Double-faced rough sets and rough communication

This paper shows that each rough set can be evaluated from two different aspects which may be considered as two facets of rough sets. One refers to the conceptual meaning of each rough set, e.g., we say that the concept of lion is included in the concept of animal and the concept of animal has a higher order of inclusion than the concept of lion. The second one refers to the amount of knowledge that each rough set exhibits, e.g., a zoologist may consider a more informative rough set for the concept of lion (he considers more kinds of lions in his set) than a rough set which proposed by a nonspecialist person. So, the first facet views the theory of rough set as an extension of the classical set theory in terms of the three-valued logic which is a proper tool of reasoning and decision making based on a solitary source of information. The second facet concerns the ability of rough set theory to knowledge manipulation and reduction among several information sources such that we do not care the soundness or falsity of the available information. We show that the second facet is the salient characteristic of rough sets which has the capability of being extended more in new application areas. As a result, we present a new extension of rough sets called rough communication as a proper tool of dealing with several information sources. At the end, we refer to some interesting mathematical symmetries between two facets which may be used to propose new extensions.