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Abstract

Two important areas of mathematics are related by modeling purposes: Biomathematics and Fuzzy Sets Theory. Both have a point in common in their history of development: a respected background in formal theory and a wide range of applications, both attained in the twentieth century. That is, both areas are new scientific tendencies in comparison to those mathematical areas with centuries of discussion and establishment.

…type-2 fuzzy sets can capture two kind of linguistic uncertainties simultaneously (the uncertainty of individual and uncertainties of a group about a word) whereas type-1 cannot…[ 29] Jerry M. Mendel (2015)

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References

  1. Bartolin, R., Bouvenot, G., Soula, G., Sanchez, E.: The fuzzy set theory as a biomedical diagnostic aid. Sem. Hop. 58(22), 1361–1365 (1982)

    Google Scholar 

  2. Bassanezi, R.C., Barros, L.C.: A simple model of life expectancy with subjective parameters. Kybernetes 24(7), 57–62 (1995)

    Article  MathSciNet  Google Scholar 

  3. Bassanezi, R., Roman, H.: Relaciones fuzzy: Optimización de diagnóstico médico. Technical report, IMECC, UNICAMP, Campinas, Brazil (1989, in Spanish)

    Google Scholar 

  4. Bertone, A., Jafelice, R., Barros, L., Bassanezi, R.: On fuzzy solutions for partial differential equations. Fuzzy Sets Syst. 219, 68–80 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Castro, J.R., Castillo, O., Martínez, L.G.: Interval type-2 fuzzy logic toolbox. Eng. Lett. 15(1) (2007)

    Google Scholar 

  6. Cecconello, M.S.: Modelagem alternativa para dinâmica populacional: sistemas dinâmicos fuzzy. Master’s thesis, IMECC-UNICAMP, Campinas, Brazil (2006, in Portuguese)

    Google Scholar 

  7. Dietz, K., Heesterbeek, J.: Daniel Bernoulli’s epidemiological model revisited. Math. Biosci. 180, 1–21 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. ETHW: Engineering and technology history wiki. https://ethw.org/Michio_Sugeno

  9. Google: Google Scholar – https://scholar.google.com/. Accessed September 2020

  10. Jafelice, R.M., Bertone, A.M.A.: Minicurso conjuntos fuzzy do tipo 2 intervalar: Teoria e aplicações. In: Minicurso (ed.) IV Congresso Brasileiro de Sistemas Fuzzy, pp. 1–44. Campinas (2016, in Portuguese)

    Google Scholar 

  11. Jafelice, R.M., Lodwick, W.A.: Interval analysis of the HIV dynamics model solution using type-2 fuzzy sets. Math. Comput. Simul. 180, 306–327 (2021)

    Article  MathSciNet  Google Scholar 

  12. Jafelice, R.M., Silva, P.N.: Studies on population dynamics using cellular automata. In: Salcido, A. (ed.) Cellular Automata: Simplicity Behind Complexity, pp. 105–130. Intech, London (2011)

    Google Scholar 

  13. Jafelice, R., Barros, L., Bassanezi, R., Gomide, F.: Fuzzy modeling in asymptomatic HIV virus infected population. Bull. Math. Biol. 66, 1463–1942 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jafelice, R.M., Bechara, B.F.Z., Barros, L.C., Bassanezi, R.C., Gomide, F.: Cellular automata with fuzzy parameters in microscopic study of positive HIV individuals. Math. Comput. Model. 50, 32–44 (2009)

    Article  MATH  Google Scholar 

  15. Jafelice, R.S.M., Almeida, C.G., Meyer, J.F.C.A., Vasconcelos, H.L.: Fuzzy parameters in a partial differential equation model for population dispersal of leaf-cutting ants. Nonlinear Anal. Real World Appl. 12, 3397–3412 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jafelice, R.S.M., Pereira, B.L., Bertone, A.M.A., Barros, L.C.: An epidemiological model for HIV infection in a population using type-2 fuzzy sets and cellular automaton. Comput. Appl. Math. 38(141) (2019)

    Google Scholar 

  17. Jang, J.S.R.: Fuzzy modeling using generalized neural networks and Kalman filter algorithm. In: Proceedings of the 9th National Conference on Artificial Intelligence, pp. 762–767 (1991)

    Google Scholar 

  18. Jang, J.S.R.: ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993)

    Article  Google Scholar 

  19. Karnik, N.N., Mendel, J.M.: Introduction to type-2 fuzzy logic systems. In: 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence, vol. 2, pp. 915–920 (1998)

