Abstract
The rough set concept was originally proposed by Pawlak as a formal tool for modeling incompleteness and imprecision in information systems. Rough set theory is an extension of set theory in which a subset of a universe is described by a pair of sets called lower and upper approximations. Near set theory was introduced by Peters as a generalization of rough set theory. In this theory, Peters depends on the features of objects to define the nearness of objects and consequently, the classification of our universal set with respect to the available information of the objects. Many sets are naturally endowed with binary operations. One concept which does this is an MV -algebra. An MV -algebra has the structure (M, ⊕, *, 0), where ⊕ is a binary operation, * is a single operation, and 0 is a constant satisfying. Indeed, an MV-algebra is an algebraic structure which models Lukasiewicz multivalued logic, and the fragment of that calculus which deals with the basic logical connectives “and”, “or”, and “not”, but in a multivalued context. This paper concerns a relationship between near sets, fuzzy sets and MV -algebra. We define lower and upper near approximations based on fuzzy ideals in an MV -algebra. Some characterizations of the above near approximations are made and some examples are presented.