Advertisement

Aggregation of Fuzzy Conformances

  • Miroslav HudecEmail author
  • Miljan Vuc̆etić
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

Abstract

Retrieving the most suitable items and sorting them downwards from the best face many challenges. The conformance measures are able to efficiently calculate similarities between the desired value and values of considered items’ attribute regardless of different data types. These measures should be suitably aggregated, because the users usually provide different preferences among atomic conformances and therefore various aggregation functions should be considered. In this paper, we examine conjunctive functions (including non t-norms) as well as averaging and hybrid ones. In the hybrid aggregation, uninorms and ordinal sums of conjunctive and disjunctive functions have shown their perspectives in aggregating conformance measures. Diverse tasks require functions of desired behaviour and properly assigned weights or parameters. Thus, the perspectives for merging aggregation functions with the machine learning to the mutual benefits are outlined.

Keywords

Conformance measure Conjunctive and disjunctive functions Averaging functions Hybrid functions Data and function fitting 

Notes

This paper was partially supported by the project: VEGA No. 1/0373/18 entitled “Big data analytics as a tool for increasing the competitiveness of enterprises and supporting informed decisions” supported by the Ministry of Education, Science, Research and Sport of the Slovak Republic.

References

  1. 1.
    Bashon, Y., Neagu, D., Ridley, M.J.: A framework for comparing heterogeneous objects: on the similarity measurements for fuzzy, numerical and categorical attributes. Soft Comput. 17(9), 1595–1615 (2013)CrossRefGoogle Scholar
  2. 2.
    Beliakov, G., Pradera, A., Calvo Sánchez, T.: Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg (2007)Google Scholar
  3. 3.
    Bojadziev, G., Bojadziev, M.: Fuzzy Logic for Business, Finance and Management, 2nd edn. World Scientific Publishing, London (2007)CrossRefGoogle Scholar
  4. 4.
    Calvo Sánchez, T., De Baets, B., Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets Syst. 120, 385–394 (2001)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 1953–1954 (1954)MathSciNetCrossRefGoogle Scholar
  6. 6.
    De Baets, B., Mesiar, R.: Ordinal sums of aggregation operators. In: 8th International Conference on Information Processing and Management of Uncertainty, IPMU 2000, Madrid (2000)Google Scholar
  7. 7.
    Dubois, D., Prade, H.: On the use of aggregation operations in information fusion processes. Fuzzy Sets Syst. 142, 143–161 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  9. 9.
    Goebel, R., Chander, A., Holzinger, K., Lecue, F., Akata, Z., Stumpf, S., Kieseberg, P., Holzinger, A.: Explainable AI: the new 42? In: Holzinger, A., Kieseberg, P., Tjoa, A., Weippl, E. (eds.) Machine Learning and Knowledge Extraction. Lecture Notes in Computer Science, LNCS, vol. 11015, pp. 295–303. Springer, Cham (2018)Google Scholar
  10. 10.
    Ishwarappa, J., Anuradha, J.: A brief introduction on big data 5Vs characteristics and hadoop technology. Procedia Comput. Sci. 48, 319–324 (2015)CrossRefGoogle Scholar
  11. 11.
    Joe, H.: Dependence Modeling with Copulas. Monographs on Statistics and Applied probability, vol. 134. CRC Press, Boca Raton (2015)zbMATHGoogle Scholar
  12. 12.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  13. 13.
    Ling, C.M.: Representation of associative functions. Publ. Math. Debrecen 12, 189–212 (1965)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Petry, F.E.: Fuzzy Databases: Principles and Applications. Kluwer, Boston (1996)CrossRefGoogle Scholar
  15. 15.
    Ruspini, E.H.: A new approach to clustering. Inf. Control 15, 22–32 (1969)CrossRefGoogle Scholar
  16. 16.
    Shenoi, S., Melton, A.: Proximity relations in the fuzzy relational database model. Fuzzy Sets Syst. 100, 51–62 (1989)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Singh, S., Ribeiro, M., Guestrin, C.: Programs as black–box explanations. In: Workshop on Interpretable Machine Learning in Complex Systems, NIPS 2016, Barcelona (2016)Google Scholar
  18. 18.
    Snasel, V., Kromer, P., Musilek, P., Nyongesa, H.O., Husek, D.: Fuzzy modeling of user needs for improvement of web search queries. In: Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 2007, San Diego (2007)Google Scholar
  19. 19.
    Sözat, M., Yazici, A.: A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations. Fuzzy Sets Syst. 117(2), 161–181 (2001)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Tung, A.K.H., Zhang, R., Koudas, N., Ooi, B.C.: Similarity search: a matching based approach. In: 32nd International Conference on Very Large Data Bases, Seoul (2006)Google Scholar
  21. 21.
    Vuc̆etić, M., Hudec, M.: A flexibile approach to matching user preferences with records in datasets based on the conformance measure and aggregation functions. In: 10th International Joint Conference on Computational Intelligence, IJCCI 2018, Seville (2018)Google Scholar
  22. 22.
    Vucetic, M., Hudec, M., Vujošević, M.: A new method for computing fuzzy functional dependencies in relational database systems. Expert Syst. Appl. 40, 2738–2745 (2013)CrossRefGoogle Scholar
  23. 23.
    Vuc̆etić, M., Vujošević, M.: A literature overview of functional dependencies in fuzzy relational database models. Technics Technol. Educ. Manag. 7, 1593–1604 (2012)Google Scholar
  24. 24.
    Yager, R.R.: Noble reinforcement in disjunctive aggregation operators. IEEE Trans. Fuzzy Syst. 11, 754–767 (2003)CrossRefGoogle Scholar
  25. 25.
    Yager, R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80, 111–120 (1996)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Economic InformaticsUniversity of Economics in BratislavaBratislavaSlovakia
  2. 2.Vlatacom Institute of High TechnologiesBelgradeSerbia
  3. 3.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia

Personalised recommendations