediction accuracy. It uses fundamental, psychological and technical analyses together with simulation and other methods. The technical analyses are represented by the regression and chaos analyses, prediction by means of dynamic models, fuzzy logic, neural networks, genetic algorithms and hybrid models. It uses chaos analyses for the test of randomness of time series. The designed methodology is used for the processing of the data to obtain the information of buy and sale signals of the share prices, currency ratio and commodities on the world markets. The case study is mentioned where the evaluation of inputs is presented. Dostál, Rais 2009 ISSN 19974116 Clustering and Soft Computing Clustering has had successful applications in many fields. There are various methods of soft computing methods possible to use for this purposes. It could be fuzzy logic, neural networks and genetic algorithms. The case study of the use of soft computing clustering methods and their comparison are mentioned in the article. Dostál 2014 ISBN 9788070808986 Business Forecasting via Soft Computing Methods Forecasting methods have had successful applications in business. Nowadays the new theories of soft computing are used in this field because it helps to lead to higher profits. There are especially the methods such as fuzzy logic, neural networks and genetic algorithms. The fields of applications of forecasting methods in business cover a wide area of applications. Dostál, Škapa 2015 ISBN: 9788087294611. The Artificial Intelligence and Business Decisions The article deals with the identification of gifted students via Artificial Neural Fuzzy Interface System (ANFIS). Students were evaluated with three criteria: Superior creativity, Logical thinking and Learning quality. The research problem is how to identify gifted students. The ANFIS was used for identification of gifted students, which will lead to inclusion of students into special educational program. The advantage of ANFIS comes from setup of fuzzy rules and membership functions via data for identification process. Dostál, Rukovanský 2016 ISBN: 9788087255735. Identification of Gifted Students via ANFIS for a Purpose of their Inclusion into Special Educational Programs The aim of the use of artificial intelligence in business is in the field of optimization minimization the costs and maximization the profit. The mostly used methods of artificial intelligence are fuzzy logic, artificial neural networks and evolutionary algorithms. The artificial intelligence have had successful applications also in business. Nowadays the new theories of artificial intelligence are used for these purposes. The applications in business, economics, and finance have specific features in comparison with others. The processes are focused on private corporate attempts at money making or decreasing expenses; therefore the details of applications, successful or not, are not published very often. The optimization methods help in decentralization of decisionmaking processes to be standardized, reproduced, and documented. The optimization plays very important roles especially in business because it helps to reduce costs that can lead to higher profits and to success in the competitive fight. Dostál, Machů, Rukovanský 2016 ISBN: 9780986041969. Chaos theoryChaos and Stock MarketThe article deals with Hurst exponent, which calculates the rate of chaos of time series, and with Lyapunov exponent, which determines the predictability of time series. These exponents are part of the Chaos Theory and Fractal Market Hypothesis. Dostál, Zmeškal 2001 ISBN 8073180308 Energy Time Series and Chaos The article deals with Hurst exponent, which calculates the rate of chaos of time series, and with Lyapunov exponent, which determines the predictability of time series. These exponents are part of the chaos theory and fractal geometry. Dostál 2002 ISBN 807318074X. Economy and Application of Chaos Theory The theory of chaos came into being in solution of technical problems, where it describes the behaviour of nonlinear systems that have some hidden order, but still behave like systems controlled by chance. A linear model can describe a real system only if it is linear. If this is not fulfilled, then such models can simulate the real system only under ideal conditions, only for a short time. If a system is a nonlinear dynamic, a deterministic system it can generate not only the permanent trends and cycles, but it can also include randomlooking behaviour. Processes of such behaviour are present in the economy. Dostál, Rukovansky ISSN: 21621357(Print), ISSN: 21621381(Online). OtherJudgmental Forecasting and SimulationThe article deals with the buildup of a model for judgmental forecasting. The built up model is described, its inputs and outputs are explained and interpretation of its results are mentioned. The two dimensional partial differential equation of second order is used for the simulation. The possible usages are mentioned such as hospital, hotels, banks, warehouses, petrol station and restaurant competitive environment. The judgmental forecasting serves as a support of decision making processes to entrepreneurs, managers and investors. Dostál 2011 ISSN 19974116 The Use of Simulation in Business Area The aim of the article is to present the possible use of simulation in business. The suggested methodology uses the partial differential equations of second order. The built up model is described, its inputs and outputs are explained and interpretation of