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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018022057
pages 511-526

NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS

Xiaohong Zhang
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021, People's Republic of China; Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, People's Republic of China
Xiaoyan Mao
College of Science and Technology, Ningbo University, Ningbo, 315212, People's Republic of China
Yuntian Wu
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021, People's Republic of China
Xuehuan Zhai
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021, People's Republic of China

ABSTRACT

The concept of the neutrosophic set was introduced by Smarandache; it is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. The notion of pseudo-BCI algebra was introduced by Dudek and Jun; it is a kind of nonclassical logic algebra and has a close connection with various noncommutative fuzzy logics. In this paper, neutrosophic set theory is applied to pseudo-BCI algebras. The new concepts of neutrosophic filter, neutrosophic normal filter, antigrouped neutrosophic filter, and neutrosophic p-filter in pseudo-BCI algebras are proposed, and their basic properties are presented. Moreover, by using the concept of (alpha, beta, gamma)-level set in neutrosophic sets, the relationships between fuzzy filters and neutrosophic filters are discussed.