In this paper, we present a generalization of the relational data model based on interval neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle incomplete information. Associated with each relation are two membership functions one is called truth-membership function T which ...

In this paper we present a new concept called “generalized neutrosophic soft set”. This concept incorporates the beneficial properties of both generalized neutrosophic set introduced by A.A.Salama [7] and soft set techniques proposed by Molodtsov [4]. We also study some properties of this concept. Some definitions and operations have been introduced on generalized neutrosophic soft set. Finally...

The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) ar...

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...

The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notion...

Interval neutrosophic set (INS) is a generalization of interval valued intuitionistic fuzzy set (IVIFS), whose the membership and non-membership values of elements consist of fuzzy range, while single valued neutrosophic set (SVNS) is regarded as extension of intuitionistic fuzzy set (IFS). In this paper, we extend the hierarchical clustering techniques proposed for IFSs and IVIFSs to SVNSs and...

Neutrosophic set is a powerful general formal framework, which generalizes the concept of the classic set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set, and interval-valued intuitionistic fuzzy set from philosophical point of view. However, it will be difficult to apply in real science and engineering areas, while a simplified neutrosophic set (SNS) is a subclass of a neutroso...

The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems. Keywords—Entropy measure, Hausdorff distance, neutrosophic ...

A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the set-theoretic operators on an i...