Rough Sets and Current Trends in Computing

Data mining is usually introduced as search for interesting patterns in data. It is often an explorative step iteratively performed within a process of knowledge discovery in data bases (KDD). A mining step typically relies on strategies for systematic search in large hypotheses spaces guided by the autonomous evaluation of statistical tests. We describe the subgroup mining approach that is based on deviation and association patterns. A typical database contains values of attributes for many objects (persons, transactions, documents). Interpretable subgroups of these objects are searched that deviate from a designated expected behavior. Many types of data analysis questions can be answered by subgroup mining with diverse specializations of general deviation and association patterns. Tests measure the statistical interestingness of subgroup deviations. After summarizing the approach by discussing the fundamental components of subgroup pattern classes concerning validation, search and interactive presentation of pattern instances, we explain how deviation patterns of subgroup mining are applied for temporal, spatial and textual databases.

We discuss philosophical and metamathematical origins of rough sets and their fundamental properties. We argue that rough sets are necessary in the light of the Platonian concept of ideal mathematical objects. We show how rough sets have been present in concept formation, diagnosis, classification and other reasoning tasks. We present examples indicating that the intuitive idea of a rough set has been used (under various names) by physicians, engineers and philosophers as a basic tool to classify and utilize concepts in their respective domains of activity. We discuss the differences between rough sets and other approaches to incomplete and imprecise information such as fuzzy logic and logics that formalize the process of “jumping to conclusions”.

The paper contains some considerations concerning the relationship between decision rules and inference rules from the rough set theory perspective. It is shown that decision rules can be interpreted as a generalization of the modus ponens inference rule, however there is an essential difference between these two concepts. Decision rules in the rough set approach are used to describe dependencies in data, whereas modus ponens is used in general to derive conclusions from premises.

In our quest for machines which are capable of performing non-trivial human tasks, we are developing a better understanding of the centrality of information granulation in human cognition, human reasoning and human decision-making. In many contexts, information granulation is a reflection of the finiteness of human ability to resolve detail and store information. In many other contexts, granulation is employed to solve a complex problem by partitioning it into simpler subproblems. This is the essence of the strategy of divide and conquer. What is remarkable is that humans are capable of performing a wide variety of tasks without any measurements and any computations. A familiar example is the task of parking a car. For a human it is an easy task so long as the final position of the car is not specified precisely. In performing this and similar tasks, humans employ their ability to exploit the tolerance for imprecision to achieve tractability, robustness and low solution cost. What is important to recognize is that this essential ability is closely linked to the modality of granulation and, more particularly, to information granulation.