Wang, Hong; Cui, Pin-Zhi Analysis of interval-valued decision formal contexts. (English) Zbl 1361.68266 J. Intell. Fuzzy Syst. 29, No. 4, 1565-1574 (2015). Summary: This study investigates a novel approach to knowledge reduction in interval-valued decision formal contexts. Applying rule acquisition, we formulate a new framework of knowledge reduction for interval-valued decision formal contexts and the presented framework can be applicable to any interval-valued decision formal contexts. Based on this reduction method, more compact decision rules that can imply all of those derived from the initial interval-valued decision formal contexts in the form of implication rules are obtained. Furthermore, a corresponding reduction method is developed by constructing a discernibility matrix and its associated Boolean function. Cited in 1 Document MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence 68T30 Knowledge representation Keywords:interval-valued decision formal contexts; large interval-valued concept lattices; knowledge reduction; rule acquisition PDFBibTeX XMLCite \textit{H. Wang} and \textit{P.-Z. Cui}, J. Intell. Fuzzy Syst. 29, No. 4, 1565--1574 (2015; Zbl 1361.68266) Full Text: DOI References: [1] Burusco, Concept lattices defined from implication operators, Fuzzy Sets and Systems 114 pp 431– (2000) · Zbl 0971.06010 [2] Elloumi, A multi-level conceptual data reduction approach based on the Lukasiewicz implication, Information Sciences 163 pp 253– (2004) · Zbl 1076.68085 [3] Ganter, Formal concept analysis (1999) [4] Jaoua, Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier, Journal of Systems and Software 60 pp 149– (2002) · Zbl 05433019 [5] Li, Attribute reduction in fuzzy concept lattices based on T implication, Knowledge-Based Systems 23 pp 497– (2010) [6] Li, A heuristic knowledge-reduction method for decision formal contexts, Computers and Mathematics with Applications 61 pp 1096– (2011) · Zbl 1217.68208 [7] Li, Knowledge reduction in decision formal contexts, Knowledge-Based Systems 24 pp 709– (2011) [8] Li, Knowledge reduction in real decision formal contexts, Information Sciences 189 pp 191– (2012) · Zbl 1247.68280 [9] Li, On rule acquisition in decision formal contexts, International Journal of Machine Learning and Cybernetics 4 pp 721– (2013) [10] Mi, Approaches to knowledge reductions based on variable precision rough sets model, Information Sciences 159 pp 255– (2004) · Zbl 1076.68089 [11] Mi, Approaches to attribute reduction in concept lattices induced by axialities, Knowledge-Based Systems 23 pp 504– (2010) [12] Shao, Relations between granular reduct and dominance reduct in formal contexts, Knowledge-Based Systems 65 pp 1– (2014) [13] Shao, Rule acquisition and complexity reduction in formal decision contexts, International Journal of Approximate Reasoning 55 pp 259– (2014) · Zbl 1316.68163 [14] Valtchev, Formal concept analysis for knowledge discovery and data mining: the new challenge, Proceedings of the 2nd International Conference on Formal Concept Analysis pp 352– (2004) · Zbl 1198.68246 [15] Wu, Knowledge reductions in random information systems via Dempster’lCShafer theory of evidence, Information Sciences 174 pp 143– (2005) · Zbl 1088.68169 [16] Wei, Attribute reduction theory of concept lattice based on decision formal contexts, Science in China: Series F &C Information Sciences 51 pp 910– (2008) · Zbl 1291.68391 [17] Wu, Granular computing and knowledge reduction in formal contexts, IEEE Transactions on Knowledge and Data Engineering 21 pp 1461– (2009) [18] Wang, Relations of attribute reduction between object and property oriented concept lattices, Knowledge-Based Syst 21 pp 398– (2008) [19] Yang, An algorithm of constructing concept lattices for CAT with cognitive diagnosis, Knowledge-Based Systems 21 pp 852– (2008) [20] Yang, Rule acquisition and attribute reduction in real decision formal contexts, Soft Computing 15 pp 1115– (2011) · Zbl 1237.68218 [21] Zhang, Attribute reduction theory and approach to concept lattice, Science in China F 48 pp 713– (2005) · Zbl 1161.68796 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.