    Google Scholar 

  20. Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132, 195–220 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics. R. Stat. Soc. 115, 700–721 (1927)

    MATH  Google Scholar 

  22. Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Philadelphia (1925)

    MATH  Google Scholar 

  23. Malthus, T.R.: An Essay on the Principle of Population. J. Johnson, London (1798)

    Google Scholar 

  24. Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7, 1–13 (1975)

    Article  MATH  Google Scholar 

  25. Massad, E., Burrattini, M.N., Ortega, N.R.S.: Fuzzy logic and measles vaccination: designing a control strategy. Int. J. Epidemiol. 28(3), 550–557 (1999)

    Article  Google Scholar 

  26. Massad, E., Ortega, N.R.S., Barros, L.C., Struchiner, C.J.: Fuzzy Logic in Action: Applications in Epidemiology. Studies in Fuzziness and Soft Computing, vol. 232. Springer, Berlin (2008)

    Google Scholar 

  27. Mcneill, D., Freiberger, P.: Fuzzy Logic: The Revolutionary Computer Technology That Is Changing Our World. Simon & Schuster, New York City (1994)

    MATH  Google Scholar 

  28. Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput. Intell. Mag. 2(1), 20–29 (2007)

    Article  Google Scholar 

  29. Mendel, J.M.: Type-2 fuzzy sets and systems: a retrospective. Informatik-Spektrum 38(6), 523–532 (2015)

    Article  Google Scholar 

  30. Mendel, J.M.: Type-2 fuzzy sets as well as computing with words. IEEE Comput. Intell. Mag. 14(1), 82–95 (2019)

    Article  Google Scholar 

  31. Mendel, J.M., Wu, D.: Perceptual Computing: Aiding People in Making Subjective Judgments. Wiley and IEEE Press, Hoboken (2010)

    Book  Google Scholar 

  32. Ortega, N.R.S., Santos, F.S., Zanetta, D.T., Massad, E.: A fuzzy reed–frost model for epidemic spreading. Bull. Math. Biol. 70, 1925–1936 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. Sanchez, E.: Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Fuzzy Automata and Decision Processes, pp. 221–234. M. M. Gupta, North-Holland, Amsterdam (1977)

    Google Scholar 

  34. Sanchez, E., Bartolin, R.: Fuzzy inference and medical diagnosis, a case study. Int. J. Biom. Fuzzy Syst. Ass. 1, 4–21 (1990)

    Google Scholar 

  35. Scott, T., Marketos, P.: On the origin of the Fibonacci sequence. MacTutor History of Mathematics archive, University of St Andrews (2014)

    Google Scholar 

  36. Silva, J.D.M.: Análise de estabilidade de sistemas dinâmicos p-fuzzy com aplicações em biomatemática. Ph.D. Thesis, IMECC – UNICAMP, Campinas, Brazil (2005, in Portuguese)

    Google Scholar 

  37. Silva, J.D.M., Leite, J., Bassanezi, R.C., Cecconcelo, M.S.: Stationary points-I: One-dimensional p-fuzzy dynamical systems. J. Appl. Math. 495864 (2013)

    Google Scholar 

  38. Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  39. Sugeno, M., Kang, G.T.: Structure identification on fuzzy model. Fuzzy Sets Syst. 28, 329–346 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  40. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  41. Verhulst, P.F.: Notice sur la loi que la population suit dans son accroissement. Correspondance mathématique et physique 10, 113–121 (1838)

    Google Scholar 

  42. Zadeh, L.: Fuzzy sets. Inf. Cont. 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  43. Zadeh, L.A.: Calculus of fuzzy restrictions. In: Zadeh, L.A., Fu, K.S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and Their Applications to Cognitive and Decision Processes, pp. 1–39. Proceedings of the U.S.-Japan Seminar on Fuzzy Sets and Their Applications, held at The University of California, Berkeley. Academic Press Inc., Cambridge (1975)

    Google Scholar 

  44. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning–1. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zadeh, L.A.: The birth and evolution of fuzzy logic. Int. J. Gen. Syst. 17(2–3), 95–105 (1990)

    Article  MATH  Google Scholar 

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Jafelice, R.S.d.M., Bertone, A.M.A. (2021). Introduction. In: Biological Models via Interval Type-2 Fuzzy Sets. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-64530-4_1

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