World Academy of Science, Engineering and Technology
Published February 4, 2017 | Version 10006701
Journal article Open

Complex Fuzzy Evolution Equation with Nonlocal Conditions

Description

The objective of this paper is to study the existence and
uniqueness of Mild solutions for a complex fuzzy evolution equation
with nonlocal conditions that accommodates the notion of fuzzy sets
defined by complex-valued membership functions. We first propose
definition of complex fuzzy strongly continuous semigroups. We then
give existence and uniqueness result relevant to the complex fuzzy
evolution equation.

Files

10006701.pdf

Files (150.4 kB)

Name Size
md5:b4825fc8b5f4b1de38b9c5b7a73bb418
150.4 kB Preview Download

Additional details

References

  • R. F. Arens, J. Eells, On embedding uniform and topological spaces, Pac. J. Math. 6 (1956) 397–403.
  • Daria Karpenko, Robert A. Van Gorder, Abraham Kandel, The Cauchy problem for complex fuzzy differential equations, Fuzzy Sets and Systems 245 (2014) 18-29.
  • A. El Allaoui, S. Melliani and L. S. Chadli, Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups, Journal of Fuzzy Set Valued Analysis 2016 No.2 (2016) 148–155.
  • K. Ezzinbi and James H. Liu, Nondensely Defined Evolution Equations with Nonlocal Conditions, Mathematical and Computer Modelling 36 (2002) 1027–1038.
  • M. Hukuhara, Integration des applications measurables dont la valeur est un compact convexe, Funk. Ekvacioj. 10 (1967) 207–223.
  • O. Kaleva. Fuzzy Diferentiel Equations, Fuzzy Sets and Systems. 24 (1987) 301–317.
  • S. Melliani, A. El Allaoui and L. S. Chadli, Relation Between Fuzzy Semigroups and Fuzzy Dynamical Systems, Nonlinear Dynamics and Systems Theory, 17 (1) (2017) 60–69.
  • J. Nieto, The Cauchy problem for continuous fuzzy differential equations, Fuzzy Sets Syst. 102 (1999) 259-262.
  • M. L. Puri, D. A. Ralescu. Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409–422. [10] Daniel Ramot, Ron Milo, Menahem Friedman, and Abraham Kandel, Complex Fuzzy Sets, IEEE Transactions on Fuzzy Systems, 10 (2002). [11] D. E. Tamir, L. Jin, A. Kandel, A new interpretation of complex membership grade, Int. J. Intell. Syst. 26 (2011) 285-312.