Near zero fuzzy solution of fully fuzzy linear systems¹

Article type: Research Article

Authors: Guo, Xiaobin^{a; *} | Liu, Kun^b

Affiliations: [a] College of Mathematics and Statistics, Northwest Normal University, China | [b] School of Mathematics and Statistics, Longdong University, China

Correspondence: [*] Corresponding author. Xiaobin Guo, College of Mathematics and Statistics, Northwest Normal University, China. Tel.: 008613919030082; E-mail: [email protected].

Note: [1] The work is supported by the Natural Scientific Funds of PR China (no.61967014, 11861059) and the Outstanding Youth Fund of Gansu Province (no. 20JR5RA540).

Abstract: This paper discusses a new approximate solution of a class of fully fuzzy linear systems A˜x˜=b˜ in which the coefficient matrix A˜ is a positive fuzzy matrix. The original fuzzy linear systems is extended into simple crisp linear equation using the obtained approximate multiplication of positive fuzzy number and near zero fuzzy number. Two cases are analysed: (a) the unknown vector x˜ is a near zero fuzzy vector with positive mean value; (b) the unknown vector x˜ is a near zero fuzzy vector with negative mean value. Two computing models are established and respective expression of the solution to fully fuzzy linear system are derived, and the sufficient condition for the existence of strong fuzzy solution are analyzed correspondingly. Some numerical examples are given to illustrated our proposed method.

Keywords: Fuzzy numbers, matrix computation, fuzzy linear systems, fuzzy approximate solutions

DOI: 10.3233/JIFS-222421

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 5, pp. 8043-8052, 2023