Mathematics Commons^™

Special Issue : Neutrosophic Multi-Criteria Decision Making, Florentin Smarandache, Jun Ye, Yan Hui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

Symbolic Neutrosophic Theory, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters T_j, I_k, F_l) in neutrosophics.

In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of A and antiA, to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of A, antiA, and neutA, in order to get a neutrosynthesis).

In the second chapter we introduce the neutrosophic system and neutrosophic dynamic system. A neutrosophic system is a quasi- or –classical system, in the sense that the neutrosophic …

New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets.

Investigation Of A Neutrosophic Group, A. Elrawy, Florentin Smarandache, Ayat A. Temraz

Branch Mathematics and Statistics Faculty and Staff Publications

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components, while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept.

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …