The Fuzzy Complex Linear Systems Based on a New Representation of Fuzzy Complex Numbers

Zhiyong Xiao () and Zengtai Gong ()
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Zhiyong Xiao: School of Mathematics and Statistics, Longdong University, Qingyang 745000, China
Zengtai Gong: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730000, China

Mathematics, 2022, vol. 10, issue 15, 1-14

Abstract: Since the product of complex numbers and rectangular fuzzy complex numbers (RFCN) is not necessarily a RFCN in the former fuzzy complex linear system (FCLS), the scalar multiplication and addition operations of complex numbers and fuzzy complex numbers (FCN) based on a new representation of FCN are proposed. We also introduce a new method for solving FCLS, which can convert FCLS into two distinct linear systems. One is an n × n complex linear system, and the other is an ( m n ) × ( m n ) real linear system, where n is the number of unknown variables, and m is the number of substitutional cyclic sets composed of coefficients of FCLS. In particular, using this method to solve one-dimensional fuzzy linear systems, a ( 2 n ) × ( 2 n ) RLS is obtained, which is consistent with Friedman’s method. Finally, FCLS based on the RFCN as a special case are also investigated.

Keywords: fuzzy numbers; fuzzy complex number; fuzzy complex linear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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