Abstract
In this paper, we present a new algebraic model for Dominance-based Rough Set Approach. Extending the Pawlak-Brouwer-Zadeh lattice introduced for indiscernibility-based rough set approach, the new model permits to distinguish between two kinds of imperfect information in case of ordered data: vagueness due to imprecision, and ambiguity due to coarseness typical to rough sets. To build the model we use the bipolar Brouwer-Zadeh lattice to represent a basic vagueness, and to introduce dominance-based rough approximations we define a new operator, called bipolar Pawlak operator. The new model we obtain in this way is called bipolar Pawlak-Brouwer-Zadeh lattice.
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Greco, S., Matarazzo, B., Słowiński, R. (2017). Distinguishing Vagueness from Ambiguity in Dominance-Based Rough Set Approach by Means of a Bipolar Pawlak-Brouwer-Zadeh Lattice. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_6
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