Mathematics and Statistics Faculty and Staff Publications

Document Type

Book

Publication Date

2018

Abstract

The notion of a neutrosophic quadruple BCK/BCI-number is considered in the first article (“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar), and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCInumbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. Techniques for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multicriteria decision-making problems. In the second research article (“Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I”), Muhammad Akram, Shumaiza, and Florentin Smarandache present the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method to solve such problems. The authors use the revised closeness degree to rank the alternatives in the bipolar neutrosophic TOPSIS method. The researchers describe the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method by flow charts, also solving numerical examples by the proposed methods and providing a comparison of these methods. In the third article (“Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra”, by Young Bae Jun, Seon Jeong Kim and Florentin Smarandache), the notion of (T(i,j),I(k,l),F(m,n))-interval neutrosophic subalgebra in BCK/BCI-algebra is introduced for i,j,k,l,m,n infoNumber 1,2,3,4, and properties and relations are investigated. The notion of interval neutrosophic length of an interval neutrosophic set is also introduced, and the related properties are investigated.

Publisher

MDPI, Basel

ISSN

978-3-03897-289-1

Language (ISO)

English

Keywords

neutrosophic quadruple BCK/BCI-number, Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra, neutrosophic set, neutrosophic logic

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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