Iwona Skalna

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.

On checking the monotonicity of parametric interval solution of linear structural systems

If the solution of a parametric linear system is monotone as a function of interval parameters, then an interval hull of parametric solution can be computed easily. Some attempts to solve the problem of checking the monotonicity of parametric solution have been made in the literature. However, no complete algorithm has been given; only some directions for further research were presented. In this paper some investigations on checking monotonicity of parametric interval solution have been made. A method based on authors earlier research is presented. Some illustrative examples of structural mechanical systems are included to check the performance of the method.

Strong regularity of parametric interval matrices

Abstract Several verifiable sufficient and necessary conditions for strong regularity of parametric interval matrices are given. The conditions are formulated in terms of the spectral radius, positive definiteness and eigenvalues of certain real matrices and a scaled maximum norm.

Direct method for solving parametric interval linear systems with non-affine dependencies

Many real-life problems can be modelled by systems of linear equations or safely transformed to the linear case. When uncertain model parameters are introduced by intervals, then a parametric interval linear system must properly be solved to meet all possible scenarios and yield useful results. In general case, system coefficients are nonlinear functions of parameters. The Direct Method for solving such systems is proposed. Affine arithmetic is used to handle nonlinear dependencies. Some illustrative examples are solved and the results are compared to the literature data produced by other methods.

Hybrid framework for investment project portfolio selection

Project selection is a complex multi-criteria decision making process that is influenced by multiple and often conflicting objectives. The complexity of the project selection problem is mainly due to the high number of projects from which an appropriate collection (an effective portfolio) of investment projects must be selected. This paper presents a new conception of a hybrid framework for construction of an effective portfolio of investment projects. The parameters of the considered model are described using both probability distributions and fuzzy numbers (possibility distributions). The proposed framework enables to take into account stochastic dependencies between model parameters and economic dependencies between projects. As a result, a set of Pareto optimal solutions is obtained. The performance of the proposed method is illustrated using an example from metallurgical industry.

Differential evolution applied to large scale parametric interval linear systems

Differential evolution (DE) is regarded to be a very effective optimisation method for continuous problems in terms of both good optimal solution approximation and short computation time. The authors applied DE method to the problem of solving large scale interval linear systems. Different variants of DE were compared and different strategies were used to ensure that candidate solutions generated in the process of recombination mechanism were always feasible. For the large scale problems the method occurred to be very sensitive to the constraint handling strategy used, so finding an appropriate strategy was very important to achieve good solutions in a reasonable time. Real world large optimisation problems coming from structural engineering were used as the test problems. Additionally DE performance was compared with evolutionary optimisation method presented in [10].

A comparison of metaheurisitics for the problem of solving parametric interval linear systems

The problem of computing a hull solution of parametric interval linear systems with general dependencies is considered. It can be reduced to the problem of solving a family of constrained optimizatiom problems. In this study, different metaheuristics are used to solve those problems. Comparison of evolutionary algorithm, simulated annealing and tabu search algorithm together with analysis of variance tests are provided on the basis of three different practical problems.

A global optimisation method for computing interval hull solution for parametric linear systems

An algorithm for computing the interval solution for a parametric interval linear system is presented. The basic idea behind the research is to combine an interval global optimisation method with the Direct Method for Checking the Monotonicity (MCM) of the parametric solution. The MCM is used to perform the monotonicity test to speed up the convergence of the global optimisation. Other acceleration techniques such as subdivision direction selection rules, multisection and the midpoint test are involved as well and checked for usefulness. By using the proposed algorithm, several examples of parametric linear systems are solved. The research proves that the proposed monotonicity test is crucial for the convergence of the interval global optimisation used for computing the interval hull for parametric solution sets, whereas other accelerating techniques are not relevant. The presented algorithm can be useful for solving real-life problems concerning structure mechanics.

Hybrid expert system for qualitative and quantitative analysis of truss structures

Abstract The so-called hybrid expert systems for the analysis of physical systems (e.g. mechanical ones) integrate modelling and simulation methods, including classical numerical ( quantitative ) methods as well as recently developed qualitative analysis methods, using the expert-system rule-based techniques. The diagrammatic representation methods also turn out to be important elements of the knowledge representation (especially the qualitative knowledge) and user interface in such systems. In this paper, problems in the construction of such systems are discussed, using an example of an experimental hybrid system for the analysis of planar truss structures (currently in the final stages of implementation).

Model Driven Architecture and classification of business rules modelling languages

An organisations activity under dynamic changes of business processes requires continuous improvement of business practices. This implies the necessity of refining decision making process. Business rules [6], [8] enable experts to transfer enterprise strategy onto the operational level using simple sentences which, in turn, can automate reactions to subsequent events both inside and outside the organisation. The main advantage of the business rules is their simplicity and flexibility so they can be easily utilised by different organisations for different purposes. In order to represent knowledge in a pseudo-natural language understandable to information systems (business rules engines) notation and description standards are required. In this study, an overview and classification of the most popular business rules description languages are presented.