Evaluation of trapezoidal fuzzy numbers on AHP based solution of multi-objective programming problems

Akbaş S., Dalkilic T.

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, vol.31, no.3, pp.1869-1879, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.3233/jifs-16041
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1869-1879
  • Keywords: Analytic hierarchy process, fuzzy multi-objective linear programming, trapezoidal fuzzy numbers, SUPPLIER SELECTION MODEL, EXTENT ANALYSIS METHOD
  • Karadeniz Technical University Affiliated: Yes


Multi-criteria decision making method is used in such cases having multiple targets. Multi-objective linear programming problems, which deal with uncertain measurements for both objectives and constraints, are solved by fuzzy multi-objective linear programming methods. Analytic hierarchy process (AHP), one of the multi-criteria decision-making methods based on weighting of objectives, is designed to solve complex problems. In this study, multiple criteria decision making problems and decision makers' opinions on these problems as well as their solution processes are discussed. Firstly, a fuzzy multi objective linear programming problem is solved using the approaches of Zimmerman and Hybrid. In the literature, these methods are applied using triangular fuzzy numbers based on decision makers' opinions only in cases where the objective function is minimization. In this study, as an alternative to the triangular fuzzy numbers, trapezoidal fuzzy numbers are defined, and both minimization and maximization of objective functions are examined. Finally, a solution algorithm for a fuzzy multi-objective linear programming problem is proposed under some given conditions. The algorithm is applied to a sample problem that involves modeling of a congress organizing which aims to place attendees to accommodations under specific objectives and constraints. In the evaluation phase of the algorithm, targets are weighted by using triangular and trapezoidal fuzzy numbers. At the end, the results of the proposed algorithm are compared with the results of other methods in the literature.