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2019 | OriginalPaper | Chapter

The Prototype View of Concepts

Authors : Ruisi Ren, Ling Wei

Published in: Rough Sets

Publisher: Springer International Publishing

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Abstract

Concepts are important and basic elements in human’s cognition process. The formal concept gives a mathematical format of the classical view of concepts in which all instances of a concept share common properties. But in some situation this view is not consistent with human’s understanding of concepts. The prototype view of concepts is more appropriate in our daily life. This view characters some analog categories as internally structured into a prototype (clearest cases, best examples of the category) and non-prototype members, with non-prototype members tending toward an order from better to poorer examples. The objective of this paper is to give a mathematical description of prototype view of concepts. Firstly, we give a similarity measurement of an object to another object in a formal context. Then based on this similarity measurement, the mathematical format of prototype view of concepts, named k-cutting concept, induced by one typical object is obtained. Finally, the properties of k-cutting concepts are studied. In addition to presenting theorems to summarize our results, we use some examples to illustrate the main ideas.

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previous chapter Rough Sets Based on Possible Indiscernibility Relations in Incomplete Information Tables with Continuous Values

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Boucher-Ryan, P., Bridge, D.: Collaborative recommending using formal concept analysis. Knowl.-Based Syst. 19(5), 309–315 (2006)CrossRef

Chen, Y.H., Yao, Y.Y.: A multiview approach for intelligent data analysis based on data operators. Inf. Sci. 178(1), 1–20 (2008)MathSciNetCrossRef

Deogun, J.S., Saquer, J.: Monotone concepts for formal concept analysis. Discrete Appl. Math. 144(1), 70–78 (2004)MathSciNetCrossRef

D\(\ddot{u}\)ntsch, I., Gediga, G.: Modal-style operators in qualitative data analysis. In: Proceedings of the 2002 IEEE International Conference on Data Mining, pp. 155–162. IEEE Computer Society, Washington, D.C. (2002)

Formica, A.: Concept similarity in formal concept analysis: an information content approach. Knowl.-Based Syst. 21(1), 80–87 (2008)MathSciNetCrossRef

Frixione, M., Lieto, A.: Representing concepts in formal ontologies: compositionality vs. typicality effects. Log. Log. Philos. 21, 391–414 (2012)MathSciNet

Frixione, M., Lieto, A.: Towards an extended model of conceptual representations in formal ontologies: a typicality-based proposal. J. Univ. Comput. Sci. 20(3), 257–276 (2014)MATH

Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2CrossRefMATH

Hu, M., Yao, Y.: Definability in incomplete information tables. In: Flores, V., et al. (eds.) IJCRS 2016. LNCS (LNAI), vol. 9920, pp. 177–186. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47160-0_16CrossRef

10.

Jiang, G.Q., Chute, C.G.: Auditing the semantic completeness of SNOMED CT using formal concept analysis. J. Am. Med. Inform. Assoc. 16(1), 89–102 (2009)CrossRef

11.

Lakoff, G.: Hedges: a study in meaning criteria and the logic of fuzzy concepts. In: Hockney, D., Harper, W., Freed, B. (eds.) Contemporary Research in Philosophical Logic and Linguistic Semantics, vol. 4, pp. 221–27. Springer, Netherlands (1975). https://doi.org/10.1007/978-94-010-1756-5_9CrossRef

12.

Li, W., Wei, L.: Data dimension reduction based on concept lattices in image mining. In: Proceedings of the Sixth IEEE International Conference on Fuzzy Systems and Knowledge Discovery, vol. 5, pp. 369–373 (2009)

13.

Ma, J.M., Zhang, W.X.: Axiomatic characterizations of dual concept lattices. Int. J. Approx. Reason. 54(5), 690–697 (2013)MathSciNetCrossRef

14.

Medin, D.L., Smith, E.E.: Concepts and concept formation. Ann. Rev. Psychol. 35(1), 113–138 (1984)CrossRef

15.

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

16.

Qi, J., Wei, L., Yao, Y.: Three-way formal concept analysis. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS (LNAI), vol. 8818, pp. 732–741. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11740-9_67CrossRef

17.

Ren, R.S., Wei, L.: The attribute reductions of three-way concept lattices. Knowl.-Based Syst. 99, 92–102 (2016)CrossRef

18.

Resnik, P.: Using information content to evaluate semantic similarity in a taxonomy. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 448–453. Morgan Kaufmann, San Francisco (1995)

19.

Rosch, E.H.: On the internal structure of perceptual and semantic categories. In: Moore, T.E. (ed.) Cognitive Development and the Aquisition of Language, pp. 111–144. Academic Press, New York (1973)CrossRef

20.

Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327–352 (1977)CrossRef

21.

Vormbrock, B., Wille, R.: Semiconcept and protoconcept algebras: the basic theorems. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3626, pp. 34–48. Springer, Heidelberg (2005). https://doi.org/10.1007/11528784_2CrossRef

22.

Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel Publishing Company, Dordrecht (1982)CrossRef

23.

Wille, R.: Preconcept algebras and generalized double boolean algebras. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 1–13. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24651-0_1CrossRef

24.

Wille, R.: Concept lattices and conceptual knowledge systems. Comput. Math. Appl. 23(6–9), 493–515 (1992)CrossRef

25.

Xiao, Q.Z., Qin, K., Guan, Z.Q., Wu, T.: Image mining for robot vision based on concept analysis. In: IEEE International Conference on Robotics and Biomimetics (ROBIO 2007), pp. 207–212 (2007)

26.

Yao, Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25929-9_6CrossRef

27.

Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 39(4), 855–866 (2009)CrossRef

28.

Yao, Y.Y.: Rough-set concept analysis: interpreting RS-definable concepts based on ideas from formal concept analysis. Inf. Sci. 346, 442–462 (2016)MathSciNetCrossRef

29.

Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRef

Title: The Prototype View of Concepts
Authors: Ruisi Ren
Ling Wei
Publisher: Springer International Publishing
Book: Rough Sets
Print ISBN: 978-3-030-22814-9

Electronic ISBN: 978-3-030-22815-6

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-22815-6_14

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