Rough Set Theory over Fuzzy Lattices

Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.

Identifying the key factors of subsidiary supervision and management using an innovative hybrid architecture in a big data environment

In a highly intertwined and connected business environment,globalized layout planning can be an effective way for enterprises to expand their market.Nevertheless,conflicts and contradictions always exist between parent and subsidiary enterprises;if they are in different countries,these conflicts can become especially problematic.Internal control systems for subsidiary supervision and management seem to be particularly important when aiming to align subsidiaries’decisions with parent enterprises’strategic intentions,and such systems undoubtedly involve numerous criteria/dimensions.An effective tool is urgently needed to clarify the relevant issues and discern the cause-and-effect relationships among them in these conflicts.Traditional statistical approaches cannot fully explain these situations due to the complexity and invisibility of the criteria/dimensions;thus,the fuzzy rough set theory(FRST),with its superior data exploration ability and impreciseness tolerance,can be considered to adequately address the complexities.Motivated by efficient integrated systems,aggregating multiple dissimilar systems’outputs and converting them into a consensus result can be useful for realizing outstanding performances.Based on this concept,we insert selected criteria/dimensions via FRST into DEMATEL to identify and analyze the dependency and feedback relations among variables of parent/subsidiary gaps and conflicts.The results present the improvement priorities based on their magnitude of impact,in the following order:organizational control structure,business and financial information system management,major financial management,business strategy management,construction of a management system,and integrated audit management.Managers can consider the potential implications herein when formulating future targeted policies to improve subsidiary supervision and strengthen overall corporate governance.