Derived operators of M-fuzzifying matroids

Article type: Research Article

Authors: Zhong, Yu^{a; b; *} | Shi, Fu-Gui^{b; *}

Affiliations: [a] College of Science, North China University of Technology, Beijing, P. R. China | [b] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P. R. China

Correspondence: [*] Corresponding authors. Yu Zhong and Fu-Gui Shi. E-mails: [email protected] (Y. Zhong) and [email protected] (F.-G. Shi).

Abstract: In this paper, a new definition of M-fuzzifying derived operators on matroids is introduced and their characterizations are given. What’s more, it is shown that there is a one-to-one correspondence between M-fuzzifying matroids and M-fuzzifying derived operators, and there is also a one-to-one correspondence between M-fuzzifying closure operators and M-fuzzifying derived operators. Besides, we can obtain an M-fuzzifying closure operator induced by an M-fuzzifying matroid directly.

Keywords: M-fuzzifying matroid,, M-fuzzifying derived operator,, M-fuzzifying closure operator,, One-to-one correspondence

DOI: 10.3233/JIFS-17789

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4673-4683, 2018