research-article

Relationships between three-way concepts and classical concepts

Authors: Hua Mao, Shufeng Zhao, Lanzhen YangAuthors Info & Claims

Journal of Intelligent & Fuzzy Systems, Volume 35, Issue 1

Pages 1063 - 1075

https://doi.org/10.3233/JIFS-17530

Published: 01 January 2018 Publication History

Abstract

In this paper, we firstly present some properties of classical concepts (i.e., formal concepts induced by positive operators and negative operators) and three-way concepts, respectively. Based on this, we systematically study the relationships between two types of three-way concepts (i.e., object-induced three-way concepts and attribute-induced three-way concepts) and classical concepts. More specifically, we can obtain all object-induced (attribute-induced) three-way concepts based on four relationships between all classical concepts and object-induced (attribute-induced) three-way concepts, where the four relationships are characterized by four theorems. After that, two algorithms are proposed to build an object-induced concept lattice and an attribute-induced concept lattice, respectively, and examples are given to verify these algorithms.

References

[1]

Wille R., Restructuring lattice theory: An approach based on hierarchies of concepts, in: Rival I. (Ed.), Ordered Sets, Reidel Publishing Company, Dordrecht- Boston, 1982, pp. 445–470.

[2]

Ganter B. and Wille R., Formal Concept Analysis, Mathe matical Foundations, Springer, Berlin, Heidelberg, 1999.

[3]

Xu F., Xing Z.Y. and Yin H.D., Attribute reductions and concept lattices in interval-valued intuitionistic fuzzy rough set theory: Construction and properties, Journal of Intelligent and Fuzzy Systems 30(2) (2016), 1231–1242.

Digital Library

[4]

Klime J., Using formal concept analysis for control in cyber-physical systems, Procedia Engineering 69(1) (2014), 1518–1522.

[5]

Poelmans J., Ignatov D.I., Kuznetsov S.O. and Dedene G., Formal concept analysis in knowledge processing: A survey on applications, Expert Systems with Applications 40(16) (2013), 6538–6560.

Digital Library

[6]

Jia X., Shang L., Zhou B. and Yao Y., Generalized attribute reduction rough set theory, Knowledge-Based Systems 91 (2016), 204–218.

Digital Library

[7]

Li J., Mei C., Xu W. and Qian Y., Concept learning via granular computing: A cognitive viewpoint, Information Sciences 298(1) (2015), 447–467.

Digital Library

[8]

Wan Q. and Wei L., Approximate concepts acquisition based on formal contexts, Knowledge-Based Systems 75 (2015), 78–86.

Digital Library

[9]

Tang P., Hui S.C. and Fong A.C., A lattice- based approach for chemical structural retrieval, Engineering Applications of Artificial Intelligence 39 (2015), 215–222.

[10]

Yao Y., An outline of a theory of three- way decisions, in: Yao J., Yang Y., Slowinski R., Greco S., Li H., Mitra S. and Pol- kowski L. (Eds.), Rough Sets and Current Trends in Computing, Lecture Notes in Computer Science, vol. 7413, Springer, Berlin, Heidelberg, 2012, pp. 1–17.

[11]

Li H. and Zhou X., Risk decision making based on decision-theoretic rough set: A three-way view decision model, International Journal of Computational Intelligence Systems 4(1) (2011), 1–11.

[12]

Yao Y., Granular computing and sequential three-way decisions, in: Lingras P., Wolski M., Cornells C., Mitra S. and Wasilewski P. (Eds.), Rough Sets and Knowledge Technology, Lecture Notes in Computer Science, vol. 8171, Springer, Berlin, Heidelberg, 2013, pp. 16–27.

[13]

Yao J. and Azam N., Web-based medical decision support systems for three-way medical decision making with game theoretic rough sets, IEEE Transactions on Fuzzy Systems 23(1) (2015), 3–15.

Digital Library

[14]

Yu H., Wang Y. and Jiao P., A three-way decisions approach to density-based over lapping clustering, in: Peters J.F., Skowron A., Li T., Yang Y., Yao J. and Nguyen H.S. (Eds.), Transactions on Rough Sets XVIII, Lecture Notes in Computer Science, vol. 8449, Springer, Berlin, Heidelberg, 2014, pp. 92–109.

[15]

Yu H., Zhang C. and Hu F., An incremental clustering approach based on three-way decisions, in: Cornells C., Kryszkiewicz M., Slezak D., Ruiz E., Bello R. and Shang L. (Eds.), Rough Sets and Current Trends in Computing, Lecture Notes in Computer Science, vol. 8536, Springer International Publishing, 2014, pp. 152–159.

[16]

Deng X. and Yao Y., Decision-theoretic three-way approximations of fuzzy sets, Information Sciences 279 (2014), 702–715.

[17]

Luo C., Li T. and Chen H., Dynamic maintenance of approximations in set-valued ordered decision systems under the attribute generalization, Information Sciences 257 (2014), 210–228.

Digital Library

[18]

Zhang Y., Zou H., Chen X., Wang X., Tang X. and Zhao S., Cost-sensitive three-way decisions model based on CCA, in: Cornells C., Kryszkiewicz M., Slezak D., Ruiz E., Bello R. and Shang L. (Eds.), Rough Sets and Current Trends in Computing, Lecture Notes in Computer Science, vol. 8536, Springer International Publishing, 2014, pp. 172–180.

