The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory

Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : [Formula: see text] , where [Formula: see text]. To use the mentioned EP meth...

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Detalles Bibliográficos
Autores principales: Allahviranloo, T., Gerami Moazam, L.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4070452/
https://www.ncbi.nlm.nih.gov/pubmed/25009826
http://dx.doi.org/10.1155/2014/156203
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author Allahviranloo, T.
Gerami Moazam, L.
author_facet Allahviranloo, T.
Gerami Moazam, L.
author_sort Allahviranloo, T.
collection PubMed
description Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : [Formula: see text] , where [Formula: see text]. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find λ and μ as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given.
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spelling pubmed-40704522014-07-09 The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory Allahviranloo, T. Gerami Moazam, L. ScientificWorldJournal Research Article Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : [Formula: see text] , where [Formula: see text]. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find λ and μ as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. Hindawi Publishing Corporation 2014 2014-06-09 /pmc/articles/PMC4070452/ /pubmed/25009826 http://dx.doi.org/10.1155/2014/156203 Text en Copyright © 2014 T. Allahviranloo and L. Gerami Moazam. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Allahviranloo, T.
Gerami Moazam, L.
The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title_full The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title_fullStr The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title_full_unstemmed The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title_short The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
title_sort solution of fully fuzzy quadratic equation based on optimization theory
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4070452/
https://www.ncbi.nlm.nih.gov/pubmed/25009826
http://dx.doi.org/10.1155/2014/156203
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