Research Article | OPEN ACCESS
Method to Defuzzify Groups of Fuzzy Numbers: Allocation Problem Application
1, 2Jehan S. Ahmed, 2Maznah Mat Kasim and 2L. Majid Zerafat Angiz
1Department of Mathematics, Baghdad University, Baghdad, Iraq
2School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah, Malaysia
Research Journal of Applied Sciences, Engineering and Technology 2016 10:1011-1017
Received: April 27, 2015 | Accepted: May 10, 2015 | Published: May 15, 2016
Abstract
The defuzzification process converts fuzzy numbers to crisp ones and is an important stage in the implementation of fuzzy systems. In many actual applications, we encounter cases, in which the observed or derived values of the variables are approximate, yet the variables themselves must satisfy a set of relationships dictated by physical principle. When the observed values do not satisfy the relationships, each value is adjusted until they satisfy the relationships among observed data indicating their mathematical dependence on one another. Hence, this study proposes a new method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy numbers. It also aims to assume that each observed value is an approximate number (or a fuzzy number) and the true value (crisp value) is found in the production possibility set of the DEA model. The proposed method partitions the fuzzy numbers and the relationships among these observed data are observed as constraints. The paper presents the model, the computational process and applications in a real problem.
Keywords:
Data envelopment analysis, defuzzification, groups of fuzzy numbers, observed data,
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Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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The authors have no competing interests.
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