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Fuzzy Regression Models and Alternative Operations for Economic and Social Sciences

  • Fabrizio MaturoEmail author
  • Šárka Hošková-Mayerová
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 66)

Abstract

The economic and social research is often based on assumptions that have little to do with reality, because all scientific knowledge of the Western world is based on the Aristotelian binary logic. Often researchers use rigid conventions and treat things as if they were black or white, but the world around us is nuanced, in other words, is fuzzy. In particular, problems inherent the inaccuracy of measurements and the vagueness of linguistic attributes has led many scholars to consider the fuzzy theory during the recent decades. In this paper we face a particular aspect of fuzzy logic, that is, fuzzy regression. After a brief review of the recent studies about this topic, we focus on some limitations of the previous approaches and suggest some possible solutions. Specifically, we propose the use of alternatives operations to solve some problems of addition and multiplication between fuzzy numbers in fuzzy regression models.

Keywords

Fuzzy regression models Alternative operations Economic and social research Bounded operations Linguistic variables 

References

  1. Achen, C.H.: Interpreting and using regression. Sage Publications, California (1982)CrossRefGoogle Scholar
  2. Bagnoli, C.: La misurazione economica sfocata. Dal numero alla parola: strumenti per la gestione della complessitá. Franco Angeli, Milano (2007)Google Scholar
  3. Ban, A.I., Bede, B.: Cross product of l-r fuzzy numbers and properties. Ann. Oradea Univ. 9, 95–108 (2003)MathSciNetzbMATHGoogle Scholar
  4. Bede, B., Fodor, J.: Product type operations between fuzzy numbers and their applications in geologys. Acta Polytechn. Hung. 3, 123–139 (2006)Google Scholar
  5. Celmins, A.: Least squares model fitting to fuzzy vector data. Fuzzy Sets Syst. 22(3), 245–269 (1987)MathSciNetCrossRefGoogle Scholar
  6. Cristea, I., Hošková-Mayerová, Š.: Fuzzy topological hypergroupoids. Iran. J. Fuzzy Syst. 6, 13–21 (2009)Google Scholar
  7. Diamond, P.: Fuzzy least squares. Inf. Sci. 46(3), 141–157 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Ferraro, M.B., Colubi, A., Gonzales-Rodriguez, A., Coppi, R.: A determination coefficient for a linear regression model with imprecise response. Environmetrics 22, 516–529 (2011)MathSciNetCrossRefGoogle Scholar
  9. Gonzales-Rodriguez, A., Blanco, A., Colubi, A., Lubiano, M.A.: Estimation of a simple linear regression model for fuzzy random variables. Fuzzy Sets Syst. 160, 357–370 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Grzegorzewski, P., Mrowska, P.: Trapezoidal approximations of fuzzy numbers. fuzzy sets and systems. Fuzzy Sets Syst. 153, 115–135 (2005)CrossRefzbMATHGoogle Scholar
  11. Gujarati, D.N.: Basic Econometrics. McGraw-Hill, New York (2003)Google Scholar
  12. Hošková-Mayerová, Š., Talhofer, V.: Mathematical model used in decision making process with respect to the reliability of geo database. Procedia-Soc. Behav. Sci. 9, 1652–1657 (2010)CrossRefGoogle Scholar
  13. Hošková-Mayerová, Š., Talhofer, V., Hofmann, A., Kubíček, P.: Mathematical model used in decision-making process with respect to the reliability of geodatabase. In: Advanced Dynamic Modeling of Economic and Social Systems, Series: Studies in Computational Intelligence, vol. 448, pp. 143–162. Springer (2013). doi: 10.1007/978-3-642-32903-6_11
  14. Kim, K.J., Moskowitz, H., Koksalan, M.: Fuzzy versus statistical linear regression. Eur. J. Oper. Res. 92(2), 417–434 (1996)CrossRefzbMATHGoogle Scholar
  15. Klir, G.J.: Uncertainty and Information: Foundations of Generalized Information Theory. Wiley, New York (2006)zbMATHGoogle Scholar
  16. Klir, G.J., Yuan, B.: Fuzzy Set And Fuzzy Logic. Upper Saddle River, New Jersey (1995)zbMATHGoogle Scholar
  17. Kratschmer, V.: Strong consistency of least-squares estimation in linear regression models with vague concepts. J. Multivar. Anal. 97, 633–654 (2006a)MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kratschmer, V.: Strong consistency of least-squares estimation in linear regression models with vague concepts. J. Multivar. Anal. 97, 1044–1069 (2006b)MathSciNetCrossRefzbMATHGoogle Scholar
  19. Maturo, A.: Alternative fuzzy operations and applications to social sciences. Int. J. Intel. Syst. 24, 1243–1264 (2009a)CrossRefzbMATHGoogle Scholar
  20. Maturo, A.: On some structures of fuzzy numbers. Iran. J. Fuzzy Syst. 6(4), 49–59 (2009b)MathSciNetzbMATHGoogle Scholar
  21. Maturo, A., Maturo, F.: Research in social sciences: Fuzzy regression and causal complexity. In: Ventre, A.G.S., Maturo, A., Hošková-Mayerová, Š., Kacprzyk, J. (eds.) Multicriteria and Multiagent Decision Making with Applications to Economic and Social Sciences. Series: Studies in Fuzziness and Soft Computing, vol. 305, pp. 237–250. Springer, Berlin (2013). doi: 10.1007/978-3-642-35635-3_18
  22. Maturo, F.: La regressione fuzzy. In: Maturo, A., Tofan, I. (eds.) Fuzzyness. Teorie e applicazioni. Aracne Editrice, Isbn: 978-88-548-9184-5, pp. 99–110 (2016)Google Scholar
  23. Peters, G.: Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst. 63(1), 45–55 (1994)MathSciNetCrossRefGoogle Scholar
  24. Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  25. Ragin, C.: Fuzzy-Set Social Science. The university of Chicago press, Chicago (2000)Google Scholar
  26. Shapiro, A.F.: Fuzzy regression and the term structure of interest rates revisited. In: Proceedings of the 14th International AFIR Colloquium, vol. 1, pp. 29–45 (2004)Google Scholar
  27. Shapiro, A.F.: Fuzzy Regression Models. ARC (2005)Google Scholar
  28. Stock, J.H., Watson, M.: Introduction to Econometrics. Pearson Addison Wesley (2009)Google Scholar
  29. Talhofer, V., Hošková-Mayerová, Š., Hofmann, A.: A decision-making process with respect to the reliability of geo-database. In: Multicriteria and Multiangent Decision Making, Social and Economical Applications, Studies in Fuzziness and Soft Computing, pp. 179–194. Springer (2013). doi: 10.1007/978-3-642-35635-3_15
  30. Taliento, M.: Ai confini del terminal value, complessitá, incertezza e sfocature estimative nelle valutazioni d’azienda in chiave fuzzy. G. Giappichelli Editore, Torino (2008)Google Scholar
  31. Tanaka, H., Guo, P.: Possibilistic Data Analysis for Operations Research. Physica-Verlag, New York (1999)zbMATHGoogle Scholar
  32. Ventre, A.G.S.: Imprecisione e sfocatura (fuzziness), insiemi sfocati e decisioni. Esi, Napoli (1983)Google Scholar
  33. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  34. Zadeh, L.A.: Fuzzy algorithms. Inf. Control 12, 94–102 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  35. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8, 199–249 (1975)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of Business AdministrationUniversity “G. d’Annunzio”, Chieti—PescaraPescaraItaly
  2. 2.Department of Mathematics and Physics, Faculty of Military TechnologyUniversity of DefenceBrnoCzech Republic

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