Cognitive Computation

, Volume 10, Issue 2, pp 228–241 | Cite as

Similar Vague Concepts Selection Using Their Euclidean Distance at Different Granulation

Article

Abstract

Recently, the calculus of fuzzy concept lattice is extensively studied with interval-valued and bipolar fuzzy set for the precise representation of vagueness in cognitive concept learning. In this process, selecting some of the semantic similar (or interesting) vague concept at user required granulation is addressed as one of the major issues. To conquer this problem, current paper aims at analyzing the cognitive concept learning based on the properties of vague graph, concept lattice and granular computing within (m × m) computational time. To mimic with the cognitive computing and its contextual data sets, two methods are proposed for the precise representation of human cognition based on the evidence to accept or reject the attributes using the calculus of vague set. The hierarchical order visualization among the extracted cognitive vague concept is shown through calculus of concept lattice for adequate description of their textual syntax analysis. In addition, another method is proposed to improve the quality of sentic (or cognitive) reasoning using semantics relationship among the discovered vague concepts at user defined information granulation. The obtained results from the proposed methods approve that the vague concept lattice and its reduction at user defined granulation provides an alternative way to analyze the cognitive contextual data set with an improved description of vague attributes “tall” and “young.” Euclidean distance provides a way to select some of the interesting vague concepts based on their semantic similarity. The obtained results from both of the proposed methods correspond to each other which validate the results. This paper establishes that cognitive contextual data set can be processed through the calculus of vague concept lattice, and granular computing. This gives an alternative and compact visualization of discovered patterns from the cognitive data set when compared to its numerical representation. In this way, the proposed method provides an adequate analysis for cognitive concept learning when compared to any of the available approaches. In addition, the proposed method provides various ways to select some of the interesting cognitive vague concepts at user defined granulation for their Euclidean distance within (m × m) computational time. However, the proposed method is unable to measure the fluctuation in uncertainty for the cognitive context at given phase of time. In the future, the author will focus on conquering this research problem with an illustrative example.

Keywords

Cognitive learning Concept lattice Formal concept analysis Formal fuzzy concept Interesting pattern Vague graph 

Notes

Acknowledgements

The author thanks the anonymous reviewers and Editor for their compliments to improve the quality of this paper.

Compliance with Ethical Standards

Conflict of Interest

The author declares that he has no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals.

