Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In recent years, rough set theory initiated by Pawlak has been intensively investigated. When the classical rough sets based on equivalence relations have been extended to generalized rough sets based on binary relations, the lor and upper rough approximations, which are the core concepts of rough set theory, have been generalized in several different ways. A common feature of these generalized approximations is that they use only one step information of the underlying relation to discern objects. By one step in a binary relation  mean that the ordered pair of the starting and end points of the step belongs to the relation. Motivated by a rich notion, bisimulation, appearing in various areas of computer science,  introduce a kind of lor and upper rough approximations for generalized rough sets in this paper. Our lor and upper approximations are based on bisimulations, in particular, bisimilarity, which is the largest bisimulation. Roughly speaking, bisimilar objects are regarded as indiscernible.  present some basic properties of the new lor and upper rough approximations and illustrate our motivation and the applicability of our results by examples. Moreover,  make a detailed comparison beten the rough approximations based on the underlying relation and the rough approximations based on bisimilarity. In particular,  provide a necessary and sufficient condition for the consistency of the two kinds of rough approximations.  introduce a kind of lor and upper rough approximations based on bisimulations. approximate binary relations by equivalence relations with bisimilarity property. present some basic properties of the new lor and upper rough approximations. compare the approximations based on an underlying relation and on bisimilarity.
['Ping Zhu', 'Huiyang Xie', 'Qiaoyan Wen']
I am writing a research paper on a idea Rough approximations based on bisimulations
[{"from": "human", "value": "I am writing a research paper on a idea Rough approximations based on bisimulations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In recent years, rough set theory initiated by Pawlak has been intensively investigated. When the classical rough sets based on equivalence relations have been extended to generalized rough sets based on binary relations, the lor and upper rough approximations, which are the core concepts of rough set theory, have been generalized in several different ways. A common feature of these generalized approximations is that they use only one step information of the underlying relation to discern objects. By one step in a binary relation  mean that the ordered pair of the starting and end points of the step belongs to the relation. Motivated by a rich notion, bisimulation, appearing in various areas of computer science,  introduce a kind of lor and upper rough approximations for generalized rough sets in this paper. Our lor and upper approximations are based on bisimulations, in particular, bisimilarity, which is the largest bisimulation. Roughly speaking, bisimilar objects are regarded as indiscernible.  present some basic properties of the new lor and upper rough approximations and illustrate our motivation and the applicability of our results by examples. Moreover,  make a detailed comparison beten the rough approximations based on the underlying relation and the rough approximations based on bisimilarity. In particular,  provide a necessary and sufficient condition for the consistency of the two kinds of rough approximations.  introduce a kind of lor and upper rough approximations based on bisimulations. approximate binary relations by equivalence relations with bisimilarity property. present some basic properties of the new lor and upper rough approximations. compare the approximations based on an underlying relation and on bisimilarity."}]