Fuzzy sets

Fuzzy sets

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Types and properties of fuzzy sets are studied. Modeling of fuzzy sets in MATLAB® and MATLAB/Simulink® are shown and MATLAB function files are developed to be used as a part of user-defined toolbox library. Fuzzy intersection, union and complement are also studied in this chapter.

Chapter Contents:

  • 2.1 Introduction
  • 2.2 Fuzzy sets and fuzzy membership functions
  • 2.2.1 Triangular membership function
  • 2.2.2 Trapezoid membership function
  • 2.2.3 Gaussian membership function
  • 2.2.4 Bell membership function
  • 2.2.5 Cauchy membership function
  • 2.2.6 Sinusoid membership function
  • 2.2.7 Sigmoid membership function
  • 2.3 Properties of fuzzy membership functions
  • 2.4 Fuzzy set operations
  • 2.4.1 Intersection: t-norm
  • 2.4.2 Union: t-conorm
  • 2.4.3 Complement
  • 2.4.4 De Morgan laws
  • 2.5 Adjustment of fuzziness
  • 2.6 Problems
  • References

Inspec keywords: mathematics computing; fuzzy set theory; digital simulation

Other keywords: fuzzy intersection; user-defined toolbox library; fuzzy set type; complement; fuzzy set properties; MATLAB/Simulink; MATLAB function files; union; fuzzy set modelling

Subjects: Mathematics computing; Combinatorial mathematics

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