International Journal of Granular Computing, Rough Sets and Intelligent Systems (3 papers in press)

• Some Topological Properties of Rough Sets and their Applications
  by BalaKrushna Tripathy 
  Abstract: Properties of approximations of sets establish that lower approximation of union of sets is not equal to the union of their lower approximations in general and the result is similar for upper approximations of intersection of sets. This leads to the observation that there is a loss of information in a distributed knowledge base than in an integrated one. In this paper we obtain necessary and sufficient conditions under which equality will hold in the above two properties. Also, we deal with the types of union and intersection of rough sets and find that there are some ambiguous cases. Using our theorems these ambiguities can be reduced. We obtain another theorem which reduces one of the remaining ambiguities. Novotny and Pawlak [2, 3, 4] introduced and studied three (bottom, top and total) types of rough equalities, which show that comparison of domains depend upon our knowledge about the universe. Also, they have obtained some properties of these approximate equalities of sets. In this paper, we obtain suitable conditions under which the top and bottom rough equalities can be interchanged in these properties which were noted earlier to be false. The sufficient conditions required for some of these cases to be true have been derived from our theorems. An example of a distributed database of employees is used throughout the paper to illustrate or support the results established.
  Keywords: Rough set, lower approximation, upper approximation, knowledge base, equivalence relation, bottom R-equal, top R-equal and R-equal.
   
• Modelling Steel Heat Treatment Data Using Granular Data Compression and Multiple Granularity Modelling
  by George Panoutsos, Mahdi Mahfouf 
  Abstract: In this paper a systematic modelling approach is presented, involving two algorithmic procedures: a) a data pre-processing and data compression algorithm using granular computing and statistics and b) a granular neural-fuzzy ensemble network consisting of multiple granularity models. Both algorithmic procedures aim to reduce the data and modelling scatter often found in real industrial complex data. The study focuses on the prediction of the mechanical property of heat treated steel, in particular Charpy Toughness. This mechanical property yields high data scatter caused by unknown underlying fractural dynamics. The proposed methodology is shown to successfully model the process under investigation using a real industrial data set.
  Keywords: Granular Computing (GrC); granular data compression; multiple granularity modelling; granular neural-fuzzy modelling; mechanical properties of heat treated steel; Charpy toughness
   
• Intelligent Technique and Its Application in Fault Diagnosis Based on Granular Computing
  by Zhang Zhousuo, Yan Xiaoxu, Cheng Wei 
  Abstract: This paper presents a new approach to intelligent fault diagnosis of the machinery based on granular computing. The tolerance granularity space mode is constructed by means of the inner-class distance defined in the attributes space. Different features of the vibration signals, including time domain statistical features and frequency domain statistical features, are extracted and selected using distance evaluation technique as the attributes to construct the granular structure. Finally, the proposed approach is applied to fault diagnosis of rolling element bearings, and testing results show that the proposed approach can reliably recognize different faulty categories and severities.
  Keywords: Granular computing;tolerance relations;granularity structure; fault diagnosis