Factors Space and its Relationship with Formal Conceptual Analysis: A General View

  • Haitao Liu Liaoning Technical University
  • Ioan Dzitac Aurel Vlaicu University of Arad
  • Sicong Guo Liaoning Technical University

Abstract

Conceptual generation is a key point and basic problem in artificial intelligence, which has been probed in the Formal Concept Analysis (FCA) established by G. Wille. Factors Space (FS) is also a branch of cognition math initiated by P.Z. Wang at the end of last century, which has been applied in information processing with fuzzy concepts effectively. This paper briefly introduces the historic background of FS and its relationship with FCA. FS can be seen as a good partner of FCA on conceptual description and structure extraction; combining FCA with FS, we can get more clear and simple statements and more fast algorithms on conceptual generation.

References

[1] Cheng, Q.F.; Wang, T.T.; Guo, S.C.; Zhang, D.Y.; Jing, K.; Feng, L.; Wang, P.Z. (2017); The Logistic Regression from the Viewpoint of the Factor Space Theory, International Journal of Computers Communications & Control, 12(4), 492–502, 2017.
https://doi.org/10.15837/ijccc.2017.4.2918

[2] Cui, T.J.; Wang, P.Z.; Ma, Y.D. (2016); Structured representation methods for 01 space fault tree, J Dalian Jiaotong Univ, 37(1), 82–87, 2016.

[3] Dzitac, I. (2015), The Fuzzification of Classical Structures: A General View, International Journal of Computers Communications & Control, 10(6), 772-788, 2015.
https://doi.org/10.15837/ijccc.2015.6.2069

[4] Dzitac, I.;Filip, F.G. ; Manolescu, M.J. (2017); Fuzzy Logic Is Not Fuzzy: World-renowned Computer Scientist Lotfi A. Zadeh, International Journal of Computers Communications & Control, 12(6), 748-789, 2017.
https://doi.org/10.15837/ijccc.2017.6.3111

[5] Ganter, B.; Wille, R. (1996); Formal concept analysis, Wissenschaftliche Zeitschrift- Technischen Universitat Dresden, 45, 8–13, 1999.

[6] Kandel, A.; Peng, X.T.; Cao, Z.Q.; Wang, P.Z. (1990); Representation of concepts by factor spaces, Cybernetics and Systems: An International Journal, 21(1), 43–57, 1990.
https://doi.org/10.1080/01969729008902223

[7] Li, H.X.; Wang P.Z.; Yen, V.C. (1998); Factor spaces theory and its applications to fuzzy information processing.(I). The basics of factor spaces, Fuzzy Sets and Systems, 95(2), 147– 160, 1998.
https://doi.org/10.1016/S0165-0114(96)00296-5

[8] Li, H.X.; Yen, V.C.; Lee, E.S. (2000); Factor space theory in fuzzy information processing- Composition of states of factors and multifactorial decision making, Computers & Mathematics with Applications, 39(1), 245–265, 2000.

[9] Li, H.X.; Yen, V.C.; Lee, E.S. (2000); Models of neurons based on factor space, Computers & Mathematics with Applications, 39(12), 91–100, 2000.
https://doi.org/10.1016/S0898-1221(00)00132-2

[10] Li, H.X.; Chen, C.P.; Yen, V.C.; Lee, E.S. (2000); Factor spaces theory and its applications to fuzzy information processing: Two kinds of factor space canes, Computers & Mathematics with Applications, 40(6-7), 835–843, 2000.
https://doi.org/10.1016/S0898-1221(00)00200-5

[11] Li, H.X.; Chen, C.P.; Lee, E.S. (2000); Factor space theory and fuzzy information processing- Fuzzy decision making based on the concepts of feedback extension, Computers & Mathematics with Applications, 40(6-7), 845–864, 2000.
https://doi.org/10.1016/S0898-1221(00)00201-7

[12] Liu, H.T.; Guo, S.C. (2015); Inference model of causality analysis, Journal of Liaoning Technical University(Natural Science), 2015, 34(1), 124–128.

[13] Liu, Z.L. (1990); Factorial Neural Networks, Beijing Normal University Press, 1990.

[14] Pawlak, Z. (1982); Rough sets, International Journal of Parallel Programming, 11(5), 341– 356, 1982.
https://doi.org/10.1007/BF01001956

[15] Thurstone L. L. (1931); Multiple factor analysis, Psychological Review, 38(5), 406–427, 1931.
https://doi.org/10.1037/h0069792

[16] Vesselenyi, T.; Dzitac, I.; Dzitac, S.; Vaida, V. (2008); Surface roughness image analysis using quasi-fractal characteristics and fuzzy clustering methods, International Journal of Computers Communications & Control, 3(3), 304–316, 2008.
https://doi.org/10.15837/ijccc.2008.3.2398

[17] Wang, P.Z. (1981); Randomness, Advance of Statistical Physics, Science and Technology Press, 1981.

