A novel difference and derivative of linearly correlated fuzzy number-valued functions

Article type: Research Article

Authors: Shen, Yonghong^{; *}

Affiliations: School of Mathematics and Statistics, Tianshui Normal University, Tianshui, P.R. China

Correspondence: [*] Corresponding author. Yonghong Shen, School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P.R. China. E-mail: [email protected]..

Abstract: In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

Keywords: Fuzzy numbers, Linearly correlated difference, Linearly correlated derivative, Canonical form, Linearly correlated fuzzy number-valued functions

DOI: 10.3233/JIFS-212908

Journal: Journal of Intelligent & Fuzzy Systems, vol. 42, no. 6, pp. 6027-6043, 2022