Abstract-In recent times enumerable number of clustering algorithms have been developed whose main function is to make sets of objects having almost the same features. But due to the presence of categorical data values, these algorithms face a challenge in their implementation. Also some algorithms which are able to take care of categorical data are not able to process uncertainty in the values and so have stability issues. Thus handling categorical data along with uncertainty has been made necessary owing to such difficulties. So, in 2007 MMR algorithm was developed which was based on basic rough set theory. MMeR was proposed in 2009 which surpassed the results of MMR in taking care of categorical data and it could also handle heterogeneous values as well. SDR and SSDR were postulated in 2011 which were able to handle hybrid data. These two showed more accuracy when compared to MMR and MMeR. In this paper, we further make improvements and conceptualize an algorithm, which we call MMeMeR or Min-Mean-Mean-Roughness. It takes care of uncertainty and also handles heterogeneous data. Standard data sets have been used to gauge its effectiveness over the other methods.

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In recent times, an enumerable number of clustering algorithms have been developed whose main function is to make sets of objects have almost the same features. But due to the presence of categorical data values, these algorithms face a challenge in their implementation. Also, some algorithms which are able to take care of categorical data are not able to process uncertainty in the values and therefore have stability issues. Thus, handling categorical data along with uncertainty has been made necessary owing to such difficulties. So, in 2007 an MMR algorithm was developed which was based on basic rough set theory. MMeR was proposed in 2009 which surpassed the results of MMR in taking care of categorical data but cannot be used robustly for hybrid data. In this article, the authors generalize the MMeR algorithm with neighborhood relations and make it a neighborhood rough set model which this article calls MMeNR (Min Mean Neighborhood Roughness). It takes care of the heterogeneous data. Also, the authors have extended the MMeNR method to make it suitable for various applications like geospatial data analysis and epidemiology.