Attributes reductions of bipolar fuzzy relation decision systems

Abstract

Attribute reduction methods constitute a very important preprocessing step for artificial intelligence and pattern recognition. It has been investigated in contexts ranging from rough sets to soft sets. In this study, firstly we propose the ideas of bipolar fuzzy relation systems and bipolar fuzzy relation decision systems. They constitute intuitive extensions of various systems, for instance decision tables, relation systems, relation decision systems, fuzzy relation systems (FRSs) and fuzzy relation decision systems (FRDSs). Secondly, relying on mathematical proofs we investigate the attribute reduction problems for bipolar fuzzy relation systems and bipolar fuzzy relation decision systems and we give their corresponding reduction algorithms. Moreover, we compute the reduction algorithms for FRSs and FRDSs as particular cases of bipolar fuzzy relation systems and bipolar fuzzy relation decision systems, respectively. The experimental results prove that the concepts in this study are valid and implementable.