Interactive Fuzzy Goal Programming Based on Taylor Series to Solve Multiobjective Nonlinear Programming Problems With Interval Type-2 Fuzzy Numbers

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, the resources, and the requirements of each kind of resources are ta...

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Published in:IEEE transactions on fuzzy systems Vol. 26; no. 4; pp. 2434 - 2449
Main Authors: Dalman, Hasan, Bayram, Mustafa
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Decision making
Equivalence
Fuzzy goal programming (FGP)
Fuzzy sets
Goal programming
interactive approach
interval type-2 (IT2) fuzzy sets
Linear programming
multiobjective nonlinear programming
Multiple objective analysis
Nonlinear programming
Pareto optimum
Planning
Programming
Taylor series
Uncertainty
ISSN:1063-6706, 1941-0034
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Abstract 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, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent multiobjective linear programming problem. By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem that can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.
AbstractList 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, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent multiobjective linear programming problem. By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem that can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.
Author Bayram, Mustafa
Dalman, Hasan
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  surname: Bayram
  fullname: Bayram, Mustafa
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  organization: Department of Computer Engineering, Istanbul Gelisim University, Istanbul, Turkey
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SubjectTerms Decision making
Equivalence
Fuzzy goal programming (FGP)
Fuzzy sets
Goal programming
interactive approach
interval type-2 (IT2) fuzzy sets
Linear programming
multiobjective nonlinear programming
Multiple objective analysis
Nonlinear programming
Pareto optimum
Planning
Programming
Taylor series
Uncertainty
Title Interactive Fuzzy Goal Programming Based on Taylor Series to Solve Multiobjective Nonlinear Programming Problems With Interval Type-2 Fuzzy Numbers
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