[19]

Yu H., Zhang C. and Wang G., A tree-based in crèmental over lapping clustering method using the three-way decision theory, Knowledge-Based Systems 91 (2015), 189–203.

[20]

Yao Y., Three-way decisions with probabilistic rough sets, Information Sciences 180(3) (2010), 341–353.

Digital Library

[21]

Yao Y., Three-way decision: An interpretation of rules in rough set theory, in: Wen P., Li Y., Polkowski L., Yao Y., Tsumoto S. and Wang G. (Eds.), Rough Sets and Knowledge Technology, Lecture in Notes Computer Science, vol. 5589, Springer, Berlin, Heidelberg, 2009, pp. 642–649.

[22]

Qi J., Wei L. and Yao Y., Three-way formal concept analysis, in: Miao D., Pedrycz W., Slezak D., Peters G., Hu Q. and Wang R. (Eds.), Rough Sets and Knowledge Technology, Lecture Notes in Computer Science, vol. 8818, Springer International Publishing, 2014, pp.732–741.

[23]

Yao Y., The superiority of three-way decisions in probabilistic rough set models, Information Sciences 181(6) (2011), 1080–1096.

Digital Library

[24]

Hu B.Q., Three-way decisions space and three-way decisions, Information Sciences 281 (2014), 21–52.

Digital Library

[25]

She Y., On determination of thresholds in three-way approximation of many-valued nm-logic, in: Cornells C., Kryszkiewicz M., Slezak D., Ruiz E., Bello R. and Shang L. (Eds.), Rough Sets and Current Trends in Computing, Lecture Notes in Computer Science, vol. 8536, Springer International Publishing, 2014, pp. 136–143.

[26]

Yao Y., Interval sets and three-way concept analysis in incomplete contexts, &, Cybernetics (2016), 1–18.

[27]

Ren R.S. and Wei L., The attribute reductions of three-way concept lattices, Knowledge -Based Systems 99 (2016), 92–102.

Digital Library

[28]

LI M.Z. and Wang G.Y., Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts, Knowledge-Based Systems 91 (2016), 165–178.

Digital Library

[29]

Singh P.K., Three-way fuzzy concept lattice representation using neutrosophic set, International Journal of Machine Learning & Cybernetics 8(1) (2016), 69–79.

[30]

Shivhare R. and Cherukuri A.K., Three-way conceptual approach for cognitive memory functionalities, International Journal of Machine Learning & Cybernetics 8(1) (2016), 21–34.

[31]

Ren R., Wei L. and Yao Y., An analysis of three types of partially-known formal concepts, Cybernetics (2017), 1–17,

[32]

Li J., Huang C., Qi J., Qian Y. and Liu W., Three-way cognitive concept learning via muti-granularity, Information Sciences 378(1) (2017), 244–263.

Digital Library

[33]

Qi J.J., Qian T. and Wei L., The connections between three-way and classical concept lattices, Knowledge-Based Systems 91 (2016), 143–151.

Digital Library

[34]

Carpineto C. and Romano G., Concept data analysis: Theory and application, John Wiley & Sons 2004, pp. 85–103.

Cited By

Mao HMa JNiu Z(2023)Two new kinds of protoconcepts based on three-way decisions modelSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08840-327:17(11973-11984)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1007/s00500-023-08840-3
Xin XSong JXue ZPeng W(2021)Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degreeJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20000240:1(1567-1583)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.3233/JIFS-200002

Index Terms

Relationships between three-way concepts and classical concepts
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
2. Theory of computation
  1. Logic

Index terms have been assigned to the content through auto-classification.

Recommendations

Adjunctive three-way concepts from positive and negative concepts in lattice-valued formal contexts
Abstract
Three-way concept analysis is an integration of formal concept analysis and three-way decision, which has been found wide applications in knowledge representation, cognitive computing and decision sciences. There have been already a ...
Approximate concepts acquisition based on formal contexts

Formal concepts are abstraction and formalization of the concepts in philosophy. Acquisition of formal concepts is the base of formal concept analysis. Besides the concrete concepts, uncertain but meaningful concepts sometimes are more appropriate for ...
Three-way dual concept analysis
Abstract
Three-way concept analysis is a mathematical theory, which combines formal concept analysis and three-way decision. The existing models, i.e., three-way concept lattices and three-way object oriented concept lattices, have been used ...

Comments

Information & Contributors

Information

Published In

cover image Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology Volume 35, Issue 1

Special Section: Recent Advances in Machine Learning and Soft Computing

2018

1149 pages

ISSN:1064-1246

Issue’s Table of Contents

© 2018 – IOS Press and the authors. All rights reserved.

Publisher

IOS Press

Netherlands

Publication History

Published: 01 January 2018

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Mao HMa JNiu Z(2023)Two new kinds of protoconcepts based on three-way decisions modelSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08840-327:17(11973-11984)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1007/s00500-023-08840-3
Xin XSong JXue ZPeng W(2021)Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degreeJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20000240:1(1567-1583)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.3233/JIFS-200002

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents