International Journal of Neutrosophic Science

In this paper we present a Maple package called Neutrosophic, which allows users to do operations on trapezoidal and triangular neutrosophic numbers including summation, subtraction, division and multiplication based on -cuts and plots the results, also the package allows users to rank numbers depending on ambiguity index and value index. This package is very useful in neutrosophic decision making problems, neutrosophic probabilities, neutrosophic statistics and in many other fields of neutrosophic researches.

  Recently, several researchers paid attention towards dealin with uncertainty in data with neutrosophic attributes. In this process, a problem is addressed while dealing with contradiction and its impact on decision making. It is considered as one of the major issues for data science researchers working in three-way fuzzy concept lattice. To deal with this issue, current paper tried to introduce the algebra of single-valued Plithogenic graph and its visualization based on infium and supremum. The proposed method also demonstated with an illustrative example for better understanding.  

  In this study, the concept of neutrosophic soft tri-topological space is defined as a generalization of neutrosophic soft bitopological space. Then neutrosophic soft tri-open and tri-closed sets are defined and in this space. Also, some basic properties of these new types of open and closed sets are investigated and supported by many examples to further clarify the study.  

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-so-sophisticated distance measure between two SVNSs is defined by considering the cross-assessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals.  

       Indeterminacy makes the main distinction between fuzzy / intuitionistic fuzzy (and other extensions of fuzzy) set / logic vs. neutrosophic set / logic, and between classical probability and neutrosophic probability. Also, between classical statistics vs. neutrosophic and plithogenic statistics, between classical algebraic structures vs. neutrosophic algebrais structures, between crisp numbers vs. neutrosophic  numbers. We present a broad definition of indeterminacy, various types of indeterminacies, and many practical applications.