@article{(Open Science Index):https://publications.waset.org/pdf/8262,
	  title     = {Multi-labeled Data Expressed by a Set of Labels},
	  author    = {Tetsuya Furukawa and  Masahiro Kuzunishi},
	  country	= {},
	  institution	= {},
	  abstract     = {Collected data must be organized to be utilized efficiently, and hierarchical classification of data is efficient approach to organize data. When data is classified to multiple categories or annotated with a set of labels, users request multi-labeled data by giving a set of labels. There are several interpretations of the data expressed by a set of labels. This paper discusses which data is expressed by a set of labels by introducing orders for sets of labels and shows that there are four types of orders, which are characterized by whether the labels of expressed data includes every label of the given set of labels within the range of the set. Desirable properties of the orders, data is also expressed by the higher set of labels and different sets of labels express different data, are discussed for the orders.
},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {4},
	  number    = {5},
	  year      = {2010},
	  pages     = {608 - 614},
	  ee        = {https://publications.waset.org/pdf/8262},
	  url   	= {https://publications.waset.org/vol/41},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 41, 2010},
	}