Topologies Induced by Relations with Applications

Abstract

Topological structures induced by relations represents the process of extracting interesting decision rules from data. The attributes reduction and the calculation of core are the essentials to extract the decision rules. Finding the reducts, core and decision rules topologically is a new mathematical tool for discovering attribute dependencies in information systems. Problem statement: These mathematical tools employ some concepts from topological spaces, relational databases, rough sets and information systems. The results using our approach are more accurate and applicable than that using the classical approaches such as in the father's approach of rough sets (Pawlak approach). Approach: Topologies generated using dominance (pre-order) relations and general binary relation are the knowledgebase of our approximations. We suggested a new algorithm (openness algorithm ) based on the topologies induced by general relations. Results: Results obtained by the proposed approach to find the reducts and core in terms of open and closed sets are compared with the existing method. Our proposed method is proved to be the accurate than results of any approaches using some types of binary relations such as order(pre-order) relations or symmetric relations. Conclusion: In this study, There are many approaches for obtaining topologies by relations and we used some of them in data reduction. These approaches were generalizations to Pawlak approaches namely, we ignored the notion of equivalence relations. Also, these approaches open the way for other approximations if we use the general topological recent concepts such as pre-open sets or semi-open sets.