M-fuzzifying matroids induced by M-fuzzy families of ciruits

Article type: Research Article

Authors: Xin, Xiu^a | Lian, Huan^{b; *}

Affiliations: [a] Department of Mathematics, Tianjin University of Technology, Tianjin, P.R. China | [b] School of Mathematics Science, Tianjin Normal University, Tianjin, P.R. China

Correspondence: [*] Corresponding author. Huan Lian, School of Mathematics Science, Tianjin Normal University, Tianjin 300387, P.R. China. Tel.: +86 13821395620; E-mail: [email protected].

Abstract: This paper attempts to study circuit axioms and connectedness of M-fuzzifying matroids. Based on the results of circuit-maps given by Yao and Shi, remarks concerning circuit-maps and connectedness of fuzzifying matroids are shown, and thus the useful notion of an M-fuzzifying matroid induced by an M-fuzzy family of circuits is introduced. Circuit axioms of an M-fuzzifying matroid induced by an M-fuzzy family of circuits are established, which are the generalizations of circuit axioms for a matroid in a normal way. Connectedness of an M-fuzzifying matroid induced by an M-fuzzy family of circuits is then defined by its M-fuzzy family of circuits, a fuzzy analog of connectedness of a matroid. Additionally, two kinds of M-fuzzifying matroids are compared.

Keywords: M-fuzzifying matroid, M-fuzzy family of circuits, connectedness

DOI: 10.3233/JIFS-171239

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2223-2234, 2018