In this paper a new branch of philosophy is presented, called neutrosophy, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The Fundamental Thesis: Any idea is T% true, I% indeterminate, and F% false, where T, I, F are standard or non-standard subsets included in the non-standard unit interval K 0, 1 M. The Fundame...

The concept of intuitionistic neutrosophic soft sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of intuitionistic neutrosophic soft sets to graphs. We introduce the concepts of intuitionistic neutrosophic soft graphs, and present applications of intuitionistic neutrosophic soft graphs in a multiple-attribute dec...

The concepts of neutrosophic normal soft group, neutrosophic soft cosets, neutrosophic soft homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established.

In this article we present three similarity measures between simplified neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space. Then based on these three defined simila...

In this paper, the cartesian product and the relations on neutrosophic soft sets have been defined in a new approach. Some properties of this concept have been discussed and verified with suitable real life examples. The neutrosophic soft composition has been defined and verified with the help of example. Then, some basic properties to it have been established. After that the concept of neutros...

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer relia...

Fuzzy classification has become of great interest because of its ability to utilize simple linguistically interpretable rules and has overcome the limitations of symbolic or crisp rule based classifiers. This paper introduces an extension to fuzzy classifier: a neutrosophic classifier, which would utilize neutrosophic logic for its working. Neutrosophic logic is a generalized logic that is capa...

In this article we present three similarity measures between simplified neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space. Then based on these three defined simila...

In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new defin...

In this study, we introduce the concept of denser property in fuzzy membership function used in neutrosophic sets. We present several new definitions and study their properties. Defuzzification methods over neutrosophic triangular dense xxxx fuzzy sets and neutrosophic triangular intuitionistic dense fuzzy sets are then given. Finally practical applicability of the methods have been discussed w...