Rough Sets Theory in Decision Analysis

This paper presents a possibility of using of the rough sets theory for a reduction of attributes (criteria, data, information) of objects in multi-attributes decision analysis in a public administration system. It is investigated one natural dimension of reducing data which is to identify equivalence classes, i.e. objects that indiscernible using the available attributes, using approximation sets. Introduction During last few years trends in public administration management have over come more waves with the aim to use advantages from information technology application. Modern era is demanding changes in organization management philosophy. A re-engineering has become a well known process with organization changes of a public administration structure with aim to change the classical management hierarchy especially on the level of central management. This level has been replaced by information technologies. In connection with this fact structure have been created which were able to react faster to changes and decide independently. The re-engineering may be realized by a process (a knowledge engineering) which expert knowledge is obtained, represented, refined and installed in computer-based diagnostic and decision-making systems. The term knowledge engineering has been used in the field of decision analysis [5,12]. Decision analysis is an engineering discipline that addresses the pragmatics of applying decision theory to real-world problems and may be applied to scheduling, capital expansion, and research and development decisions. The five important elements of the decision analysis are: the objectives, the alternatives, the impact, the criteria and the model [12]. In the search for the best alternative may be viewed as taking place in five stages (phases) that, in logical order, are: formulation (clarifying and constraining the problem and determining the objective), search (identifying, designing, and screening the alternatives), forecasting (predicting the future environment or operational context), modelling (building and using models to determine the impacts), and synthesis (comparing and ranking the alternatives). Generally speaking, a decision problem [12] involves a set of objects (actions, courses of action, states, competitors, etc.) described or evaluated by a set of attributes (criteria, features, issues, etc.). Independently of further interpretation, a decision situation may be represented by a table rows which correspond to objects and columns to attributes; for each pair (objectattribute) there is known a value called descriptor. We can also say that the table represents knowledge about a decision situation. Typically, one or several decision makers (experts, agents, nature, etc.) are also involved in a decision problem. By a decision maker we understand a person or thing that works to reduce a result (observation, decision, evaluation, etc.). The attributes used to describe objects are build on some elementary features of objects. They may be nominal (also called categorical or quantitative, e.g. male or female) or cardinal 1 The discipline of decision analysis emerged in the 1960s; it grew out of a recognition that probability and decision theory, until now applied primarily to problems of statistical estimation, also could be applied to realworld decision problems.