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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]

In this paper, we first introduce the concept of neutrosophic vague soft expert sets (NVSESs for short) which combines neutrosophic vague sets and soft expert sets to be more effective and useful. We also define its basic operations, namely complement, union, intersection, AND and OR along with illustrative examples, and study some related properties with supporting proofs. Lastly, this concept is applied to a decision making problem and its effectiveness is demonstrated using a hypothetical example. [ABSTRACT FROM AUTHOR]

A Q-neutrosophic soft environment is an innovative hybrid tool that combines features of both a Q-neutrosophic set (Q-NS) and a parametric tool "soft set" (SS) in order to manage imprecise and indeterminate situations in various mathematical problems. In this article, we introduce a new algebraic approach called Q-neutrosophic soft matrices (Q-NSMs) to address the issues of two-dimensional (two variables) in a universal set by representing the concept of Q-neutrosophic soft sets (Q-NSSs) in matrices. On Q-NSMs, we define the fundamental set operations and some algebraic operations, i.e., complement, union, intersection, addition, subtraction, multiplication, and scalar multiplication, and prove related properties of these operations. Moreover, these operations are illustrated via several numerical examples. Then, two algorithms are proposed to tackle group decision making (GDM) problems: The first depends on the score function of Q-NSMs, and the second is based on the aggregation operator of Q-NSMs. Finally, this study is supported by a brief comparison with some relevant previous models. [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]

Introduction: The soft set theory has drawn the attention of many researchers, particularly for dealing with uncertainty in decision-making problems. Despite its remarkable advantages, the soft set theory has only been used to tackle decision-making problems that aim to choose the best option. However, there exist different forms of decision-making problems that involve different forms of uncertainty. Methods: In this study, we present various algorithms based on the soft set theory in order to handle the cases where one has different uncertainty forms in decision-making problems. Some new concepts such as object code, personal object code, parameter significance weight and new distance measures have been introduced to the literature for the construction of these algorithms. Furthermore, we show the application results of those algorithms and provide several examples. Results and Conclusions: As a result, a comparison among the application results of the algorithms implies that the best objects might not always yield the most efficient outcomes. [ABSTRACT FROM AUTHOR]