TY - CHAP

T1 - Distinguishing vagueness from ambiguity by means of pawlak-brouwer-zadeh lattices

AU - Greco, Salvatore

AU - Matarazzo, B.

AU - Słowiński, R.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-642-31709-5_63

DO - 10.1007/978-3-642-31709-5_63

M3 - Chapter (peer-reviewed)

SN - 9783642317088

VL - 297

T3 - Communications in computer and information science

SP - 624

EP - 632

BT - Advances on computational intelligence: 14th international conference on information processing and management of uncertainty in knowledge-based systems, proceedings, part 1

A2 - Greco, Salvatore

A2 - Bouchon-Meunier, B.

A2 - Coletti, G.

A2 - Fedrizzi, M.

A2 - Matarazzo, B.

A2 - Yager, R.

PB - Springer

CY - Berlin

ER -