Please wait a minute...
Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

邮发代号 80-970

2019 Impact Factor: 1.275

Frontiers of Computer Science  2015, Vol. 9 Issue (4): 636-642   https://doi.org/10.1007/s11704-015-3162-x
  本期目录
Basic theorem as representation of heterogeneous concept lattices
Jozef PÓCS1,2,*(),Jana PÓCSOVÁ3
1. Palacký University Olomouc, Department of Algebra and Geometry, Olomouc 779 00, Czech Republic
2. Mathematical Institute, Slovak Academy of Sciences, Košice 040 01, Slovakia
3. Technical University of Košice, BERG Faculty, Institute of Control and Informatization of Production Processes, Košice 043 84, Slovakia
 全文: PDF(278 KB)  
Abstract

We propose a method for representing heterogeneous concept lattices as classical concept lattices. Particularly, we describe a transformation of heterogeneous formal context into a binary one, such that corresponding concept lattices will be isomorphic. We prove the correctness of this transformation by the basic theorem for heterogeneous as well as classical concept lattices.

Key wordsbasic theorem    heterogeneous concept lattice    representation
收稿日期: 2013-05-13      出版日期: 2015-09-07
Corresponding Author(s): Jozef PÓCS   
 引用本文:   
. [J]. Frontiers of Computer Science, 2015, 9(4): 636-642.
Jozef PÓCS,Jana PÓCSOVÁ. Basic theorem as representation of heterogeneous concept lattices. Front. Comput. Sci., 2015, 9(4): 636-642.
 链接本文:  
https://academic.hep.com.cn/fcs/CN/10.1007/s11704-015-3162-x
https://academic.hep.com.cn/fcs/CN/Y2015/V9/I4/636
1 Belohlávek R. Lattices generated by binary fuzzy relations. Tatra Mountains Mathematical Publications, 1999, 16: 11―19
2 Belohlávek R. Lattices of fixed points of fuzzy galois connections. Mathematical Logic Quarterly, 2001, 47(1): 111―116
https://doi.org/10.1002/1521-3870(200101)47:1<111::AID-MALQ111>3.0.CO;2-A
3 Krajci S. Cluster based efficient generation of fuzzy concepts. Neural Network World, 2003, 13(5): 521&horbar;530
4 Krajci S. A generalized concept lattice. Logic Journal of IGPL, 2005, 13(5): 543&horbar;550
https://doi.org/10.1093/jigpal/jzi045
5 Krajci S. The basic theorem on generalized concept lattice. In: Proceedings of the CLA 2004 International Workshop on Concept Lattices and their Applications. 2004, 25&horbar;33
6 Krajci S. A categorical view at generalized concept lattices. Kybernetika 2007, 43(2): 255&horbar;264
7 Medina J, Ojeda-Aciego M, Ruiz-Calvi?o J. Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems, 2009, 160: 130&horbar;144
https://doi.org/10.1016/j.fss.2008.05.004
8 Medina J, Ojeda-Aciego M. Multi-adjoint t-concept lattices. Information Sciences, 2012, 180(5): 712&horbar;725
https://doi.org/10.1016/j.ins.2009.11.018
9 Medina J, Ojeda-Aciego M. On multi-adjoint concept lattices based on heterogeneous conjunctors. Fuzzy Sets and Systems, 2012, 208: 95&horbar;110
https://doi.org/10.1016/j.fss.2012.02.008
10 Belohlávek R. What is a fuzzy concept lattice? Lecture Notes in Artificial Intelligence, 2011, 6743: 19&horbar;26
https://doi.org/10.1007/978-3-642-21881-1_4
11 Belohlávek R, Vychodil V. Formal concept analysis and linguistic hedges. International Journal of General Systems, 2012, 41(5): 503&horbar;532
https://doi.org/10.1080/03081079.2012.685936
12 Ben Yahia S, Jaoua A. Discovering knowledge from fuzzy concept lattice. In: A. Kandel, M. Last, and H. Bunke, eds. Data Mining and Computational Intelligence, Physica-Verlag, 2001, 167&horbar;190
https://doi.org/10.1007/978-3-7908-1825-3_7
13 Butka P. Use of FCA in the ontology extraction step for the improvement of the semantic information retrieval. In: Proceedings of the SOFSEM 2006: Theory and Practice of Computer Science, Prague. 2006, 74&horbar;82
