Prime (distributive) fuzzy posets

Article type: Research Article

Authors: Wang, Rongrong | Han, Shengwei^{; *}

Affiliations: Department of Mathematics, Shaanxi Normal University, P.R. China

Correspondence: [*] Corresponding author. Shengwei Han, Department of Mathematics, Shaanxi Normal University, Xi’an 710119, P.R. China. E-mails: wrr161551@snnu.edu.cn; hansw@snnu.edu.cn.

Abstract: Fuzzy posets can be regarded as a generalization of classical posets. Many concepts and results in posets can be generalized to fuzzy posets. In order to further improve the fuzzy poset theory, in this paper, we shall introduce the concept of prime (distributive) fuzzy posets which can be seen as the correspondence of prime (distributive) posets in fuzzy setting. First, we consider the extensions of fuzzy ideals in a fuzzy poset. Then by the extensions of fuzzy ideals, we give a characterization for prime (distributive) fuzzy posets, that is, a fuzzy poset X is prime (distributive) if and only if all extensions of normal fuzzy ideals of X are Frink (strong) fuzzy ideals. This paper generalizes the work of Halas in posets into fuzzy posets.

Keywords: Fuzzy poset, extension of fuzzy ideal, prime fuzzy poset, distributive fuzzy poset

DOI: 10.3233/JIFS-181352

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5513-5520, 2019