A Study of Multiple-Source Approximation Systems

摘要

The article continues an investigation of multiple-source approximation systems (MSASs) [1,2]. These are collections of Pawlak approximation spaces over the same domain, and embody the situation where information arrives from a collection of sources. Notions of strong/weak lower and upper approximations of a subset of the domain were introduced in [1]. These result in a division of the domain into five mutually disjoint sets. Different kinds of definability of a set are then defined. In this paper, we study further properties of all these concepts in a structure called multiple-source approximation system with group knowledge base (MSASa), where we also have equivalence relations representing the combined knowledge base of each group of sources. Some of the properties of combined knowledge base are presented and its relationship with the strong/weak lower and upper approximation is explored. Specifically, ordered structures that arise from these concepts are studied in some detail. In this context, notions of dependency, that reflect how much the information provided by a MSASa depends on an individual source or group of sources, are introduced. Membership functions for MSASs were investigated in [2]. These are also studied afresh here.