References

  1. 1.
    Abdullah A, Hussain A. A cognitively inspired approach to two–way cluster extraction from one–way clustered data. Cogn Comput 2015;7(1):161–182.CrossRefGoogle Scholar
  2. 2.
    Agarwal B, Poria S, Mittal N, Gelbukh A, Hussain A. Concept–level sentiment analysis with dependency–based semantic parsing: a novel approach. Cogn Comput 2016;7(4):487–499.CrossRefGoogle Scholar
  3. 3.
    Akram M, Feng F, Sarwar S, Jun YB. Certain type of vague graphs. UPB Bull Sci Series 2014;76 (1):143–154.Google Scholar
  4. 4.
    Alcalde C, Burusco A, Fuentez–Gonzales R. The use of two relations in L–fuzzy contexts. Inf Sci 2015; 301:1–12.CrossRefGoogle Scholar
  5. 5.
    Antoni L, Krajči S, Krìdlo O, Macek B, Piskoví L. On heterogeneous formal contexts. Fuzzy Sets Syst 2014;234:22–33.CrossRefGoogle Scholar
  6. 6.
    Ayesh A, Blewitt W. Models for computational emotions from psychological theories using Type-II fuzzy logic. Cogn Comput 2015;7(3):309–332.CrossRefGoogle Scholar
  7. 7.
    Bělohlívek R. Concept lattices and order in fuzzy logic. Ann Pure Appl Logic 2004;128(1–3):277–298.CrossRefGoogle Scholar
  8. 8.
    Bělohlívek R, Vychodil V. What is fuzzy concept lattice. In: Proceedings of CLA Olomuc; 2005 Czech Republic. p. 34–45.Google Scholar
  9. 9.
    Berry A, Sigayret A. Representing concept lattice by a graph. Discret Appl Math 2004;144(1–2):27–42.CrossRefGoogle Scholar
  10. 10.
    Bloch I. Geometry of spatial vague sets based on vague numbers and mathematical morphology. In: Fuzzy logic and applications, lecture notes in computer science; 2009, vol. 5571, p. 237–245.Google Scholar
  11. 11.
    Borzooei RA, Rashmanlou H. 2016. New concepts of vague graphs. Int J Mach Learn Cybern.  https://doi.org/https://doi.org/10.1007/s13042-015-0475-x.
  12. 12.
    Burusco A, Fuentes–Gonzalez R. The study of the L-fuzzy concept lattice. Matheware Soft Comput 1994; 1(3):209–218.Google Scholar
  13. 13.
    Burusco A, Fuentes–Gonzales R. The study on interval–valued contexts. Fuzzy Set Syst 2001;121(3):439–452.CrossRefGoogle Scholar
  14. 14.
    Cambria E, Fu J, Bisio F, Poria S. AffectiveSpace 2: enabling affective intuition for concept-level sentiment analysis. In: Proceedings of 29th AAAI conference on artificial intelligence; 2015, p. 508–514.Google Scholar
  15. 15.
    Cambria E, Hussain A. Sentic computing. Cogn Comput 2016;7:183–18.CrossRefGoogle Scholar
  16. 16.
    Chen SM. Measures of similarity between vague sets. Fuzzy Sets Syst 1995;74:217–223.CrossRefGoogle Scholar
  17. 17.
    Chen SM. Similarity measure between vague sets and between elements. IEEE Trans Syst Man Cybernet 1997; 27:153–158.CrossRefGoogle Scholar
  18. 18.
    Chunsheng C, Zhenchun Z, Feng L, Ying Q. Application of vague set in recommender systems. In: Proceedings of 2nd International conference on logistics, informatics and service science (LISS); 2012, p. 1353–1359  https://doi.org/10.1007/978-3-642-32054-5-192.
  19. 19.
    Djouadi Y. Extended Galois derivation operators for information retrieval based on fuzzy formal concept lattice. SUM 2011. In: Benferhal S. and Goant J., editors. LNAI: Springer–Verlag; 2011. p. 346–358.Google Scholar
  20. 20.
    Djouadi Y, Prade H. Interval–valued fuzzy formal concept analysis. ISMIS 2009. In: Rauch et al., editors. LNAI: Springer–Verlag; 2009. p. 592–601.Google Scholar
  21. 21.
    Dubois D, Prade H. Formal concept analysis from the standpoint of possibility theory. Proceedings of ICFCA 2015. LNAI; 2015. p. 21–38.Google Scholar
  22. 22.
    Ganter B, Wille R. Formal concept analysis: mathematical foundation. Berlin: Springer–Verlag; 1999, p. 1999.CrossRefGoogle Scholar
  23. 23.
    Gau WL, Buehrer DJ. Vague sets. IEEE Trans Syst Man Cybern 1993;23(2):610–614.CrossRefGoogle Scholar
  24. 24.
