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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]

This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the parameter set and the opinions of all experts in one model, thus making it highly suitable for use in decision-making problems where the time factor plays a key role in determining the final decision. The complex neutrosophic soft expert set and complex neutrosophic soft expert relation are both defined. Utilizing the properties of CNSER introduced, an empirical study is conducted on the relationship between the variability of the currency exchange rate and Malaysian exports and the time frame (phase) of the interaction between these two variables. This study is supported further by an algorithm to determine the type and the degree of this relationship. A comparison between different existing relations and CNSER to show the ascendancy of our proposed CNSER is provided. Then, the notion of the inverse, complement and composition of CNSERs along with some related theorems and properties are introduced. Finally, we define the symmetry, transitivity and reflexivity of CNSERs, as well as the equivalence relation and equivalence classes on CNSESs. Some interesting properties are also obtained. [ABSTRACT FROM AUTHOR]

This paper presents a novel complex neutrosophic soft expert set (CNSES) concept. The range of values of CNSES is extended to the unit circle in the complex plane by adding an additional term called the phase term which describes CNSES's elements in terms of the time aspect. CNSES is a hybrid structure of soft sets and single-valued neutrosophic sets (SVNSs) defined in a complex setting where the experts' opinions are included, thus making it highly suitable for use in decision-making problems that involve uncertain and indeterminate data where the time factor plays a key role in determining the final decision. Based on this new concept we define some concepts related to this notion as well as some basic operations namely the complement, union, intersection, AND and OR. The basic properties and relevant laws pertaining to this concept such as the De Morgan's laws are also verified. Lastly, we propose an algorithm to solve complex neutrosophic soft expert decision-making problem by converting it from the complex state to the real state and subsequently provided the detailed decision steps. This study is supported by the comparison with other existing methods. [ABSTRACT FROM AUTHOR]

Interval complex neutrosophic soft set (ICNSS) is the generalization of complex neutrosophic soft set (CNSS) as it provides an interval-based membership structure to handle the complex neutrosophic soft data. However, in the definition of the ICNSS, 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. Therefore, we introduce the concept of fuzzy parameterized interval complex neutrosophic soft set (FP-ICNSS) based on idea that each of elements of parameters set has got an importance degree. The basic theoretical operations and properties are defined and verified on FP-ICNSS. For FP-ICNSS, we conceptualize the relevant mapping and study the properties of the FP-ICNSS images and inverse images. Then, we propose a new algorithm that is applicable in the field of medical diagnosis and decision-making problems for selection right product. Moreover, an illustrative example is presented which depicts its validity for successful application to the problems involving vagueness and uncertainties. Eventually, a comparison between the proposed model and the existing methods is conducted to clarify the importance of this model. [ABSTRACT FROM AUTHOR]

Interval complex neutrosophic soft sets (I-CNSSs) refers to interval neutrosophic soft sets (I-NSSs) featuring three two-dimensional independent membership functions accordingly (falsity, indeterminacy, as well as uncertainty interval). A relation is a tool that helps in describing consistency and agreement between objects. Throughout this paper, we insert and discuss the interval complex neutrosophic soft relation (simply denoted by I-CNSR), a novel soft computing technique used to examine the interaction degree among corresponding models known as I-CNSSs. We present the definition of the Cartesian product of I-CNSSs followed by the definition of I-CNSR. Furthermore, the definitions and some theorems and properties related to the composition, inverse, and complement of I-CNSR are provided. The notions of symmetric, reflexive, transitive, and equivalent of I-CNSRs are proposed, and the algebraic properties of these concepts are verified. Furthermore, we demonstrate the relevance of our notion to real-world situations by offering a suggested method for solving a decision-making issue in the field of economics. Ultimately, an analysis is made between the current relationships and the proposed model to determine the model's significance. [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]