Knowledge and Information Systems

, Volume 60, Issue 2, pp 715–739 | Cite as

Similarity reasoning in formal concept analysis: from one- to many-valued contexts

  • Anna FormicaEmail author
Regular Paper


In this paper, concept similarity in formal concept analysis (FCA) with many-valued contexts is addressed. In particular, this work focuses on FCA many-valued contexts where attribute values are intervals (FCA with interordinal scaling), here referred to as IFCA. IFCA is based on interval type-2 fuzzy sets, which provide a simplification of the more general type-2 fuzzy sets. In this work, a method for evaluating concept similarity in IFCA is proposed, which is a problem that has not been adequately investigated in the literature, although the increasing interest in the combination of FCA with fuzzy sets. Note that the topic addressed in this paper is presented by providing simple examples in order to reach a broad audience of readers.


Formal concept analysis Similarity reasoning Interval type-2 fuzzy sets Many-valued contexts FCA with interordinal scaling 


  1. 1.
    Akmal S, Batres R (2013) A methodology for developing manufacturing process ontologies. J Jpn Ind Manag Assoc 64:303–316Google Scholar
  2. 2.
    Akmal S, Shih L, Batres R (2014) Ontology-based similarity for product information retrieval. Comput Ind 65:91–107CrossRefGoogle Scholar
  3. 3.
    Alam M, Buzmakov A, Napoli A, Sailanbayev A (2015) Revisiting pattern structures for structured attribute sets. In: Proceedings of international conference on concept lattices and their applications, Clermont-Ferrand, France, 13–16 October 2015, CEUR workshop proceedings, pp 241–252Google Scholar
  4. 4.
    Alam M, Napoli A (2015) Interactive exploration over RDF data using formal concept analysis. In: IEEE international conference on data science and advanced analytics (DSAA), pp 1–10Google Scholar
  5. 5.
    Bai L, Liu M (2008) A fuzzy-set based semantic similarity matching algorithm for web service. In: Proceedings of the IEEE international conference on services computing, vol 2. IEEE Computer SocietyGoogle Scholar
  6. 6.
    Belohlávek R, Vychodil V (2005) What is a fuzzy concept lattice? In: Belohlávek R, Snásel V (eds) Proceedings of concept lattices and their applications (CLA), Olomouc, Czech Republic, 7–9 September 2005, pp 34–45Google Scholar
  7. 7.
    Belohlávek R, Outrata J, Vychodil V (2008) Fast factorization by similarity of fuzzy concept lattices with hedges. Int J Found Comput Sci 19(2):255–269MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Berners-Lee T, Hendler J, Lassila O (2001) The semantic web. Sci Am 284(5):34–43CrossRefGoogle Scholar
  9. 9.
    Bilgin A, Hagras H, Alghazzawi D, Malibari A, Alhaddad MJ (2015) Employing an enhanced interval approach to encode words into linear general type-2 fuzzy sets for computing with words applications. In: IEEE international conference on fuzzy systems (FUZZ-IEEE), Istanbul, TurkeyGoogle Scholar
  10. 10.
    Burusco A, Fuentes-Gonzlez R (2001) The study of the interval-valued contexts. Fuzzy Sets Syst 121(3):439–452MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    De Luca A, Termini S (1972) A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Comput 20:301–312MathSciNetzbMATHGoogle Scholar
  12. 12.
    Djouadi Y, Prade H (2009) Interval-valued fuzzy formal concept analysis. In: Rauch et al (eds) Foundations of intelligent systems, ISMIS 2009, LNAI, vol 5722, pp 592–601Google Scholar
  13. 13.
    Dubois D, Prade H (2012) Fundamentals of fuzzy sets. Springer, New YorkzbMATHGoogle Scholar
  14. 14.
    Ferr S, Cellier P (2016) Graph-FCA in practice. In: International conference on conceptual structures (ICCS), pp 107–121Google Scholar
  15. 15.
    Formica A (2006) Ontology-based concept similarity in formal concept analysis. Inf Sci 176(18):2624–2641MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Formica A (2008) Concept similarity in formal concept analysis: an information content approach. Knowl Based Syst 21(1):80–87MathSciNetCrossRefGoogle Scholar
