What is it about?

Linear system of equations is very common in mathematical and scientific analysis. It becomes a fully fuzzy linear system (FFLS) when all the variables and coefficients are considered to be fuzzy numbers. A fuzzy number is a number represented by fuzzy set. A fuzzy set is a set whose elements can have membership grade between 0 and 1 inclusive. This work attempts to present a graphical interpretation to the existence of solution of a FFLS. It also features an application of FFLS in circuit analysis where weak solution (solution that are weakly fuzzy) arises. It proposes a new way to define triangular fuzzy number so that this weakness can be omitted.

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Why is it important?

Fuzzy set is an extension of normal set. It paves the way to fuzzy numbers and fuzzy logic which are very crucial to numerous branches of applications such as neural network, machine learning. This work addresses some of the basic questions of FFLS: When does a FFLS have a solution or no solution? How can we graphically interpret those? Why does weak solution arise and how can we deal with them? Since there exist robust and unambiguous analyses of these questions in case of linear system, similar analyses are must for the fuzzy counterpart. That is what this work is aimed for.

Perspectives

Though fuzzy set theory is relatively a newer branch in mathematics, it has already become an area of huge interest among scientists due to it's applicability to various real life problems. While writing this paper, I felt that there is much work to do in this field that can have great potential to be applied to other branches of mathematics and sciences.

Md. Mijanur Rahman
University of Dhaka

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This page is a summary of: Graphical visualization of FFLS to explain the existence of solution and weak solution in circuit analysis, Soft Computing, May 2016, Springer Science + Business Media, DOI: 10.1007/s00500-016-2197-8.
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