On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces

Article type: Research Article

Authors: Wu, Xiu-Yun^{a; b; *} | Bai, Shi-Zhong^c

Affiliations: [a] School of Science, Hunan University of Science and Engineering, Hunan, China | [b] School of Mathematics and Computational Science, Xiangtan University, Hunan, China | [c] School of Mathematics and Computational Science, Wuyi University, Guangdong, China

Correspondence: [*] Corresponding author. Xiu-Yun Wu. Tel.: +86 18374601897; Fax: +86 0746 6381374; E-mail: [email protected].

Abstract: In this paper, relations between hull operators which correspond to convex structures formed by cut sets of a given M-fuzzifying convex structure and cut sets of the hull operator of that M-fuzzifying convex structure are discussed. Then concepts of M-fuzzifying Join-Hull Commutativity property and M-fuzzifying Peano property are introduced and characterized, respectively. Also, it is proved that an M-fuzzifying convex structure which has M-fuzzifying JHC property is of arity ≤ 2 and that the segment operator of an M-fuzzifying convex structure of arity ≤2 has M-fuzzifying JHC property iff it has M-fuzzifying Peano property.

Keywords: M-fuzzifying convexity, M-fuzzifying JHC property, M-fuzzifying Peano property, M-fuzzifying interval operator

DOI: 10.3233/IFS-152015

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2447-2458, 2016