Paper:

# Non Metric Model Based on Rough Set Representation

## Yasunori Endo^{*}, Ayako Heki^{**}, and Yukihiro Hamasuna^{***}

^{*}Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

^{**}Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

^{***}Department of Informatics, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan

The non metricmodel is a kind of clustering method in which belongingness or the membership grade of each object in each cluster is calculated directly from dissimilarities between objects and in which cluster centers are not used. The clustering field has recently begun to focus on rough set representation instead of fuzzy set representation. Conventional clustering algorithms classify a set of objects into clusters with clear boundaries, that is, one object must belong to one cluster. Many objects in the real world, however, belong to more than one cluster because cluster boundaries overlap each other. Fuzzy set representation of clusters makes it possible for each object to belong to more than one cluster. The fuzzy degree of membership may, however, be too descriptive for interpreting clustering results. Rough set representation handles such cases. Clustering based on rough sets could provide a solution that is less restrictive than conventional clustering and more descriptive than fuzzy clustering. This paper covers two types of Rough-set-based Non Metric model (RNM). One algorithm is the Roughset-based Hard Non Metric model (RHNM) and the other is the Rough-set-based Fuzzy Non Metric model (RFNM). In both algorithms, clusters are represented by rough sets and each cluster consists of lower and upper approximation. The effectiveness of proposed algorithms is evaluated through numerical examples.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.17, No.4, pp. 540-551, 2013.

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