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We establish the hybrid concept of complex bipolar- valued neutrosophic soft set (CBVNSS) as a hybrid model of bipolar neutrosophic soft set (BNSS)and complex fuzzy set (CFS). A CBVNSS is highly suitable for use in real life situations where the decision makers are interested to deal with bipolarity as well as truth membership, indeterminacy membership and falsity membership grades to the alternatives in an extended range with complex numbers. Certain operations on CBVNSS like complement, subset, union and intersection operations are defined. Some related examples are also given to enhance the understanding of the proposed concept. The basic properties are also verified. We then provide a decision-making method on the CBVNSS. Finally, a numerical example has been presented to verify validity and feasibility of the developed method. [ABSTRACT FROM AUTHOR]

In 1995, Smarandache initiated the theory of neutrosophic set as new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. Molodtsov initiated the theory of soft set as a new mathematical tool for dealing with uncertainties, which traditional mathematical tools cannot handle. He has showed several applications of this theory for solving many practical problems in economics, engineering, social science, medical science, etc. In 2017 Smarandache initiated the theory of Plithogenic Set and their properties. He also generalized the soft set to the hypersoft set by transforming the function F into a multi-attribute function and introduced the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set. In this research, for the first time we define the concept of Plithogenic soft set, and give it some generalizations and study some of its operations. Furthermore, We give examples for these concepts and operations. Finally, the similarities between two Plithogenic soft sets are also given. [ABSTRACT FROM AUTHOR]

Neutrosophic set is a powerful general formal framework. A lot of studies on neutrosophic had been proposed and recently, in multi-valued interval values. However, sometimes there is problem involving elements of ambiguity and uncertainties in which the function of membership is difficult to be set in a particular case. Clearly, these problems can be solved by soft set since it is able to solve the lack of parameterization tool of theory. Thus, this paper introduces a concept of multi-valued interval neutrosophic soft set which amalgamates multi-valued interval neutrosophic set and soft set. The proposed set extends the notions of fuzzy set, intuitionistic fuzzy set, neutrosophic set, interval-valued neutrosophic set, multi-valued neutrosophic set, soft set and neutrosophic soft set. Further, we study some basic operations such as complement, equality, inclusion, union, intersection, "AND" and "OR" for multi-valued interval neutrosophic soft elements and discuss its associated properties. Moreover, the derivation of its properties, related examples and some proofs on the propositions are included. [ABSTRACT FROM AUTHOR]

The term topology was introduced by Johann Beredict Listing in the 19th century. Closed sets are fundamental objects in a topological space. In this paper, we use neutrosophic vague sets and topological spaces and we construct and develop a new concept namely "neutrosophic vague topological spaces". By using the fundamental definition and necessary example we have defined the neutrosophic vague topological spaces and have also discussed some of its properties. Also we have defined the neutrosophic vague continuity and neutrosophic vague compact space in neutrosophic vague topological spaces and their properties are deliberated. [ABSTRACT FROM AUTHOR]

In 1995, Smarandache talked for the first time about neutrosophy and he defined one of the most important new mathematical tool which is a neutrosophic set theory as a new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. He also defined the neutrosophic norm and conorms namely N-norm and Nconorm respectively. In this paper we give generating theorems for N-norm and N-conorm. Given an N-norm we can generate a class of N-norms and N-cnorms, and given an Nconorm we can generate a class of N-conorms and N-norms. We also give bijective generating theorems for N-norms and N-conorms. [ABSTRACT FROM AUTHOR]

In 1995 Smarandache introduced the concept of neutrosophic set which is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. In 2013 Maji introduced the concept of neutrosophic soft set theory as a general mathematical tool for dealing with uncertainty. In this paper we define the notion of a mapping on classes where the neutrosophic soft classes are collections of neutrosophic soft set. We also define and study the properties of neutrosophic soft images and neutrosophic soft inverse images of neutrosophic soft sets. [ABSTRACT FROM AUTHOR]