The axiomatic characterizations on L-generalized fuzzy neighborhood system-based approximation operators

Abstract

The rough sets based on L-fuzzy relations and L-fuzzy coverings are the two most well-known L-fuzzy rough sets. Quite recently, we prove that some of these rough sets can be unified into one framework—rough sets based on L-generalized fuzzy neighborhood systems. So, the study on the rough sets based on L-generalized fuzzy neighborhood system has more general significance. Axiomatic characterization is the foundation of L-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence of L-fuzzy relations, L-fuzzy coverings that reproduce the approximation operators. In this paper, we shall give an axiomatic study on L-generalized fuzzy neighborhood system-based approximation operators. In particular, we will seek the axiomatic sets to characterize the approximation operators generated by serial, reflexive, unary and transitive L-generalized fuzzy neighborhood systems, respectively.

Keywords:

• Rough set
• L-generalized fuzzy neighborhood system
• upper approximation operator
• lower approximation operator
• complete residuated lattice

Acknowledgements

The authors thank the reviewers and the editor for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11501278], [grant number 11471152]; and Shandong Provincial Natural Science Foundation, China [grant number ZR2013AQ011], [grant number ZR2014AQ011].