The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.

The aim of this manuscript is to propose a new extension of the MULTIMOORAmethod adapted for usage with a neutrosophic set. By using single valued neutrosophic sets, the MULTIMOORA method can be more efficient for solving complex problems whose solving requires assessment and prediction, i.e. those problems associated with inaccurate and unreliable data. The suitability of the proposed approach...

In this research paper, based on the notion of generalized single valued neutrosophic graphs of type 1, we presented a new type of neutrosophic graphs called generalized bipolar neutrosophic graphs of type 1 (GBNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of GBNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1) and g...

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutro...

A simplified neutrosophic set (SNS) is a subclass of neutrosophic set and contains a single-valued neutrosophic set (SVNS) and an interval neutrosophic set (INS). It was proposed as a generalization of an intuitionistic fuzzy set (IFS) and an interval-valued intuitionistic fuzzy set (IVIFS) in order to deal with indeterminate and inconsistent information. The paper proposes another form of the ...

Abstract: Clustering plays an important role in data mining, pattern recognition, and machine learning. Then, single-valued neutrosophic sets (SVNSs) are a useful means to describe and handle indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-value neutrosophic information, the artic...

Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neu...

The purpose of this paper is to introduce multiattribute decision making based on the concept of interval neutrosophic sets. While the concept of neutrosophic sets is a powerful tool to deal with indeterminate and inconsistent data, the interval neutrosophic set is also a powerful mathematical tool as well as more flexible to deal with incompleteness. The rating of all alternatives is expressed...