# Overview

## Fuzzy logic

In classical logic, each proposition is assigned a truth degree 1 (proposition is true) or 0 (proposition is false). This is called the principle of bivalence of classical logic. As an example, truth degree 1 is assigned to proposition “2+2 equals 4” while 0 is assigned to proposition “New York is a capital of United States”. This is not appropriate when dealing with propositions involving empirical concepts such as “Gas prices are high” or “Inside temperature is very low”. Neither “high price” nor “very low tempretature” is a bivalent concept. As a result, classical logic cannot be applied to these propositions. Fuzzy logic extends classical logic in that it is capable of dealing with empirical concepts such as “high price”. Fuzzy logic involves both fundamental theoretical research and applications in various areas where classical logic and classical mathematics has limited applicability. These areas include decision making and reasoning with uncertainty, control of complex systems, knowledge discovery and representation, data analysis. Best known applications of fuzzy logic are in consumer electronics, industrial control, and economics and management. Fuzzy logic is a very active research area and is considered to represent a new paradigm. Fundamental discoveries regarding both foundations and applications of fuzzy logic are still being expected.

## Data and Knowledge Engineering, Data Analysis & Data Mining

Information in our society is stored in computers in huge amounts of data. How do we efficiently represent the data? How do we represent human knowledge? How do we retrieve information from data and how do we extract knowledge from data, i.e. how do we transform data, inncomprehensible by humans, to something useful? These are the fundamental questions pertaining to data and knowledge engineering, data analysis and data mining. Several methods of data mining have been proposed recently. We specialize in conceptual knowledge processing, in particular in formal concept analysis. The main aim is to represent knowledge and discover knowledge in data in form of concepts and conceptual structures, i.e. close to the way humans represent knowledge. Data mining techniques have been applied in numerous domains including biological data, sociological data, homeland security, marketing and management, education and psychology, and finance.