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https://hdl.handle.net/2440/101302
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Type: | Journal article |
Title: | On fuzzy ellipsoid numbers and membership functions |
Author: | Wang, G. Shi, P. Agarwal, R. Shi, Y. |
Citation: | Journal of Intelligent and Fuzzy Systems, 2016; 31(1):391-403 |
Publisher: | IOS Press |
Issue Date: | 2016 |
ISSN: | 1064-1246 1875-8967 |
Statement of Responsibility: | Guixiang Wang, Peng Shi, Ramesh K. Agarwal and Yan Shi |
Abstract: | In this paper, the operations of fuzzy ellipsoid numbers and the direct relationship between the joint membership function and the edge membership functions are investigated. First, we prove that the general scalar multiplication (defined by Zadeh’s expansion) of fuzzy ellipsoid numbers preserves the closeness of the operation, but the general addition (defined by Zadeh’s expansion) does not preserve the closeness of the operation. Then, a new addition “⊕” of fuzzy ellipsoid numbers is defined, and it is shown that the new addition “⊕” preserves the closeness of the operation, and is the best approximation of the general addition operation in all addition operations which preserves the closeness of the operation for fuzzy ellipsoid numbers. Next, a bijection is established between fuzzy n−ellipsoid number space and n dimension fuzzy vector space. Furthermore a formula is obtained to express the edge membership functions with the joint membership function, and an iterative algorithm is proposed to calculate the joint membership function value as the edge membership functions are known, and the convergence of the iterative algorithm is demonstrated. |
Keywords: | Fuzzy numbers; fuzzy cell numbers; fuzzy ellipsoid numbers; operations of fuzzy numbers; membership functions |
Rights: | © 2016 – IOS Press and the authors. All rights reserved |
DOI: | 10.3233/IFS-162152 |
Grant ID: | http://purl.org/au-research/grants/arc/DP140102180 http://purl.org/au-research/grants/arc/LP140100471 http://purl.org/au-research/grants/arc/LE150100079 |
Published version: | http://dx.doi.org/10.3233/ifs-162152 |
Appears in Collections: | Aurora harvest 7 Electrical and Electronic Engineering publications |
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