Enhanced Algorithms for Fuzzy Formal Concepts Analysis

Abstract

Fuzzy formal concept analysis (FFCA) is a generalized form of traditional formal concept analysis (FCA) that exploits fuzzy set theory to process uncertain data efficiently. Generally, most real world applications incorporate uncertain data at least for some extent. Consequently, they need reliable approaches to discover potentially useful non-trivial knowledge. Commonly, FFCA aims mainly to reach such knowledge in form of fuzzy formal concepts. It is used widely in data analysis tasks, association rule discovery and extraction of essential ontology components. This paper proposes two enhanced algorithms for extracting fuzzy formal concepts based on fuzzy sets of objects and crisp sets of attributes. Such kind of FFCA best suits Ontology construction and association rule mining tasks. Commonly, extracting fuzzy concepts is considered the most time consuming process in FCA and FFCA. So, the proposed enhanced algorithms aim mainly to reduce the complexity and extraction time of fuzzy formal concepts’ extraction process. The first enhanced algorithm best fits in case of the existence of symmetric correlated attributes. On the other hand, the second enhanced algorithm generally reduces the complexity as a result of reducing total number of generated fuzzy concepts. It works extremely better when the number of distinct intents of objects is relatively smaller. The results of testing the proposed enhanced algorithms show their added value.