A theoretical study on object-oriented and property-oriented multi-scale formal concept analysis
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In traditional formal concept analysis, the attributes in the formal context are considered fixed. However, in the real world data set, attributes always have different levels of granularity, correspondingly, the derived concept lattice may reveal different information and patterns. Therefore, the capability to change the level of granularity of an attribute in formal concept analysis to capture relevant patterns in data is a natural requirement. In this paper, a theoretical study has been undertaken in multi-scale formal contexts, where attributes with different levels of granularity possess different attribute values. Two types of formal concepts, i.e., object-oriented and property-oriented multi-scale concepts, are introduced and studied in detail. The collection of object-oriented concept lattices and property-oriented concept lattices can be obtained at different granularity levels of attributes. It has been shown that the set of extents in the derived concept lattices increases when we choose to use a finer level of granularity. Moreover, a corresponding bidirectional approach to concept construction(i.e., from coarser to finer and from finer to coarser, respectively) is exhibited, and some characterization theorems have been obtained.
KeywordsGranularity Formal concept analysis Object-oriented multi-scale concept Property-oriented multi-scale concept
This work is supported by the National Nature Science Foundation of China (nos. 61976244, 61472471 and 11531009), Innovation Talent Promotion Plan of Shaanxi Province for Young Sci-Tech New Star (2017KJXX-60) and Scientific Research Program of Shaanxi Provincial Education Department (no. 18JK0625).
- 1.Bargiela A, Pedrycz W (2016) Granular computing. In: Angelov PP (ed) Handbook on computational intelligence. Fuzzy logic, systems, artificial neural networks, and learning systems, vol 1. Kluwer Academic Publishers, Boston, pp 43–66Google Scholar
- 4.Düntsch I, Gediga G (2002) Modal-style operators in qualitative data analysis. In: Proceedings of the 2002 IEEE international conference on data mining, pp 155-162Google Scholar
- 20.Liu Z, Li B, Pei Z, et al. (2017) Formal concept analysis via multi-granulation attributes. In: 12th International conference on intelligent systems and knowledge engineering (ISKE) IEEE, pp 1–6Google Scholar
- 28.Ren Y, Li J, Kumar C, Liu W (2014) Rule acquisition in formal decision contexts based on formal, object-oriented and property-oriented concept lattices. Sci World J 2014:1–10Google Scholar
- 43.Yao YY (2000) Granular computing: basic issues and possible solutions. In: proceedings of the 5th joint conference on information sciencesm, vol 1, pp 186–189Google Scholar
- 44.Yao YY (2004) Concept lattices in rough set theory. In: Proceedings of 2004 annual meeting of the north American fuzzy information processing society, Banff, Canada, pp 796–801Google Scholar
- 45.Yao Y, Chen Y (2004) Rough set approximations in formal concept analysis. In: Dick S, Kurgan L, Pedrycz W, Reformat M (eds) Proceedings of 2004 annual meeting of the North American fuzzy information processing society (NAFIPS 2004), June 27–30, pp 73–78Google Scholar
- 53.Zhang QH, Xing YK (2010) Formal concept analysis based on granular computing. J Comput Inf Syst 6(7):2287–2296Google Scholar
- 54.Zen W, She Y (2018) Object-oriented multigranulation formal concept analysis. Comput Sci 45(10):51–53 (in Chinese)Google Scholar