  17. 17.
    Formica A, Pourabbas E (2009) Content based similarity of geographic classes organized as partition hierarchies. Knowl Inf Syst 20(2):221–241CrossRefGoogle Scholar
  18. 18.
    Formica A (2010) Concept similarity in fuzzy formal concept analysis for semantic web. Int J Uncertain Fuzziness Knowl Based Syst 18(2):153–167MathSciNetCrossRefGoogle Scholar
  19. 19.
    Formica A (2012) Semantic web search based on rough sets and fuzzy formal concept analysis. Knowl Based Syst 26:40–47CrossRefGoogle Scholar
  20. 20.
    Formica A (2013) Similarity reasoning for the semantic web based on fuzzy concept lattices: an informal approach. Inf Syst Front 15(3):511–520CrossRefGoogle Scholar
  21. 21.
    Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin. ISBN 978-3-540-62771-5zbMATHCrossRefGoogle Scholar
  22. 22.
    Ganter B, Kuznetsov SO (2001) Pattern structures and their projections. In: Delugach HS, Stumme G (eds) International conference on conceptual structures (ICCS). LNAI, vol 2120. Springer, pp 129–142Google Scholar
  23. 23.
    Hao M, Mendel JM (2016) Encoding words into normal interval type-2 fuzzy sets: HM approach. IEEE Trans Fuzzy Syst 24(4):865–879CrossRefGoogle Scholar
  24. 24.
    Hitzler P, Krötzsch M, Rudolph S (2009) Foundations of semantic web technologies. Chapman & Hall/CRC, LondonCrossRefGoogle Scholar
  25. 25.
    Hitzler P (2011) What’s happening in semantic web ... and what FCA could have to do with it. In: 9th International conference on formal concept analysis (ICFCA) Nicosia, Cyprus, 2–6 May 2011. LNCS 6628, Springer, pp 18–23Google Scholar
  26. 26.
    Jaccard P (1908) Nouvelles recherches sur la distribution florale. Bull Soc Vauddes Sci Nat 44:223Google Scholar
  27. 27.
    Jay N, Nuemi G, Gadreau M, Quantin C (2013) A data mining approach for grouping and analyzing trajectories of care using claim data: the example of breast cancer. BMC Med Inform Decis Mak 13:130CrossRefGoogle Scholar
  28. 28.
    Kaytoue M, Kuznetsov SO, Napoli A, Duplessis S (2011) Mining gene expression data with pattern structures in formal concept analysis. Inf Sci 181(10):1989–2001MathSciNetCrossRefGoogle Scholar
  29. 29.
    Kirchberg M, Leonardi E, Tan YS, Link S, Ko RKL, Lee BS (2012) Formal concept discovery in semantic web data. In: Domenach F, Ignatov DI, Poelmans J (eds) International conference on formal concept analysis (ICFCA). Springer, Berlin, pp 164–179CrossRefGoogle Scholar
  30. 30.
    Keler C (2007) Similarity measurement in context. In: Kokinov B (ed) CONTEXT’07. LNAI, vol 4635. Springer, Berlin, pp 277–290Google Scholar
  31. 31.
    Kuhn HW (1955) The Hungarian method for the assignment problem. Naval Res Logist Q 2:83–97MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Li C, Li J, He M (2016) Concept lattice compression in incomplete contexts based on K-medoids clustering. Int J Mach Learn Cybern 7(4):539–552MathSciNetCrossRefGoogle Scholar
  33. 33.
    Li J, Mei C, Lv Y (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Lin D (1998) An information-theoretic definition of similarity. In: Proceedings of the international conference on machine learning, Madison, Wisconsin, USA, Morgan Kaufmann, pp 296–304Google Scholar
  35. 35.
    Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8(5):535–550CrossRefGoogle Scholar
  36. 36.
    Liu F, Mendel JM (2008) Encoding words into interval Type-2 fuzzy sets using an interval approach. IEEE Trans Fuzzy Syst 16(6):1503–1521CrossRefGoogle Scholar
  37. 37.
    Maarek YS, Berry DM, Kaiser GE (1991) An information retrieval approach for automatically constructing software libraries. IEEE Trans Softw Eng 17(8):800–813CrossRefGoogle Scholar
  38. 38.
    Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821CrossRefGoogle Scholar
  39. 39.
    Mendel JM (2007) Computing with words and its relationship with fuzzistics. Inf Sci 177:988–1006MathSciNetCrossRefGoogle Scholar
  40. 40.
    Mendel JM (2007) Computing with words: Zadeh, Turing, Popper and Occam. IEEE Comput Intell Mag 2(4):10–17CrossRefGoogle Scholar
  41. 41.
