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

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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.

## Keywords

Graphical interpretation Fully fuzzy linear equation Symmetric triangular fuzzy number Fully fuzzy linear system Circuit analysis Weak solution## Notes

## Compliance with ethical standards

## Conflict of interest

Md. Mijanur Rahman declares that he has no conflict of interest. G. M. Ashikur Rahman declares that he has no conflict of interest.

## Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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