Rough Set Based Decision Support

In this chapter, we are concerned with discovering knowledge from data. The aim is to find concise classification patterns that agree with

situations

that are described by the data. Such patterns are useful for explanation of the data and for the prediction of future situations. They are particularly useful in such decision problems as technical diagnostics, performance evaluation and risk assessment. The situations are described by a set of

attributes

, which we might also call properties, features, characteristics, etc. Such attributes may be concerned with either the

input

or

output

of a situation. These situations may refer to states, examples, etc. Within this chapter, we will refer to them as

objects

. The goal of the chapter is to present a knowledge discovery paradigm for multi-attribute and multicriteria decision making, which is based upon the concept of rough sets. Rough set theory was introduced by (

Pawlak 1982

,

Pawlak 1991

). Since then, it has often proved to be an excellent mathematical tool for the analysis of a

vague

description of objects. The adjective vague (referring to the quality of information) is concerned with inconsistency or ambiguity. The rough set philosophy is based on the assumption that with every object of the universe

U

there is associated a certain amount of information (data, knowledge). This information can be expressed by means of a number of attributes. The attributes describe the object. Objects which have the same description are said to be indiscernible (similar) with respect to the available information.