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

Haitao Liu, Ioan Dzitac, Sicong Guo


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.


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

Full Text:



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.

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.

Dzitac, I. (2015), The Fuzzification of Classical Structures: A General View, International Journal of Computers Communications & Control, 10(6), 772-788, 2015.

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.

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

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.

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.

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.

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.

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.

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.

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

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

Pawlak, Z. (1982); Rough sets, International Journal of Parallel Programming, 11(5), 341– 356, 1982.

Thurstone L. L. (1931); Multiple factor analysis, Psychological Review, 38(5), 406–427, 1931.

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.

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

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

Wang, P.Z. (1990); A factor spaces approach to knowledge representation, Fuzzy Sets and Systems, 36(1), 113–124, 1990.

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

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

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

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.

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.

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

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

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.

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.

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

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.

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.

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

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

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.

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.

Zadeh, L.A. (1965); Fuzzy sets, Information and control, 8(3), 338–353, 1965.

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

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.

DOI: https://doi.org/10.15837/ijccc.2018.1.3033

Copyright (c) 2018 Haitao Liu, Ioan Dzitac, Sicong Guo

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.