A new approach to the fuzzification of arity, JHC and CUP of L-convexities

Article type: Research Article

Authors: Chen, Fan-Hong^{a; b; c} | Shen, Chong^{a; b} | Shi, Fu-Gui^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China | [c] School of Mechanical Engineering, Yanching Institute of Technology, Hebei, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi. E-mail: fuguishi@bit.edu.cn.

Abstract: In this paper, the notions of arity, Corn-union property (CUP), Join-hull commutativity (JHC) and weakly Join-hull commutativity (weakly JHC) are generalized to the fuzzy case. Also, it is proved that Corn-union property, Join-hull commutativity and weakly Join-hull commutativity L-convexities are of arity ≤2. Moreover, the CP and CC mappings between L-convexities with arity property are characterized.

Keywords: L-convexity, arity, join-hull commutativity, corn-union property, CP mapping, CC mapping

DOI: 10.3233/JIFS-171142

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 221-231, 2018