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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
Forthcoming Article

Neutrosophic Filters in Pseudo-BCI algebras

Xiaohong Zhang
Shanghai Maritime University
Xiaoyan Mao
Ningbo University
Yuntian Wu
Shaanxi University of Science & Technology
Xuehuan Zhai
Shaanxi University of Science & Technology

ABSTRACT

The concept of neutrosophic set is introduced by F. Smarandache, it is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. The notion of pseudo-BCI algebra is introduced by W. A. Dudek and Y. B. Jun, it is a kind of non-classical logic algebra and close connection with various non-commutative fuzzy logics. In this paper, neutrosophic set theory is applied to pseudo-BCI algebras. The new concepts of neutrosophic filter, neutrosophic normal filter, anti-grouped 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.