A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-16
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers.
This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method.
To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of α -level sets.
By using α -level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each α -level set.
The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function.
Based on the K th-best algorithm, the two subproblems can be solved sequentially.
Based on a series of α -level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem.
Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach.
American Psychological Association (APA)
Ren, Aihong. 2015. A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1073398
Modern Language Association (MLA)
Ren, Aihong. A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem. Mathematical Problems in Engineering No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1073398
American Medical Association (AMA)
Ren, Aihong. A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1073398
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073398