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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]

The aim of this paper is to correct the assertions (3) and (4) of Proposition 5.2 proposed by Alkhazaleh [Journal of Intelligent and Fuzzy Systems 30 (2016) 1087-1098]. Every notions involved are extend to the arbitrary set case in a clear, rigorous, and non-burdensome manner. A counterexample illustrates the flaw of the assertions. We introduce some new notions describing 'subset' of time-neutrosophic soft sets (T-NSSs for short) and 'equal' of T-NSSs, and give some examples and related propositions. Then we use these results to remedy the flaw of the assertions, and to improve the work of Alkhazaleh. [ABSTRACT FROM AUTHOR]

In this paper as a generalization of neutrosophic soft set we introduce the concept of n-valued refined neutrosophic soft set and study some of its properties. We also, define its basic operations, complement, union intersection, "AND" and "OR" and study their properties. [ABSTRACT FROM AUTHOR]

In 2013 Ayman A. Hazaymeh in his PhD thesis introduced the concept of time-fuzzy soft set as a generalization of fuzzy soft set. In this paper and as a generalization of neutrosophic soft set we introduce the concept of time-neutrosophic soft set and study some of its properties. We also, define its basic operations, complement, union intersection, "AND" and "OR" and study their properties. Also, we give hypothetical application of this concept in decision making problems. [ABSTRACT FROM AUTHOR]

In 1993, Gau and Buehrer proposed the theory of vague sets as an extension of fuzzy set theory. Vague sets are regarded as a special case of context-dependent fuzzy sets. In 1995, Smarandache talked for the first time about neutrosophy, and he defined the neutrosophic set theory as a new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. In this paper, we define the concept of a neutrosophic vague set as a combination of neutrosophic set and vague set. We also define and study the operations and properties of neutrosophic vague set and give some examples. [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]

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set. [ABSTRACT FROM AUTHOR]

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of Wrapping Lindley Distribution (WLD), we suggest a new circular distribution called the Wrapping Quasi Lindley Distribution (WQLD). We obtain the probability density function and derive the formula of a cumulative distribution function, characteristic function, trigonometric moments, and some related parameters for this WQLD. The maximum likelihood estimation method is used for the estimation of parameters. [ABSTRACT FROM AUTHOR]

This paper aims first to recall the generalized Mittag-Leffler function and propose several properties of the generalized matrix Mittag-Leffler function. Afterward, we set a definition for a further extension of the generalized matrix Mittag-Leffler function and then show that this function is absolutely convergent under a certain condition. [ABSTRACT FROM AUTHOR]

The basic aim of soft computing is to trade precision for a tractableness and reduction in solution cost by pushing the limits of tolerance for imprecision and uncertainty. This paper introduces a novel soft computing technique called complex neutrosophic relation (CNR) to evaluate the degree of interaction between two complex neutrosophic sets (CNSs). CNSs are used to represent two-dimensional information that are imprecise, uncertain, incomplete and indeterminate. The Cartesian product of CNSs and subsequently the complex neutrosophic relation is formally defined. This relation is generalised from a conventional single valued neutrosophic relation (SVNR), based on CNSs, where the ranges of values of CNR are extended to the unit circle in complex plane for its membership functions instead of [0, 1] as in the conventional SVNR. A new algorithm is created using a comparison matrix of the SVNR after mapping the complex membership functions from complex space to the real space. This algorithm is then applied to scrutinise the impact of some teaching strategies on the student performance and the time frame(phase) of the interaction between these two variables. The notion of inverse, complement and composition of CNRs along with some related theorems and properties are introduced. The performance and utility of the composition concept in real-life situations is also demonstrated. Then, we define the concepts of projection and cylindric extension for CNRs along with illustrative examples. Some interesting properties are also obtained. Finally, a comparison between different existing relations and CNR to show the ascendancy of our proposed CNR is provided. [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]

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]

In the definition of the complex neutrosophic soft expert set (CNSES), parameters set is a classical set, and the parameters have the same degree of importance, which is considered as 1. This poses a limitation in modeling of some problems. This paper introduces the concept of fuzzy parameterized complex neutrosophic soft expert set (FP-CNSES) to handle this issue by assigning a degree of importance to each of the problem parameters. We further develop FP-CNSES by establishing the concept of weighted fuzzy parameterized complex neutrosophic soft expert set (WFP-CNSES) based on the idea that each expert has a relative weight. These new mathematical frameworks reduce the chance of unfairness in the decision making process. Some essential operations with their properties and relevant laws related to the notion of FP-CNSES are defined and verified. The notation of mapping on fuzzy parameterized complex neutrosophic soft expert classes is defined and some properties of fuzzy parameterized complex neutrosophic soft expert images and inverse images was investigated. FP-CNSES is used to put forth an algorithm on decision-making by converting it from complex state to real state and subsequently provided the detailed decision steps. Then, we provide the comparison of FP-CNSES to the current methods to show the ascendancy of our proposed method. [ABSTRACT FROM AUTHOR]