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Searching Musical Representative Phrases Using Decision Making Based on Fuzzy Similarities

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Handbook on Decision Making

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 33))

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Abstract

A new method to find representative phrases from a musical score is given in this paper. It is based on the computation and use of a fuzzy proximity relation on a set of phrases. This relation is computed as a conjunction of values given by a W-indistinguishability on a set of variation of notes in the phrases, where W is the Lukasiewicz t-norm. Different fuzzy logics are used and compared in order to show their influence on the final decision. The proposed method to find the most representative phrase has been proved successful on different musical scores.

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References

  1. Andreatta, M.: On group-theoretical methods applied to music: some compositional and implementational aspects. In: Mazzola, G., Noll, T., Lluis-Puebla, E. (eds.) Perspectives in Mathematical and Computational Music Theory, pp. 169–193. Electronic Publishing Osnabrück, Osnabrück (2004)

    Google Scholar 

  2. Beliakov, G., Pradera, A., Calvo, T.: Aggregation functions: a guide for practitioners. Studies in fuzziness and soft computing. Springer, Heidelberg (2007)

    Google Scholar 

  3. Castañeda, E., Garmendia, L., Santos, M.: Searching musical representative phrases using W-indistinguishabilities and proximities. In: Proc. EUROFUSE 2009 Workshop Preference Modeling and Decision Analysis, pp. 213–218 (2009b)

    Google Scholar 

  4. Castañeda, E., Garmendia, L., Santos, M.: Intelligent System for Computer Aided Musical Composition. In: Intelligent Decision Making Systems, pp. 13–18. World Scientific (2009a)

    Google Scholar 

  5. Castañeda, E. Garmendia, L.: Searching musical representative phrases using similarities. In: International Conference on the Logic of Soft Computing and 5th Workshop of the ERCIM Working Group of Soft Computing. LCS-ERCIM2006 satellite International Congress of Mathematicians, ICM (2006)

    Google Scholar 

  6. Garmendia, L., Yager, R.R., Trillas, E., Salvador, A.: Measures of Specificity of Fuzzy Sets Under T-Indistinguishabilities. IEEE Transactions on Fuzzy Systems 14(4), 568–572 (2006)

    Article  Google Scholar 

  7. Klement, E., Mesiar, R., Pap, E.: Triangular norms. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  8. Overill, R.E.: On the combinatorial complexity of fuzzy pattern matching in music analysis. Computers and the Humanities 27(2), 105–110 (1993)

    Article  Google Scholar 

  9. Schweizer, B., Sklar, A.: Probabilistic metric spaces. North-Holland, Amsterdam (1983)

    MATH  Google Scholar 

  10. Trillas, E., Valverde, L.: On mode and implication in approximate reasoning. In: Gupta, M.M., et al. (eds.) Approximate Reasoning in Expert Systems. Elsevier, North-Holland, Amsterdam (1985)

    Google Scholar 

  11. Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17, 313–328 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yager, R.R.: Ordinal measures of specificity. International Journal of General Systems 17, 57–72 (1990)

    Article  MATH  Google Scholar 

  13. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zadeh, L.A.: Similarity relations and fuzzy orderings. Inform. Sci. 3, 177–200 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning, parts I, II, III. Inform. Sci. 8, 199–249; 8, 301–357; 9, 43–48 (1975)

    Article  MathSciNet  Google Scholar 

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Castañeda, E., Garmendia, L., Santos, M. (2012). Searching Musical Representative Phrases Using Decision Making Based on Fuzzy Similarities. In: Lu, J., Jain, L.C., Zhang, G. (eds) Handbook on Decision Making. Intelligent Systems Reference Library, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25755-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-25755-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25754-4

  • Online ISBN: 978-3-642-25755-1

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