[18] Wang, P.Z. (1985); Fuzzy sets and falling shadows of random set, Beijing Normal University Press, 1985.

[19] Wang, P.Z. (1990); A factor spaces approach to knowledge representation, Fuzzy Sets and Systems, 36(1), 113–124, 1990.
https://doi.org/10.1016/0165-0114(90)90085-K

[20] Wang, P.Z. (1992); Factor space and concept description, Journal of Software, 1, 30–40, 1992.

[21] Wang, P.Z. (2013); Factor spaces and factor data-bases, Journal of Liaoning Technical University (Natural Science), 32(10), 1–8, 2013.

[22] Wang, P.Z. (2015); Factors space and data science, Journal of Liaoning Technical University (Natural Science), 34(2), 273–280, 2015.

[23] Wang, P.Z.; Guo, S.C.; Bao, Y.K.; Liu, H.T. (2014); Causality analysis in factor spaces, Journal of Liaoning Technical University (Natural Science), 33(7), 1–6, 2015.

[24] Wang, P.Z.; Jiang, A. (2002); Rules detecting and rules-data mutual enhancement based on factors space theory, International Journal of Information Technology & Decision Making, 1(01), 73–90, 2002.
https://doi.org/10.1142/S0219622002000087

[25] Wang, P.Z.; Li, H.X. (1995); Fuzzy system theory and fuzzy computer, Publishing Company of Science, 1995.

[26] Wang, P.Z.; Li, H.X. (1994); A mathematical theory on knowledge representation, Tianjin Scientific and Technical Press, 1994.

[27] Wang, P.Z.; Liu, Z.L.; Shi, Y.; Guo, S.C. (2014); Factor space, the theoretical base of data science, Annals of Data Science, 1(2), 233–251, 2014.
https://doi.org/10.1007/s40745-014-0017-5

[28] Wang, P.Z.; Ouyang, H.; Zhong, Y.X.; He, H.C. (2016); Cognition math based on factor space, Annals of Data Science, 3(3), 281–303, 2016.
https://doi.org/10.1007/s40745-016-0084-x

[29] Wang, P.Z., Sugeno, M. (1982); The factor fields and background structure for fuzzy subsets, Fuzzy Mathematics, 2(2), 45–54, 1982.

[30] Wang, H.D.; Wang, P.Z.; Shi, Y.; Liu, H.T. (2014); Improved factorial analysis algorithm in factor spaces, International Conference on Informatics, 201–204, 2014.

[31] Wang, P.Z.; Zhang, X.H.; Lui, H.C.; Zhang, H.M., Xu, W. (1995); Mathematical theory of truth-valued flow inference, Fuzzy Sets and Systems, 72(2), 221–238, 1995.
https://doi.org/10.1016/0165-0114(94)00354-A

[32] Wille, R. (1982); Restructuring lattice theory: an approach based on hierarchies of concepts, Ordered sets, Springer Netherlands, 445–470, 1982.

[33] Yao, Y. (2009); Three-Way Decision: An Interpretation of Rules in Rough Set Theory, RSKT, 9, 642–649, 2009.

[34] Yuan, X.H.; Wang, P.Z.; Lee, E.S. (1992); Factor space and its algebraic representation theory, J Math Anal Appl., 171(1), 256–276, 1992.
https://doi.org/10.1016/0022-247X(92)90388-T

[35] Yuan, X.H.; Wang, P.Z.; Lee, E.S. (1994); Factor Rattans, Category FR (Y), and Factor Space, Journal of Mathematical Analysis and Applications, 186(1), 254–264, 1994.
https://doi.org/10.1006/jmaa.1994.1297

[36] Zadeh, L.A. (1965); Fuzzy sets, Information and control, 8(3), 338–353, 1965.
https://doi.org/10.1016/S0019-9958(65)90241-X

[37] Zeng, F.H.; Zheng, L. (2017); Sample cultivation in Factorial analysis, Journal of Liaoning Technical University (Natural Science), 36(3), 320–323, 2017.

[38] Zeng, F.H.; Li, Y. (2017); An improved decision tree algorithm based on factor space theory, Journal of Liaoning Technical University (Natural Science), 36(3), 109–112, 2017.
Published
2018-02-12
How to Cite
LIU, Haitao; DZITAC, Ioan; GUO, Sicong. Factors Space and its Relationship with Formal Conceptual Analysis: A General View. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 13, n. 1, p. 83-98, feb. 2018. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3033>. Date accessed: 04 july 2020. doi: https://doi.org/10.15837/ijccc.2018.1.3033.

Keywords

Factors Space (FS), Formal Concept Analysis (FCA), rough sets, conceptual generation, basic concept semi-lattice, fuzzy logic