its results are mentioned. The case study is presented on simulation in business. The conclusion covers the advantages and disadvantages of simulation. The simulation serves as a support of decision making processes to entrepreneurs. Dostál 2011 ISBN 9785752603495 The Solution of Decision Making Problems in MATLAB This paper deals with the way of solution of decision making problem by means of fuzzy logic in program language MATLAB where multiply rule boxes must be used. The fuzzy logic enables to work with vague terms that are quite used in business and public services. The designed solution could be used for decision making processes to be successful in business also at cross border regions of southeast Moravia. Dostál, Kratochvíl 2011 The Calculation of Entropy of Financial Time Series A number of variations of calculation of entropy have been developed to measure the regularity of time series. The article deals with the calculation of approximate entropy used in physic. Some measures of time series can be made in financial branch. The article presents the used method of calculation programed in MATLAB. The case study is dedicated to evaluation of indexes of eastern states, such as Poland, Hungary, Estonia, Lithuania, Slovenia and Czechia. Dostál, Kratochvíl 2011 ISBN 9788073142216 Simulation Model for Decision Making:Build Up a New Warehouse The article deals with the decision making in the field of economy and management. The tool for decision making is represented by two dimensional partial differential equations of second order. The solution is focused on the judgmental forecasting of competitive environment in the branch of warehouses. At first the theory is mentioned, then the way of building up a model and finally the case study of competitive environment of placement of a new warehouse is mentioned. Dostál, Kříž 2011 ISSN 12109479121 Database System and Soft Computing The present article deals with use of advanced analytical functions resulting in information for support of decisionmaking. Utilization of this information can bring about measurable economic effects to the company. There are various methods of soft computing, usable for this purpose, such as fuzzy logic, neural networks, evolutional algorithms, theory of chaos etc. Some of these methods are part of Business Intelligence (BI) over Microsoft SQL Server 2008 (SQL Server) platform. This article uses the Microsoft Neural Network algorithm, selected from the nine algorithms implemented in BI, for prediction of prices of used cars and verification of probability of the predicted prices. Dostál, Kříž 2010 ISSN 12109479121 Matlab Competetive Environment Simulation The article deals with the buildup of a model for competitive environment simulation. It presents the model, explains the used variables and their interpretation in the competitive environment. The possible use is in various branches. The two dimensional partial differential equation of second order is used for the simulation as a support of decision making process. Dostál, Kratochvíl 2010 ISBN 9788097051907 Simulation of Petrol Station Competitive Environment The article deals with the decision making in the field of economy and management. The tool for decision making is represented by two dimensional partial differential equations of second order. The solution is focused on the judgmental forecasting of competitive environment in the branch of petrol stations. At first the theory is mentioned, then the way of building up a model and finally the case study of competitive environment of placement of a new petrol station is discussed. Dostál 2010 ISBN 9788021441200 Decision Making for Closing Branch of Bank: a Simulation Model The article deals with the method of simulation as a support for decision making. The two dimensional partial differential equations and fuzzy logic theory are used. At first the theory is mentioned, than the way of buildup of a model and finally the case study deals with simulations leads to close of a branch of the bank to reduce the costs. Dostál, Kratochvíl 2010 ISSN 19974116 The Decision Making Process  The Way of Solution of Legal Dispute The article deals with the use of fuzzy logic at support of manager decision making. The brief description of fuzzy logic and the process of calculation are mentioned. The usage is presented on the example, whether to solve or not the legal dispute by means of judicial process. The scheme of models, rule blocks, attributes and their membership functions are mentioned. The use of fuzzy logic is the advantage especially at decision making processes at law uncertainty. Dostál 2010 ISSN 18033814 The Comparison of Methods Solving the Travel Salesman Problem The travel salesman problem is a well known problem which has become a comparison benchmark test for different computational methods. Its solution is computationally difficult, although the problem is easily expressed. A salesperson must make a closed complete tour of a given number of cities. All cities are connected by roads, and each city can be visited only once. The program must solve the optimization problem by minimizing the value represented by total tour length, and by changing the order of the city. Dostál, Kratochvíl 2010 ISBN 977–80–7314–2018 Prediction of Competitive Environment in Business The article deals with the possible build up of a model of competitive environment in business. Two dimensional partial differential equations of second order are used. At first the theory is