    Ghosh P, Kundu K, Sarkar D. Fuzzy graph representation of a fuzzy concept lattice. Fuzzy Set Syst. 2010;161(12):1669–1675.CrossRefGoogle Scholar
  25. 25.
    Hu BQ. Three-way decision spaces based on partially ordered sets and three–way decisions based on hesitant fuzzy sets. Knowled–Based Syst 2016;91:16–31.Google Scholar
  26. 26.
    Hussain A, Tao D, Wu J, Zhao D. Computational intelligence for changing environments. IEEE Comput Intell Mag 2015;10(4):10–11.CrossRefGoogle Scholar
  27. 27.
    Kang XP, Li DY, Wang SG, Qu KS. Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Set Syst 2012;203:33–48.CrossRefGoogle Scholar
  28. 28.
    Khan S, Gani A, Wahab AW Ab, Singh PK. 2017. Feature selection of Denial-of-Service attacks using entropy and granular computing. Arab J Sci Eng,  https://doi.org/10.1007/s13369-017-2634-8.
  29. 29.
    ŁadyŻyńskia P, Grzegorzewski P. Vague preferences in recommender systems. Expert Syst Appl. 2015; 42(24):9402–9411.CrossRefGoogle Scholar
  30. 30.
    Li J, Mei C, Lv Y. Incomplete decision contexts: approximate concept construction. Rule acquisition and knowledge reduction. Int J Approx Reason. 2013;54(1):149–165.CrossRefGoogle Scholar
  31. 31.
    Li J, Mei CL, Xu WH, Qian YH. Concept learning via granular computing: a cognitive viewpoint. Inform Sci. 2015;298:447– 467.CrossRefGoogle Scholar
  32. 32.
    Li J, Huang C, Qi J, Qian Y, Liu W. Three-way cognitive concept learning via multi-granularity. Inf Sci 2017;378:244–263.CrossRefGoogle Scholar
  33. 33.
    Li J, Ren Y, Mei C, Qian Y, Yang X. A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl-Based Syst 2016;91:152–164.CrossRefGoogle Scholar
  34. 34.
    Li C, Li J, He M. Concept lattice compression in incomplete contexts based on K-medoids clustering. Int J Mach Learn Cybern. 2016;7(4):539–552.CrossRefGoogle Scholar
  35. 35.
    Li Y, Olson D L, Qin Z. Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recogn Lett. 2007;28:278–285.CrossRefGoogle Scholar
  36. 36.
    Liu H, Li Q, Zhou X. L–information systems and complete L–lattices. Neural Comput Applic. 2012;23 (3):1139–1147.Google Scholar
  37. 37.
    Liu P., Tang G. Multi–criteria group decision–making based on interval neutrosophic uncertain linguistic variables and choquet integral. Cogn Comput 2016;8(6):1036–1056.CrossRefGoogle Scholar
  38. 38.
    Meng F, Wang C, Chen X. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput. 2016;8(1):52–68.CrossRefGoogle Scholar
  39. 39.
    Oneto L, Bisio F, Cambria E, Anguita D. Semi–supervised learning for affective common–sense reasoning. Cogn Comput 2017;9(1):18–42.CrossRefGoogle Scholar
  40. 40.
    Pandey LK, Ojha KK, Singh PK, Singh CS, Dwivedi S, Bergey EA. Diatoms image database of India (DIDI): a research tool. Environ Technol Innov 2016;5:148–160.CrossRefGoogle Scholar
  41. 41.
    Pollandt S. Fuzzy Begriffe. Berlin–Heidelberg: Springer–Verlag; 1997, p. 1997.CrossRefGoogle Scholar
  42. 42.
    Pedrycz W. Granular computing: analysis and design of intelligent systems. Boca Raton: CRC Press/Francis Taylor; 2013, p. 2013.CrossRefGoogle Scholar
  43. 43.
    Pedrycz W. Knowledge management and semantic modeling: a role of information granularity. Int J Softw Eng Knowl Eng 2013;23(1):5–11.CrossRefGoogle Scholar
  44. 44.
    Qin X, Liu Y, Xu Y. Vague congruences and quotient lattice implication algebras. Sci World J 2014; Article ID 197403:7.  https://doi.org/10.1155/2014/197403.Google Scholar
  45. 45.
    Ramakrishna N. Vague graphs. International Journal of Computational Cognition 2009;7:51–58.Google Scholar
  46. 46.
    Rosenfeld A. Fuzzy graphs. Fuzzy sets and their applications. In: Zadeh L A, Fu K S, and Shimura M, editors. New York: Academic Press; 1975. p. 77–95.Google Scholar
  47. 47.