14 Butka P, Sarnovsky M, Bednar P. One approach to combination of FCA-based local conceptual models for text analysis grid-based approach. In: Proceedings of the 6th International Conference SAMI. 2008, 131&horbar;135
https://doi.org/10.1109/sami.2008.4469150
15 Jaoua A, Elloumi S. Galois connection, formal concepts and galois lattice in real relations: application in a real classifier. The Journal of Systems and Software, 2002, 60: 149&horbar;163
https://doi.org/10.1016/S0164-1212(01)00087-5
16 Kang X, Li D, Wang S, Qu K. Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets and Systems, 2012, 203: 33&horbar;48
https://doi.org/10.1016/j.fss.2012.03.003
17 Kang X, Li D, Wang S, Qu K. Rough set model based on formal concept analysis. Information Sciences, 2013, 222: 611&horbar;625
https://doi.org/10.1016/j.ins.2012.07.052
18 Li Q, Guo L. Formal query systems on contexts and a representation of algebraic lattices. Information Sciences, 2013, 239: 72&horbar;84
https://doi.org/10.1016/j.ins.2013.03.032
19 Sarnovsky M, Butka P, Paralic J. Grid-based support for different text mining tasks. Acta Polytechnica Hungarica, 2009, 6(4): 5&horbar;27
20 Sarnovsky M, Butka P. Cloud computing as a platform for distributed data analysis. In: Proceedings of the 7th Workshop on Intelligent and Knowledge Oriented Technologies. 2012, 177&horbar;180
21 Singh P K, Kumar C A. A method for reduction of fuzzy relation in fuzzy formal context. Mathematical Modelling and Scientific Computation, Communications in Computer and Information Science, 2012, 283: 343&horbar;350
https://doi.org/10.1007/978-3-642-28926-2_37
22 Singh P K, Kumar C A. A method for decomposition of fuzzy formal context. Procedia Engineering, 2012, 38: 1852&horbar;1857
https://doi.org/10.1016/j.proeng.2012.06.228
23 Singh P K, Kumar C A. Interval-valued fuzzy graph representation of concept lattices. In: Proceedings of the 12th International Conference on Intelligent Systems Design and Applications. 2012, 604&horbar;609
https://doi.org/10.1109/isda.2012.6416606
24 Song X, Wang X, Zhang W. Axiomatic approaches of fuzzy concept operators. In: Proceedings of the 2012 International Conference on Machine Learning and Cybernetics. 2012, 249&horbar;254
https://doi.org/10.1109/ICMLC.2012.6358920
25 Pócs J. Note on generating fuzzy concept lattices via galois connections. Information Sciences, 2012, 185(1): 128&horbar;136
https://doi.org/10.1016/j.ins.2011.09.021
26 Pócs J. On possible generalization of fuzzy concept lattices using dually isomorphic retracts. Information Sciences, 2012, 210: 89&horbar;98
https://doi.org/10.1016/j.ins.2012.05.004
27 Antoni L, Krajci S, Krídlo O, Macek B, Pisková L. Relationship between two FCA approaches on heterogeneous formal contexts. In: Proceedings of the 9th International Conference on Concept Lattices and Their Applications. 2012, 93&horbar;102
28 Antoni L, Krajci S, Krídlo O, Macek B, Pisková L. On heterogeneous formal contexts. Fuzzy Sets and Systems, 2014, 234: 72&horbar;84
https://doi.org/10.1016/j.fss.2013.04.008
29 Ganter B, Wille R. Formal Concept Analysis. Berlin: Mathematical Foundations. Springer, 1999
https://doi.org/10.1007/978-3-642-59830-2
30 Nourine L, Raynaud O. A fast incremental algorithm for building lattices. Journal of Experimental and Theoretical Artificial Intelligence, 2002, 14: 217&horbar;227
https://doi.org/10.1080/09528130210164152
31 Butka P, Pócs J. Generalization of one-sided concept lattices. Computing and Informatics, 2013, 32(2): 355&horbar;370
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed