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Hypersoft sets (HSSs) have gained popularity because of their ability to formulate data in the form of several trait-valued disjoint sets that blend various traits. Motivated by this idea, in this study, we present a new hyper-approach referred to as bipolar neutrosophic hypersoft sets (BNHSSs) by a generalization of neutro-sophic hypersoft sets (NHSSs) and bipolar fuzzy hypersoft sets (BFHSSs) or by merging and subjecting both HSSs and neutrosophic sets (NSs) to a bipolarity property of real numbers. By utilizing positive and negative neutrosophic structures, we construct different notions and operations on the basis of BNHSSs, such as an absolute BNHSS, a null BNHSS, a complement, subset-hood, a restricted and extended union, and a restricted and extended intersection, along with their related properties. Also, some operations like OR and AND on BNHSS have been initiated. In addition, some properties are displayed paired together, and some numerical hypothetical examples are given to clarify the mechanism of using these instruments. Finally, to prove the efficiency and applicability of the proposed model, we established two novel algorithms based on mathematical techniques (aggregation operator and score function) applied to our model (BNHSS). The aforementioned meth-ods have been utilized in the resolution of a multi-attribute group decision-making (MAGDM) problem. Some discussions and comparisons between the given techniques are also presented to demonstrate their effectiveness and applicability. [ABSTRACT FROM AUTHOR]

The idea of an interval complex neutrosophic soft set (I-CNSS) emerges from the interval neutrosophic soft set (I-NSS) by the extension of its three membership functions (T, I, F) from real space to complex space (unit disc) to better handle uncertainties, vagueness, indeterminacy, and imprecision of information in the periodic nature. The novelty of I-CNSS lies in its more significant range of activity compared to CNS. Measures of similarity and distance are important tools that can be used to solve many problems in real life. Hence, this paper presents some interval complex neutrosophic soft similarities based on Hamming and Euclidean distances of I-CNSSs to deal with real-life problems that include uncertain information such as decision-making issues and medical diagnosis stats. Firstly, this paper reviews the definition of an interval complex neutrosophic soft set. Secondly, we defined distance Hamming measures and distance Euclidean measures on I-CNSSs. Next, the axiomatic definition of similarity measures based on Hamming and Euclidean distances of I-CNSSs is proposed. Moreover, a numerical example is given and relations between these measures are introduced and verified. Meanwhile, some applications are given to show how similarity can be used to help the user in making decisions and making medical diagnoses. Finally, a comparison of some current approaches is used to back up this study. [ABSTRACT FROM AUTHOR]

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 this paper, the notion of the interval valued complex neutrosophic soft set (IV-CNSS) is defined as a combination of interval valued complex neutrosophic set and soft set. Then, we introduce the IV-CNSS's operations such as union, intersection and complement. To explore the study further, we present some basic operational rules, and investigate their properties. A new algorithm is developed by transforming the interval complex neutrosophic soft values from complex space to the real space using a practical formula which gives a decision-making with a simple computational process without the need to carry out directed operations by complex numbers. This algorithm is then applied to evaluate two kinds of a certain product from a manufacturer and choose the most suitable one. IV-CNSS provides an interval-based membership structure to handle the uncertain data. This feature allows decision makers to record their hesitancy in assigning membership values which in turn best catch the obscurity and the complexity of such data. [ABSTRACT FROM AUTHOR]

The notion of classical soft multisets is extended to neutrosophic vague soft multisets by applying the theory of soft multisets to neutrosophic vague sets to be more effective and useful. We also define its basic operations, namely complement, subset, union, intersection along with illustrative examples, and study some related properties with supporting proofs. Lastly, this notion is applied to a decision making problem and its effectiveness is demonstrated using an illustrative example. [ABSTRACT FROM AUTHOR]

To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided. [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]