Thresholds and Shifted Attributes in Formal Concept Analysis of Data with Fuzzy Attributes
We focus on two approaches to formal concept analysis (FCA) of data with fuzzy attributes recently proposed in the literature, namely, on the approach via hedges and the approach via thresholds. Both of the approaches present parameterized ways to FCA of data with fuzzy attributes. Our paper shows basic relationships between the two of the approaches. Furthermore, we show that the approaches can be combined in a natural way, i.e. we present an approach in which one deals with both thresholds and hedges. We argue that while the approach via thresholds is intuitively appealing, it can be considered a special case of the approach via hedges. An important role in this analysis is played by so-called shifts of fuzzy attributes which appeared earlier in the study of factorization of fuzzy concept lattices. In addition to fuzzy concept lattices, we consider the idea of thresholds for the treatment of attribute implications from tables with fuzzy attributes and prove basic results concerning validity and non-redundant bases.
KeywordsFuzzy Logic Data Table Complete Lattice Residuated Lattice Concept Lattice
Unable to display preview. Download preview PDF.
- 5.Bělohlávek, R.: A note on variable precision concept lattices. Draft (2006)Google Scholar
- 6.Bělohlávek, R., Chlupová, M., Vychodil, V.: Implications from data with fuzzy attributes. In: AISTA 2004 in cooperation with IEEE Computer Society Proceedings, November 15–18, 2004, p. 5, Kirchberg - Luxembourg (2004)Google Scholar
- 7.Bělohlávek, R., Dvořák, J., Outrata, J.: Direct factorization in formal concept analysis by factorization of input data. In: Proc. 5th Int. Conf. on Recent Advances in Soft Computing, RASC 2004, Nottingham, United Kingdom, December 16–18, pp. 578–583 (2004)Google Scholar
- 8.Bělohlávek, R., Funioková, T., Vychodil, V.: Galois connections with hedges. In: Liu, Y., Chen, G., Ying, M. (eds.) Fuzzy Logic, Soft Computing & Computational Intelligence: Eleventh International Fuzzy Systems Association World Congress, vol. II, pp. 1250–1255. Tsinghua University Press and Springer (2005)Google Scholar
- 10.Bělohlávek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: FUZZ-IEEE 2005, The IEEE International Conference on Fuzzy Systems, Reno, Nevada, USA, May 22–25, pp. 663–668 (2005)Google Scholar
- 11.Bělohlávek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Proc. CLA 2005, 3rd Int. Conference on Concept Lattices and Their Applications, Olomouc, Czech Republic, September 7-9, 2005, pp. 34–45 (2005), http://ceur-ws.org/Vol-162/
- 12.Bělohlávek, R., Vychodil, V.: Fuzzy attribute logic: attribute implications, their validity, entailment, and non-redundant basis. In: Liu, Y., Chen, G., Ying, M. (eds.) Fuzzy Logic, Soft Computing & Computational Intelligence: Eleventh International Fuzzy Systems Association World Congress, vol. I, pp. 622–627. Tsinghua University Press and Springer (2005) ISBN 7–302–11377–7Google Scholar
- 13.Bělohlávek, R., Vychodil, V.: Axiomatizations of fuzzy attribute logic. In: Prasad, B. (ed.) IICAI 2005, Proceedings of the 2nd Indian International Conference on Artificial Intelligence, IICAI 2005, pp. 2178–2193 (2005) ISBN 0–9727412–1–6 Google Scholar
- 14.Ben Yahia, S., Jaoua, A.: Discovering knowledge from fuzzy concept lattice. In: Kandel, A., Last, M., Bunke, H. (eds.) Data Mining and Computational Intelligence, pp. 167–190. Physica-Verlag, Heidelberg (2001)Google Scholar
- 16.Fan, S.Q., Zhang, W.X.: Variable threshold concept lattice. Inf. Sci (submitted)Google Scholar
- 18.Goguen, J.A.: The logic of inexact concepts. Synthese 18, 325–373 (1968-1969)Google Scholar
- 22.Krajči, S.: Cluster based efficient generation of fuzzy concepts. Neural Network World 5, 521–530 (2003)Google Scholar