Incremental fuzzy probabilistic rough sets over two universes

Abstract

The fuzzy Information System over Two Universes (ISTU) formalizing a data table corresponding to two universes as well as their relations is common in real-world applications, e.g., recommender system and clinical diagnosis system. The fuzzy probabilistic rough sets over two universes (FPRSMTU) can deal with a fuzzy relation and allow a tolerance inaccuracy in the construction of rough approximations in a fuzzy ISTU, which is a generalization of classic rough sets with fuzzy and probabilistic theories. As a necessary step for knowledge discovery based on rough sets, the fuzzy rough approximations of fuzzy ISTU need to be updated efficiently under dynamic data environment. Incremental technique is an efficient approach for dynamic information processing by making full use of previously obtained knowledge. In this paper, incremental approaches for updating approximations of fuzzy ISTU are proposed while some objects adding into or deleting from the two universes, and the corresponding incremental algorithms are designed. Experimental evaluations on real datasets as well as artificial datasets show the effectiveness of the proposed incremental updating method compared with the non-incremental method.

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

“…These two theories are not competing, but rather complement each other. Many models have been proposed to hybridise rough sets and fuzzy sets [6,29,30,34,39,[170][171][172][173][174][175][176][177][178]. A fuzzy-rough set is the pair of lower and upper approximations of a fuzzy set in a universe on which a fuzzy relation is defined.…”

“…Sun et al [62] proposed the new fuzzy-rough set on a probabilistic approximation space and used it with respect to decisionmaking in unconventional emergency management. Hu et al [171] proposed a new incremental method to update approximations of fuzzy information system over two universes. Fan et al [72] introduced several double-quantitative DTRS (DQ-DTRFS) models based on logical conjunction and disjunction operations.…”

Matrix-Based Approaches for Updating Approximations in Multigranulation Rough Set While Adding and Deleting Attributes

“…The issue of computing and updating approximations in MGRSs and their derived models attracts much research interest. These studies are often categorized into four classes by scholars, namely, how to update approximations while varying attributes [33,34], how to update approximations while varying attribute values [35,36], how to update approximations while varying decision attribute values [33,37], and how to update approximations while varying object set [38,39].…”

Dynamic composite decision-theoretic rough set under the change of attributes

“…Recently, the incremental updating strategies have been widely researched in rough sets 7,6,19,21,20,30,4,26,38,8 . To efficiently obtain the useful acknowledge under the change of information system, we can propose the incremental updating methods to reduce the computational time in the theory of rough sets.…”