A NEW ALGORITHM FOR SOLVING FULLY FUZZY BI-LEVEL QUADRATIC PROGRAMMING PROBLEMS
H. Äzza. Operations Research and Applications : An International Journal (ORAJ), 5 (2):
01-15(May 2018)
DOI: 10.5121/oraj.2018.5201
Abstract
This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFNs). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this preference information for ULDM and solves his/her problem subject to the ULDMs restrictions. Finally, the decomposed method is illustrated by numerical example.
%0 Journal Article
%1 noauthororeditor
%A Äzza, H. Amer"
%D 2018
%J Operations Research and Applications : An International Journal (ORAJ)
%K Bi-Level Decomposed Fully Fuzzy Method Non-Linear Numbers Problems Programming Quadratic Triangular
%N 2
%P 01-15
%R 10.5121/oraj.2018.5201
%T A NEW ALGORITHM FOR SOLVING FULLY FUZZY BI-LEVEL QUADRATIC PROGRAMMING PROBLEMS
%U http://airccse.com/oraj/papers/5218oraj01.pdf
%V 5
%X This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFNs). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this preference information for ULDM and solves his/her problem subject to the ULDMs restrictions. Finally, the decomposed method is illustrated by numerical example.
@article{noauthororeditor,
abstract = {This paper is concerned with new method to find the fuzzy optimal solution of fully fuzzy bi-level non-linear (quadratic) programming (FFBLQP) problems where all the coefficients and decision variables of both objective functions and the constraints are triangular fuzzy numbers (TFNs). A new method is based on decomposed the given problem into bi-level problem with three crisp quadratic objective functions and bounded variables constraints. In order to often a fuzzy optimal solution of the FFBLQP problems, the concept of tolerance membership function is used to develop a fuzzy max-min decision model for generating satisfactory fuzzy solution for FFBLQP problems in which the upper-level decision maker (ULDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the lower-level decision maker (LLDM) uses this preference information for ULDM and solves his/her problem subject to the ULDMs restrictions. Finally, the decomposed method is illustrated by numerical example. },
added-at = {2018-06-20T14:42:10.000+0200},
author = {"Azza, H. Amer"},
biburl = {https://www.bibsonomy.org/bibtex/2186bec81b2d0aa585706a181c8a05c4e/oraj},
doi = {10.5121/oraj.2018.5201},
interhash = {49daab6039651100262319250aacd1a4},
intrahash = {186bec81b2d0aa585706a181c8a05c4e},
journal = {Operations Research and Applications : An International Journal (ORAJ)},
keywords = {Bi-Level Decomposed Fully Fuzzy Method Non-Linear Numbers Problems Programming Quadratic Triangular},
month = may,
number = 2,
pages = {01-15},
timestamp = {2018-06-20T14:42:10.000+0200},
title = {A NEW ALGORITHM FOR SOLVING FULLY FUZZY BI-LEVEL QUADRATIC PROGRAMMING PROBLEMS},
url = {http://airccse.com/oraj/papers/5218oraj01.pdf},
volume = 5,
year = 2018
}