    Mendel JM, Wu D (2008) Perceptual reasoning for perceptual computing. IEEE Trans Fuzzy Syst 16(6):1550–1564CrossRefGoogle Scholar
  42. 42.
    Mendel JM, Wu D (2010) Perceptual computing: aiding people in making subjective judgments. Wiley, New YorkCrossRefGoogle Scholar
  43. 43.
    Mendel JM (2015) Type-2 fuzzy sets and systems: a retrospective. Inform Spektrum 38(6):523–532CrossRefGoogle Scholar
  44. 44.
    Mendel JM (2016) A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words. Granul Comput 1:59–69CrossRefGoogle Scholar
  45. 45.
    Park S, Suresh NC, Jeong B (2008) Sequence-based clustering for Web usage mining: a new experimental framework and ANN-enhanced K-means algorithm. Data Knowl Eng 65(3):512–543CrossRefGoogle Scholar
  46. 46.
    Poelmans J, Ignatov DI, Kuznetsov SO, Dedene G (2013) Formal concept analysis in knowledge processing: a survey on applications. Expert Syst Appl 40(16):6538–6560CrossRefGoogle Scholar
  47. 47.
    Resnik P (1995) Using information content to evaluate semantic similarity in a taxonomy. In: Proceedings of the fourteenth international joint conference on artificial intelligence, (IJCAI), Montral Qubec, Canada, 20–25 August 1995, Morgan Kaufmann, pp 448–453Google Scholar
  48. 48.
    Resnik P (1999) Semantic similarity in a taxonomy: an information-based measure and its application to problems of ambiguity in natural language. J Artif Intell Res 11:95–130zbMATHCrossRefGoogle Scholar
  49. 49.
    Rodriguez A, Egenhofer M (2004) Comparing geospatial entity classes: an asymmetric and context-dependent similarity measure. Int J Geogr Inf Sci 18(3):229–256CrossRefGoogle Scholar
  50. 50.
    Rosch E (1973) Natural categories. Cogn Psychol 4:328–350CrossRefGoogle Scholar
  51. 51.
    Safaeipour H, Zarandi MHF, Turksen IB (2013) Developing type-2 fuzzy FCA for similarity reasoning in the semantic web. Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). IEEE, pp 1477–1482Google Scholar
  52. 52.
    Sertkaya B (2010) A survey on how description logic ontologies benefit from FCA. In: Proceedings of international conference on concept lattices and their applications (CLA), Seville, Spain, 19–21 October 2010, pp 2–21Google Scholar
  53. 53.
    Singh PK, Aswani Kumar C, Li J (2016) Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20:1485–1502zbMATHCrossRefGoogle Scholar
  54. 54.
    Stumme G, Maedche A (2001) FCA-MERGE: bottom-up merging of ontologies. In: Proceedings of international joint conference on artificial intelligence (IJCAI), Seattle, USA, pp 225–234Google Scholar
  55. 55.
    Tho QT, Hui SC, Cheuk A, Fong M, Cao TH (2006) Automatic fuzzy ontology generation for semantic web. IEEE Trans Knowl Data Eng 18(6):842–856CrossRefGoogle Scholar
  56. 56.
    Wang JH, Hao J (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14(3):435–445CrossRefGoogle Scholar
  57. 57.
    WordNet: a lexical database for the English language (2010). Accessed 10 Oct 2013
  58. 58.
    Wu D, Mendel JM (2007) Uncertainty measures for interval type-2 fuzzy sets. Inf Sci 177:5378–5393MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    Wu D, Mendel JM (2009) A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf Sci 179:1169–1192MathSciNetCrossRefGoogle Scholar
  60. 60.
    Yao Y (2017) Interval sets and three-way concept analysis in incomplete contexts. Int J Mach Learn Cybern 8(1):3–20CrossRefGoogle Scholar
  61. 61.
    Zadeh LA (1965) Fuzzy sets. Inf. Control 8:338–353MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-1. Inf Sci 8:199–249MathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Zadeh LA (1996) Fuzzy logic = computing with words. IEEE Trans Fuzzy Syst 4(2):103–111CrossRefGoogle Scholar
  64. 64.
    Zhao Y, Li J, Liu W, Xu W (2017) Cognitive concept learning from incomplete information. Int J Mach Learn Cyber 8(1):159–170CrossRefGoogle Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Istituto di Analisi dei Sistemi ed Informatica (IASI) “Antonio Ruberti”National Research CouncilRomeItaly

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