Interactive goal programming algorithm with Taylor series and interval type 2 fuzzy numbers

DALMAN H., BAYRAM M.

International Journal of Machine Learning and Cybernetics, vol.10, no.6, pp.1563-1579, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1007/s13042-018-0835-4
  • Journal Name: International Journal of Machine Learning and Cybernetics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1563-1579
  • Keywords: Fuzzy goals, Interactive mechanism, Interval type 2 fuzzy sets, Multiobjective nonlinear programming, Taylor series
  • Istanbul Gelisim University Affiliated: Yes

Abstract

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.This paper presents an interactive fuzzy goal programming (FGP) approach for solving Multiobjective Nonlinear Programming Problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered fuzzy problem is first transformed into an equivalent crisp MONLPP, and then the MONLPP is converted into an equivalent multiobjective linear programming problem (MOLPP). By using an algorithm based on Taylor series, this problem is also reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by a numerical example.