A comparison of two types of rough sets induced by coverings

Rough set theory is an important technique in knowledge discovery in databases. In covering-based rough sets, many types of rough set models were established in recent years. In this paper, we compare the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang. We further explore the properties and structures of these types of rough set models. We also consider the reduction of coverings. Finally, the axiomatic systems for the lower and upper approximations defined by Xu and Zhang are constructed

New Generalized Definitions of Rough Membership Relations and Functions from Topological Point of View

In this paper, we shall integrate some ideas in terms of concepts in topology. In fact, we introduce two different views to define generalized membership relations and functions as mathematical tools to classify the sets and help for measuring exactness and roughness of sets. Moreover, we define several types of fuzzy sets. Comparisons between the induced operations were discussed. Finally, many results, examples and counter examples to indicate connections are investigated

A New Approach to Analyzing Patterns of Collaboration in Co-authorship Networks - Mesoscopic Analysis and Interpretation

This paper focuses on methods to study patterns of collaboration in co-authorship networks at the mesoscopic level. We combine qualitative methods (participant interviews) with quantitative methods (network analysis) and demonstrate the application and value of our approach in a case study comparing three research fields in chemistry. A mesoscopic level of analysis means that in addition to the basic analytic unit of the individual researcher as node in a co-author network, we base our analysis on the observed modular structure of co-author networks. We interpret the clustering of authors into groups as bibliometric footprints of the basic collective units of knowledge production in a research specialty. We find two types of coauthor-linking patterns between author clusters that we interpret as representing two different forms of cooperative behavior, transfer-type connections due to career migrations or one-off services rendered, and stronger, dedicated inter-group collaboration. Hence the generic coauthor network of a research specialty can be understood as the overlay of two distinct types of cooperative networks between groups of authors publishing in a research specialty. We show how our analytic approach exposes field specific differences in the social organization of research.Comment: An earlier version of the paper was presented at ISSI 2009, 14-17 July, Rio de Janeiro, Brazil. Revised version accepted on 2 April 2010 for publication in Scientometrics. Removed part on node-role connectivity profile analysis after finding error in calculation and deciding to postpone analysis