On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective funct...

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Autores principales:	Namrata Rani, Vandana Goyal, Deepak Gupta
Formato:	article
Lenguaje:	EN
Publicado:	International Journal of Mathematical, Engineering and Management Sciences 2021
Materias:	α-cut set bl-mo optimization model fuzzy programming fully quadratic fractional programming Technology T Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a965e7aad8354dd284ffe5994f0a5e30
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spelling	oai:doaj.org-article:a965e7aad8354dd284ffe5994f0a5e302021-12-04T05:18:39ZOn Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands10.33889/IJMEMS.2021.6.6.0962455-7749https://doaj.org/article/a965e7aad8354dd284ffe5994f0a5e302021-12-01T00:00:00Zhttps://ijmems.in/cms/storage/app/public/uploads/volumes/96-IJMEMS-21-0216-6-6-1612-1628-2021.pdfhttps://doaj.org/toc/2455-7749This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.Namrata RaniVandana GoyalDeepak GuptaInternational Journal of Mathematical, Engineering and Management Sciencesarticleα-cut setbl-mo optimization modelfuzzy programmingfully quadratic fractional programmingTechnologyTMathematicsQA1-939ENInternational Journal of Mathematical, Engineering and Management Sciences, Vol 6, Iss 6, Pp 1612-1628 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	α-cut set bl-mo optimization model fuzzy programming fully quadratic fractional programming Technology T Mathematics QA1-939
spellingShingle	α-cut set bl-mo optimization model fuzzy programming fully quadratic fractional programming Technology T Mathematics QA1-939 Namrata Rani Vandana Goyal Deepak Gupta On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
description	This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.
format	article
author	Namrata Rani Vandana Goyal Deepak Gupta
author_facet	Namrata Rani Vandana Goyal Deepak Gupta
author_sort	Namrata Rani
title	On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
title_short	On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
title_full	On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
title_fullStr	On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
title_full_unstemmed	On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
title_sort	on solving bi-level multi-objective fully quadratic fractional optimization model with fuzzy demands
publisher	International Journal of Mathematical, Engineering and Management Sciences
publishDate	2021
url	https://doaj.org/article/a965e7aad8354dd284ffe5994f0a5e30
work_keys_str_mv	AT namratarani onsolvingbilevelmultiobjectivefullyquadraticfractionaloptimizationmodelwithfuzzydemands AT vandanagoyal onsolvingbilevelmultiobjectivefullyquadraticfractionaloptimizationmodelwithfuzzydemands AT deepakgupta onsolvingbilevelmultiobjectivefullyquadraticfractionaloptimizationmodelwithfuzzydemands
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On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

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