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Issue:Intuitionistic fuzzy logic is not always equivalent to interval-valued one

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Title of paper: Intuitionistic fuzzy logic is not always equivalent to interval-valued one
Author(s):
Christian Servin
Information Technology Department, El Paso Community College, 919 Hunter, El Paso TX 79915, USA
cservin@gmail.com
Vladik Kreinovich
Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
vladik@utep.edu
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 22, 2016, Number 5, pages 1—11
Download:  PDF (123  Kb, File info)
Abstract: It has been shown that from the purely mathematical viewpoint, the (traditional) intuitionistic fuzzy logic is equivalent to interval-valued fuzzy logic. In this paper, we show that if we go beyond the traditional "and"- and "or"-operations, then intuitionistic fuzzy logic becomes more general than the interval-valued one.
Keywords: Intuitionistic fuzzy logic, Interval-valued fuzzy logics, And, Or.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
  2. Atanassov, K. (1999) Intuitionistic Fuzzy Sets, Springer-Verlag, Heidelberg.
  3. Atanassov, K. T., et al. (eds). (2016) Novel Developments in Uncertainty Representation and Processing, Springer Verlag, Cham, Switzerland, 2016.
  4. Klir, G. & Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic, Prentice Hall, Upper Saddle River, New Jersey.
  5. Kreinovich, V., Quintana, C., Lea, R., Fuentes, O., Lokshin, A., Kumar, S., Boricheva, I. & Reznik, L. (1992) What non-linearity to choose? Mathematical foundations of fuzzy control, Proceedings of the 1992 International Conference on Fuzzy Systems and Intelligent Control, Louisville, KY, 349–412.
  6. Mendel, J. M. (2001) Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Prentice-Hall, Upper Saddle River.
  7. Mendel, J. M. &Wu, D. (2010) Perceptual Computing: Aiding People in Making Subjective Judgments, IEEE Press and Wiley, New York.
  8. Nguyen, H. T. & Kreinovich, V. (1998) Methodology of fuzzy control: an introduction, In: H. T. Nguyen and M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, MA, 19–62.
  9. Nguyen, H. T., Kreinovich, V. & Zuo, Q.(1997) Interval-valued degrees of belief: applications of interval computations to expert systems and intelligent control, International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems (IJUFKS), 5(3), 317–358.
  10. Nguyen, H. T. & Walker, E. A. (2006) A First Course in Fuzzy Logic, Chapman and Hall/CRC, Boca Raton, Florida.
  11. Smith, M. H. & Kreinovich, V. (1995) Optimal strategy of switching reasoning methods in fuzzy control, In: H. T. Nguyen, M. Sugeno, R. Tong, and R. Yager (eds.), Theoretical Aspects of Fuzzy Control, J. Wiley, New York, 117–146.
  12. Zadeh, L. A. (1965) Fuzzy sets, Information and Control, 1965, 8, 338–353.
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