Showing papers on "Rough set published in 1982"

Rough sets. Algebraic and topological approach

Abstract: W: ICS PAS Reports 482/82, pages 1-32. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland, 1982

On a concept of rough seis

Abstract: In t roduc t ion In [ 1 ] Z.Pjawlak introduced the not ion of a rough se t used to def ine approximate operat ions on s e t s , approximate e q u a l i ty of s e t s and approximate inc lus ion of s e t s . The notion of a rough se t can be viewed as an a l t e r n a t i v e to fuzzy set [ 2 ] , however there are some e s s e n t i a l d i f f e r e n c e s between these two no t ions . Theory of fuzzy s e t s , theory of to le rance spaces £3] and theory of ro> .. w i l l be cal led an approximation space. Equivalence c l a s se s of the r e l a t i o n R w i l l be r e f e r r e d to as elementary s e t s in A ( s h o r t : elementary s e t s ) . Every union of elementary s e t s in A and an empty se t w i l l be ca l led a composed set i n A ( sho r t : composed s e t ) . Let X c U. The l e a s t composed set i n A containing X w i l l be ca l l ed the best upper approximation of X in A, denoted as AX. The g r e a t e s t composed set in A contained i n X w i l l be cal led the beet lower approximation of X in A, denoted as AX. In [1] the fol lowing condi t ions are the axioms f o r approximations val id in every approximation space

Rough sets. Power set hierarchy

Abstract: W: ICS PAS Reports 470/82, pages 1-27. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland, 1982

Fuzzy sets as set classes.

Abstract: Fuzzy sets have been studied in various forms. We now offer a presentation of fuzzy sets whereby they are conceived as representatives of a whole class of sets (that are themselves subsets of the universe of objects on which the fuzzy set is defined).