Knowledge reduction of pessimistic multigranulation rough sets in incomplete information systems

Abstract

The multigranulation rough set model is a critical issue in rough set theory, where target concepts are approximated based on multiple binary relations on the universe. In this work, we show that in an incomplete information system, a novel approach for knowledge reduction is proposed from the discernibility techniques in multigranulation rough set theory. First, we introduce the notions of knowledge reduction in incomplete multigranulation approximation spaces, and prove that pessimistic lower and upper reduct results are different under the surrounding of decision attributes. Second, a decision function mapping each object into the decision options of its neighborhood granule is defined. To find knowledge reducts, three pairs of discernibility matrices and discernibility functions are sequentially measured. Third, the pessimistic lower (upper) approximation granular quality function is employed utilizing the dependent degree. We determine that pessimistic lower and upper consistent sets, respectively, are equivalent to pessimistic lower and upper approximation granular selections, respectively. In other words, these discernibility tools provide a unified standard with respect to knowledge reduction which aims to select valuable and remove worthless knowledges. Finally, numerical experiments using several datasets from UCI are given to show the feasibility and effectiveness of the proposed algorithms.