Beata Basiura

Advances in Fuzzy Decision Making

This book shows how common operation management methods and algorithms can be extended to deal with vague or imprecise information in decision-making problems. It describes how to combine decision trees, clustering, multi-attribute decision-making algorithms and Monte Carlo Simulation with the mathematical description of imprecise or vague information, and how to visualize such information. Moreover, it discusses a broad spectrum of real-life management problems including forecasting the apparent consumption of steel products, planning and scheduling of production processes, project portfolio selection and economic-risk estimation. It is a concise, yet comprehensive, reference source for researchers in decision-making and decision-makers in business organizations alike.

Multi-attribute Decision Making Process and Its Application

This chapter proposes the integrated fuzzy approach to solve Multi Attribute Decision Problems. Fuzzy Analytical Hierarchy Process (FAHP) is used to assign relative weights to criteria, and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is employed to rank the alternatives. The use of the proposed approach is illustrated using a real case from a steel industry.

Selected Issues of Visualisation of Fuzziness in Cardiac Imaging Data

This chapter proposes an approach to visualisation of fuzzy numbers in one-, two- and more-dimensional spaces. The proposed approach is based on ScPovPlot3D templates for POVRay.

Fuzzy Random Variable and the Dempster-Shafer Theory of Evidence

This chapter presents the concept of uncertainty propagation in real world desicion problems, where some input parameters are stochastic while information about others is partial and is represented by fuzzy random variable. It also introduces fuzzy random variable and the Dempster-Shafer theory which provide mathematical background for such propagation.

Application of Fuzzy Decision Trees in Analog Forecasting

This chapter presents a new method for forecasting the level and structure of market demand for industrial goods. The method employs two data mining methods: k-means clustering and fuzzy decision tree learning. The k-means method serves to separate groups with items of a similar consumption level and structure of the analysed products. Whereas, fuzzy decision tree learning are used to determine the dependencies between consumption patterns and predictors. The proposed method is verified using the extensive statistical material on the level and structure of steel products consumption in selected countries in the years 1960–2010.

Risk Assessment in the Presence of Uncertainty

This chapter is devoted to a method which is able to process hybrid data, i.e., to jointly handle both randomness and imprecision. Random variables are described by probability distributions and imprecise values are modelled using possibility distributions. The main advantage of the proposed method is that it takes into account the dependencies between economic parameters.

Application of Fuzzy Theory in Steel Production Planning and Scheduling

This chapter describes the application of fuzzy sets to planning and scheduling of production in the steel industry. Primarily, the problem of steel grade assignment to customer’ orders is analysed. Fuzzy sets are used to reduce the variety of potential steel grades and to describe characteristic of materials by decision makers. Next, fuzzy logic systems for steel production scheduling are examined. Fuzzy parameters and fuzzy constraints are used to describe some aspects of the steel production process, with a special respect to the continuous casting. Finally, the cooperation of steel production planning between different shops using a multi-agent approach and fuzzy sets is discussed and the practical example of a genetic algorithm applied to solve a fuzzy lot-sizing problem for a continuous casting planning agent is presented.

Ordering of Fuzzy Numbers

This chapter describes different methods for comparing and ordering fuzzy numbers. Theoretically, fuzzy numbers can only be partially ordered, and hence cannot be compared. However, in practical applications, such as decision making, scheduling, market analysis or optimisation with fuzzy uncertainties, the comparison of fuzzy numbers becomes crucial.