mentioned, than the way of build up of a model and finally the test and real cases are mentioned. The method can be used in any field of competitive environment such as markets, banks, firms, suppliercustomer relations, etc. Dostál 2008 ISSN 19974116, ISSN 19974124 The Prediction of Hospital Competitive Environment The article deals with the possible build up of a model of hospital competitive environment. Two dimensional partial differential equations of second order are used. At first the theory is mentioned, than the way of build up of a model and finally the case study in health sector is mentioned. The two and three dimensional graph together with polar graph is used for evaluation. The method can be used in any field of competitive environment such as markets, banks, firms, suppliercustomer relations, etc. Dostál, Kratochvíl 2009 ISSN 19974116 Competing for New Hospital Locations: A Simulation Modeling Approach Hospitals compete with each other for patients and medical service offerings in much the same way as other types of businesses. Not all patients go to the hospital nearest to their homes due to brand name perceptions or association with a specific physician. However, some patient migration occurs between affiliated hospitals, because of a need for special services. This represents a complex competitive environment among hospitals which can be viewed positively or negatively. The negative manner means real competition for a relatively small local community, but the positive manner means the 'partnership' of hospitals to take advantage of size, centralization, expertise, and sophisticated medical specialties which require a critical mass of activity to be effective.. In a consolidating, competitive environment requiring fewer hospital beds and expensive facilities some hospitals do not wish to compete with each other, but rather cooperate by forming hospital partnerships or oligopolies. In this constrained environment modelling or optimization effort must consider both the positive and negative ramifications of competition along with the influence of natural boundaries (such as water features and bridges that separate communities) while seeking to find strategic opportunities to serve the communities in need of Health Care Services. Dostál, Levenbach, Savage 2009 ISSN 19974116 Simulation of Production and Financial Systems The article deals with applying the simulation and identification of production and financial dynamical systems by means of second order of differential equations. The analogy and the method of build up of models are demonstrated on simple examples. Dostál 2004 ISBN 8070805501 Risk management and Soft Computing This paper deals with the use of artificial intelligence in risk management. The artificial intelligence includes the fuzzy logic, neural networks, genetic algorithms, etc. These methods can solve many problems from practice. The risk management belong among them. The use of fuzzy logic, neural networks and genetic algorithm use is presented by evaluation of risk of client. Dostál 2007 ISBN 9788024814063 Distribution Problem Solved by Artificial Intelligence Methods This article deals with the use of artificial intelligence that can solved many problems in entrepreneurial and economic field. The artificial intelligence includes genetic algorithms and neural networks. These methods can solve many problems from practice. The distribution problems belong among them. The correct solution of such problems enables us to minimize the cost, save time and nature. The methods mentioned in the article can be used for many similar cases and various places. Dostál, Kratochvíl 2009 ISSN 16871103, ISBN 9772371723 The Decision Making Under Law Uncertainty by Means of Fuzzy Logic The article deals with the use of fuzzy logic at support of manager decision making. The brief description of fuzzy logic and the process of calculation are mentioned. The use is demonstrated on the example such as the decision making whether to accept, entertain or reject the client of law office. The scheme of models, rule blocks, attributes and their membership functions are mentioned. The use of fuzzy logic is the advantage especially at decision making processes at law uncertainty. Dostál 2009 ISBN 9788073141639 The Use of Mapping Toolbox In Economy The article deals with the use of mapping toolbox in economy. There are various methods of evaluation of economic strength of the states of the world. The results of analyses and evaluations serve as a support of decision making. The results are suitable to visualise by the so called choroplets maps. Dostál, Kratochvíl, Jirkovský 2013 ISBN 9788097051945 The Simulation of ProductionFinancial Proces Via Differential Equations The article presents one of the possible methods of simulation in business, where the system of differential equations of first order is used. The productionfinancial system is searched and MATLAB program is used. Dostál 2013, ISBN 9788073142919 Stock Market and Vortex TThe article deals with the possible method of simulation  vortex theory on capital market. There is mentioned the theory and its possible use on the stock market. The MATLAB program is used. Dostál 2015, ISBN 9788073143169 Game of Firms The simulation of competitive environment of firms was based on theory of Game of life. The theory was modified on the business environment and rules of Game of firms were set up. Dostál 2014, ISSN 23361662, ISBN: 9788070809365 
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