Affiliations: [a]
College of Science, Xi’an Shiyou University, Xi’an, China
| [b]
College of Computer Science, Xi’an Shiyou University, Xi’an, China
Correspondence:
[*]
Corresponding author. Yanhong She, College of Science, Xi’an Shiyou University, Xi’an, China. E-mail: yanhongshe@gmail.com.
Note: [1] This work is partially supported by the National Nature Science Fundation of China (Grant Nos. 61472471 and 11531009) and the Innovation Talent Promotion Plan of Shaanxi Province for Young Sci-Tech New Star (No. 2017KJXX-60). Funded by Scientific Research Program of Shaanxi Provincial Education Department (No.18JK0625).
Abstract: Formal concept analysis, originally proposed by Wille, is a mathematical tool to analyse and represent data in the form of complete formal context. However, in situations with incomplete information, one only has partial knowledge about a concept, recently, a common conceptual framework of the notions of interval sets and incomplete formal contexts for representing partially-known concepts were presented. In this study, we examine and reinterpret the existing studies on partially known concepts by means of three-valued logics. By treating an incomplete formal context as a three-valued formal context and considering the one-to-one correspondence between interval sets and three-valued mappings, we investigate the condition under which the four types of partially known concepts can be generated by using three-valued implication operators. Moreover, we also evaluate the role of three-valued logic in characterizing attribute implications. A sufficient and necessary condition for computing the true value of an implication correctly in the sense of Kriple semantics is provided.
