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Soft Computing
Published in: Soft Computing 21/2017

30-05-2016 | Methodologies and Application

Graphical visualization of FFLS to explain the existence of solution and weak solution in circuit analysis

Authors: Md. Mijanur Rahman, G. M. Ashikur Rahman

Published in: Soft Computing | Issue 21/2017

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Abstract

In this paper, an unambiguous graphical interpretation of fully fuzzy linear equation in two variables where all the parameters are symmetric triangular fuzzy number (STFN) is presented. Several new terminologies such as disassembled fuzzy straight line and assembled fuzzy straight line are proposed and theorems concerning those are established. This interpretation is extended to \(2\times 2\) fully fuzzy linear system (FFLS) with STFN which enables to comment on the existence of solution of the system. Then an application of FFLS is focused in a real-life circuit analysis problem where the solving procedure using available method in the literature leads to weak solution. Why this happens is explained using the proposed geometrical interpretation. Finally, a modification to the definition of TFN is proposed to manage the situation easily where weak solution arises.
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Metadata
Title
Graphical visualization of FFLS to explain the existence of solution and weak solution in circuit analysis
Authors
Md. Mijanur Rahman
G. M. Ashikur Rahman
Publication date
30-05-2016
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 21/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-016-2197-8

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