Attribute Reduction in Intuitionistic Fuzzy Concept Lattices

Jinzhong Pang,Weihua Xu,Xiaoyan Zhang

doi:10.1155/2013/271398

Jinzhong Pang, Weihua Xu + Show 1 more

Open Access

https://doi.org/10.1155/2013/271398

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Abstract

As an effective tool for knowledge discovery, concept lattice has been successfully applied to various fields. And one of the key problems of knowledge discovery is attribute reduction. In order to understand the problems better, the attribute reduction is necessary to perfect the theory as well as expand application of concept lattice. This paper introduces the intuitionistic fuzzy theory into the concept lattice theory and proposes a kind of intuitionistic fuzzy concept lattice. Then, an approach to attribute reduction based on the discernibility matrix is proposed and investigated, which makes the discovery of implicit knowledge easier and the representation simpler in data; furthermore, the theory of concept lattice is perfected. The theory of intuitionistic fuzzy concept lattice is useful and meaningful in view of the complexity and fuzziness of information in real world, and the potential value of dealing with information is expected in the future.

Highlights

Concept lattice stems from the so-called formal concept analysis proposed by Wille in 1982 [1], which can be depicted by a Hasse diagram, where each node expresses a formal concept
This paper introduced the intuitionistic fuzzy set into the concept lattice theory firstly
We offered the related definitions and propositions of attribute reduction in concept lattices which were examined by some examples

Summary

Introduction

Concept lattice stems from the so-called formal concept analysis proposed by Wille in 1982 [1], which can be depicted by a Hasse diagram, where each node expresses a formal concept. The study on attribute reduction for intuitionistic fuzzy formal context has not been investigated perfectly, the discernibility matrix was proposed by using of the cuts of IF sets and established the method of the attribute reduction of IF concept lattice in paper [24]. Because it leaves out some useful information about transforming the concept lattice based on the IF the formal context to a classical one only by using the cuts of the IF sets.

Preliminaries

IF Concept Lattice

Attribute Reduction in IF Concept Lattices

Approach to Reduction

6: Compute

Conclusion