Multi-fuzzy rough sets and relations

Pawlak’s Rough set theory was originally proposed as a general mathematical tool for dealing with uncertainty in modeling imperfect knowledge. The purpose of this paper is to introduce the concept of multifuzzy rough sets by combining the multi-fuzzy set and rough set models. Some operations such as Complement, Union, Intersection etc. are defined for multi-fuzzy rough sets and De Morgan’s laws are proved. Finally, the concept of multi-fuzzy rough relations and composition of multi-fuzzy rough relations are introduced and some properties of such relations are studied. 2010 AMS Classification: 68T30, 03E72