Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction

Abstract

Incomplete decision contexts are a kind of decision formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete decision contexts is of interest because such databases are frequently encountered in the real world. This paper mainly focuses on the issues of approximate concept construction, rule acquisition and knowledge reduction in incomplete decision contexts. We propose a novel method for building the approximate concept lattice of an incomplete context. Then, we present the notion of an approximate decision rule and an approach for extracting non-redundant approximate decision rules from an incomplete decision context. Furthermore, in order to make the rule acquisition easier and the extracted approximate decision rules more compact, a knowledge reduction framework with a reduction procedure for incomplete decision contexts is formulated by constructing a discernibility matrix and its associated Boolean function. Finally, some numerical experiments are conducted to assess the efficiency of the proposed method.

On inference rules in decision formal contexts

“…Moreover, we have figured out the exact number of the superfluous decision implications that we can additionally remove by using the proposed inference rule compared with the existing one and an illustrative example has been used to show this advantage vividly. From the point of view of real applications, the results obtained in this paper need to be further extended to the case of fuzzy decision formal contexts 51 , incomplete decision formal contexts 52 or even real decision formal contexts 53,54 since in practice the relationship between some objects and attributes of a decision formal context may be fuzzy-valued, interval-valued or real-valued.…”

A Note on Computing the Crisp Order Context of a Fuzzy Formal Context for Knowledge Reduction

“…Table 1 provides some possible conditions in a given fuzzy formal context. Very recently, a few investigations have been available in the FCA literature for an incomplete fuzzy relation, condition (a), as shown by in Table 1 [24][25][26][27].…”

“…Prade [25] Aswani Kumar Bartl et al [41] Skowron et al [44] For detailed illustrations about generating the formal concepts from a given formal context, readers can refer to references including [1][2][3][4][5][6][7][8]13,16,[24][25][26][27][29][30][31][32][33][34][35][36][37][38][39][40]. Reducing the number of formal concepts and the size of the lattice structure are open issues for researchers as knowledge reduction problems.…”

A Method of Description on the Data Association Based on Granulation Trees

“…In the meanwhile, the researches cover further investigations on new topics. This vigorously promotes the progress of data research, and gives rise to different research directions, such as data mining [1][2][3][4], data reasoning [5][6][7][8], data reduction [9][10][11], data warehousing [12,13], as well as big data, and so on which are all subjects focused on by researchers and have become academic branches. Many topics involved by the directions always inspire the interest of investigators, and are often taken as focus issues to be studied by experts.…”