Characterization of prefilters of EQ-algebra by falling shadow

Article type: Research Article

Authors: Li, Yijun^{a; b; *} | Saeid, Arsham Borumand^c | Wang, Jun Tao^d

Affiliations: [a] Sun Yat Sen University, Lingnan Coll, Guangzhou, P.R. China | [b] College of Science, Xi’an Shiyou University, Xi’an, P.R. China | [c] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar, University of Kerman, Kerman, Iran | [d] School of Mathematics, Northwest University, Xi’an, P.R. China

Correspondence: [*] Corresponding author. Yijun Li. E-mail: liyijun6@mail.sysu.edu.cn.

Abstract: In this paper, some types of falling fuzzy prefilters of EQ-algebras are introduced and studied. The notion of falling fuzzy prefilters of EQ-algebras are introduced, and the relationships between falling fuzzy prefilters and fuzzy prefilters are discussed. Moreover, the notions of falling fuzzy positive implicative (implicative, fantastic) prefilters are also proposed and some of their characterizations are displayed. The relationships among these special falling fuzzy prefilters are mainly investigated by using their characterizations. In particular, some conditions for a falling fuzzy positive implicative prefilter is equivalent to a falling fuzzy implicative prefilter are provided.

Keywords: EQ-algebra, falling shadow, falling fuzzy prefilter, falling fuzzy (positive) implicative prefilter, falling fuzzy fantastic prefilter

DOI: 10.3233/JIFS-17680

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3805-3818, 2017