Abstract
The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.
Highlights
The fuzzy arithmetic has many applications in various sciences
The aim of this work was to solve the fuzzy system of linear equations
After presenting the solving process, we compared the number of operations to show the abilities of the proposed method. It shows that the mentioned method decreased the maximum number of multiplication operations (MNMOs) in comparison with Friedman and Ezzati’s methods and it was one of the main novelties of this research
Summary
The fuzzy arithmetic has many applications in various sciences. In [4], Stanujkić et al applied the fuzzy mathematics for solving decision-making problems, in [5], Stojić et al presented a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet, and in [6], Si et al studied an approach to rank picture fuzzy numbers for decision-making problems. One of the main fields in fuzzy mathematics is solving fuzzy system of linear equations (FSLEs), which we refer to in this work. Based on numerical- and semi-analytical methods for solving FSLEs, we can study fuzzy bio-mathematical models. Studying the mathematical methods for solving the FSLE is important in theories and applications
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