Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm

In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assume...

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Bibliographic Details
Published in:Opsearch Vol. 51; no. 2; pp. 280 - 296
Main Authors: Baky, Ibrahim A., Eid, Mohamed H., El Sayed, Mohamed A.
Format: Journal Article
Language:English
Published: India Springer India 01.06.2014
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Demand
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Management
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Operations research
Operations Research/Decision Theory
Programming
Set theory
Studies
Theoretical Article
Fuzzy sets
Fuzzy goal programming
Bi-level programming
Multi-objective programming
Fuzzy demands
Goal programming
ISSN:0030-3887, 0975-0320
Online Access:Get full text
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Summary:In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assumed to be characterized as fuzzy numbers. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels, as well as the membership functions for the vector of decision variables controlled by FLDM are developed in the model formulation of the problem. Then FGP algorithm is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical example is given to demonstrate the proposed algorithm.
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ISSN:0030-3887
0975-0320
DOI:10.1007/s12597-013-0145-2