6533b820fe1ef96bd127a39f

RESEARCH PRODUCT

Algebraic Structures of Rough Sets

Zbigniew Bonikowski

subject

Set (abstract data type)Discrete mathematicsRelation (database)Algebraic structureEquivalence relationEmpty setRough setAlgebraic numberSpace (mathematics)Mathematics

description

This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].

yearjournalcountryeditionlanguage
1994-01-01
https://doi.org/10.1007/978-1-4471-3238-7_29