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Keywords = RDM fuzzy arithmetic

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13 pages, 432 KB  
Article
Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?
by Joanna Kołodziejczyk, Andrzej Piegat and Wojciech Sałabun
Mathematics 2020, 8(9), 1507; https://doi.org/10.3390/math8091507 - 4 Sep 2020
Cited by 8 | Viewed by 2106
Abstract
To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy [...] Read more.
To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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