In this paper we present a new algebraic model for rough set theory that permits to distinguish between two kinds of "imperfect" information: on one hand, vagueness due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity due to indiscernibility and coarseness typical of rough sets. In other words, we wish to distinguish between fuzziness and granularity of information. To build our model we are using the Brouwer-Zadeh lattice representing a basic vagueness or uncertainty, and to introduce rough approximation in this context, we define a new operator, called Pawlak operator. The new model we obtain in this way is called Pawlak-Brouwer-Zadeh lattice. Analyzing the Pawlak-Brouwer-Zadeh lattice, and discussing its relationships with the Brouwer-Zadeh lattices, we obtain some interesting results, including some representation theorems, that are important also for the Brouwer-Zadeh lattices.
|Title of host publication||Advances on computational intelligence: 14th international conference on information processing and management of uncertainty in knowledge-based systems, proceedings, part 1|
|Editors||Salvatore Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, R. Yager|
|Place of Publication||Berlin|
|Number of pages||9|
|Publication status||Published - 2012|
|Name||Communications in computer and information science|