    Singh PK, Aswani Kumar C. Bipolar fuzzy graph representation of concept lattice. Inform Sci. 2014;288: 437–448.CrossRefGoogle Scholar
  48. 48.
    Singh PK, Aswani Kumar C. A note on computing crisp order context of a fuzzy formal context for knowledge reduction. J Inf Process Syst 2015;11(2):184–204.Google Scholar
  49. 49.
    Singh PK, Gani A. Fuzzy concept lattice reduction using Shannon entropy and Huffman coding. J Appl Non-Classical Logics 2015;25(2):101–119.CrossRefGoogle Scholar
  50. 50.
    Singh PK, Aswani Kumar C, Li J. Knowledge representation using interval–valued fuzzy concept lattice. Soft Comput 2016;20(4):1485–1502.CrossRefGoogle Scholar
  51. 51.
    Singh PK, Aswani Kumar C, Gani A. A comprehensive survey on formal concept analysis and its research trends. Int J Appl Math Comput Sci. 2016;26(2):495–516.CrossRefGoogle Scholar
  52. 52.
    Singh PK. Processing linked formal fuzzy context using non-commutative composition. Inst Integr Omics Appl Biotechnol (IIOAB) J 2016;7(5):21–32.Google Scholar
  53. 53.
    Singh PK, Aswani Kumar Ch. Concept lattice reduction using different subset of attributes as information granules. Granul Comput 2017;2(3):159–173.CrossRefGoogle Scholar
  54. 54.
    Singh PK. Three–way fuzzy concept lattice representation using neutrosophic set. Int J Mach Learn Cybern 2017;8(1):69–79.CrossRefGoogle Scholar
  55. 55.
    Singh PK. Complex vague set based concept lattice. Chaos, Solitons and Fractals 2017;96:145–153.CrossRefGoogle Scholar
  56. 56.
    Singh PK. 2017. Concept learning using vague concept lattice. Neural Process Lett; 2017,  https://doi.org/10.1007/s11063-017-9699-y.
  57. 57.
    Singh PK. m–polar fuzzy graph representation of concept lattice. Eng Appl Artif Intell 2018;67:52–63.CrossRefGoogle Scholar
  58. 58.
    Skowron A. Rough sets and vague concepts. Fundam Inform. 2005;64(2005):417–431.Google Scholar
  59. 59.
    Sun Z, Zao Y, Cao D, Hao H. Hierarchical multilabel classification with optimal path predictions. Neural Process Lett 2017;45(1):263–277.CrossRefGoogle Scholar
  60. 60.
    Tran HN, Cambria E, Hussain A. Towards GPU–based common-sense reasoning: using fast subgraph matching. Cogn Comput. 2016;8(6):1074–1086.CrossRefGoogle Scholar
  61. 61.
    Wille R. Restructuring lattice theory: an approach based on hierarchies of concepts. Ordered sets. In: Rival I., editors. NATO Advanced Study Institutes Series; 1982. p. 445–470.Google Scholar
  62. 62.
    Yang HL, Li SG, Wang WH, Lu Y. Notes on “Bipolar fuzzy graphs”. Inform Sci. 2013;242:113–121.CrossRefGoogle Scholar
  63. 63.
    Yao YY. Concept lattices in rough set theory. Proceedings of 2004 Annual meeting of the North American fuzzy information processing society. Washington D.C.: IEEE Computer Society; 2004. p. 796–801.Google Scholar
  64. 64.
    Yao YY. Interval sets and three-way concept analysis in incomplete contexts. Int J Mach Learn Cybern 2017; 8(1):3–20.CrossRefGoogle Scholar
  65. 65.
    Zeng W, Zhao Y, Gu Y. Similarity measure for vague sets based on implication functions. Knowl–Based Syst 2016;94:124–131.Google Scholar
  66. 66.
    Zhang Q, Zeng G, Xiao C, Yue Y. A rule conflict resolution method based on Vague set. Soft Comput. 2014;18:549–555.CrossRefGoogle Scholar
  67. 67.
    Zhang Q, Wanga J, Wanga G, Hong Y. The approximation set of a vague set in rough approximation space. Inform Sci. 2015;300(2015):1–19.CrossRefGoogle Scholar
  68. 68.
    Zhang QS, Jiang SY. A note on information entropy measures for vague sets and its applications. Inform Sci. 2008;178:4184–4191.CrossRefGoogle Scholar
  69. 69.
    Zhang WR, Zhang L. YinYang bipolar logic and bipolar fuzzy logic. Inform Sci. 2004;165(3–4):265–287.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Amity Institute of Information TechnologyAmity UniversityNoidaIndia

Personalised recommendations