Neutrosophic Soft Sets Research Articles

An Integrated Algorithmic MADM Approach for Heart Diseases' Diagnosis Based on Neutrosophic Hypersoft Set with Possibility Degree-Based Setting.

The possibility neutrosophic hypersoft set (pNHs-set) is a generalized version of the possibility neutrosophic soft set (pNs-set). It tackles the limitations of the pNs-set regarding the use of the multi-argument approximate function. This function maps sub-parametric tuples to a power set of the universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. This makes the decision-making process more flexible and reliable. In this study, after characterizing some elementary notions and algebraic operations of the pNHs-set, Sanchez’s method (a classical approach for medical diagnosis) is modified under the pNHs-set environment. A modified algorithm is proposed for the medical diagnosis of heart diseases by integrating the concept of the pNHs-set and the modified Sanchez’s method. The authenticity of the proposed algorithm is evaluated through its implementation in a real-world scenario with real data from the Cleveland data set for heart diseases. The beneficial aspects of the proposed approach are evaluated through a structural comparison with some pertinent existing approaches.

Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem

Molodtsov introduced a soft set (SS) to model uncertainty parametrically, and Chaterjee et al. proposed the notion of quadripartitioned neutrosophic set (QNS) by dividing indeterminacy into two independent components, namely contradiction (C) and unknown (U). Afterwards, by combining the SS and QNS, a new concept known as quadripartitioned neutrosophic soft set (QNSS) is introduced. In relation to the concept of QNSS, another concept called interval-valued intuitionistic quadripartitioned neutrosophic soft set (in short IVIQNSS) is established to handle more complex indeterminate information parametrically with the restricted conditions. This paper aims to further generalize the existing soft models by introducing an IVIQNSS to explore another kind of imprecise knowledge. The IVIQNSS model can be viewed as a more flexible and powerful framework to encounter indeterminacy parametrically with T,F,C, and U as dependent interval quadripartitioned neutrosophic components where T,F,C,U⊆[0,1] such that sup⁡T+sup⁡F≤1, and sup⁡C+sup⁡U≤1. So, by using the IVIQNSS framework we are capable to address the indeterminate, inconsistent, and incomplete information more accurately. Different operations such as complement, AND, OR, union, intersection, etc. are defined on IVIQNSSs. Furthermore, an algorithm is constructed to solve decision-making (DM) problems based on IVIQNSS. Finally, an illustrative example is executed to validate the proposed study.

The Sequence of Neutrosophic Soft Sets and a Decision-Making Problem in Medical Diagnosis

The Sequence of Neutrosophic Soft Sets and a Decision-Making Problem in Medical Diagnosis

Fuzzy Quadripartitioned Neutrosophic Soft Matrix Theory and Its Decision-Making Approach

Earlier several fuzzy oriented matrix theories have been proposed by the researchers to model uncertainty for real-world decision-making (DM). Among them, fuzzy neutrosophic soft matrix (FNSM) theory has been developed recently by combining the fuzzy neutrosophic set and soft set to handle the indeterminate information parametrically. The main purpose to represent this paper is to introduce the notion of fuzzy quadripartitioned neutrosophic soft matrix (FQNSM) theory to generalize the FNSM concept. Moreover, several properties and matrix operations on fuzzy quadripartitioned neutrosophic soft sets are investigated with appropriate examples. Finally, a DM model based on FQNSMs has been developed and thus validated by showing an application to real problems.

Interval-Valued Neutrosophic Soft Expert Set from Real Space to Complex Space

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation. In the decision-making process, fuzzy system and soft computing are effective tools that are tolerant to imprecision, uncertainty, and partial truths. Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy, dual fuzzy, hesitant fuzzy, neutrosophic, plithogenic representations, etc. Moreover, by capturing compound features and convey multi-dimensional data, complex numbers are utilized to generalize fuzzy and neutrosophic fuzzy sets. In this paper, a representation of neutrosophic soft expert systems based on the real and complex numbers in the interval form is proposed. The interval-valued neutrosophic soft expert set (I-VNSES) is defined, and the interval-valued complex neutrosophic soft expert set (I-VCNSES) is formally generalized from the concept of I-VNSES. For both I-VNSES and I-VCNSES, we introduce the relevant basic theoretical operations and study their properties. Based on these new concepts, a generalized algorithm is proposed and applied to handle the imbedded indeterminacy in the two-dimensional interval data. The proposed algorithm is tested on the economic factors that affected the Malaysian economy in 2020 to see which ones are the most influential. Eventually, a comparison of three current approaches is used to back up this study.

A new approach for operations on neutrosophic soft sets based on the novel norms for constructing topological structures

<abstract> <p>Neutrosophic sets have recently emerged as a tool for dealing with imprecise, indeterminate, inconsistent data, while soft sets may have the potential to deal with uncertainties that classical methods cannot control. Combining these two types of sets results in a unique hybrid structure, a neutrosophic soft set (NS-set), for working effectively in uncertain environments. This paper focuses on determining operations on NS-sets through two novel norms. Accordingly, the $ {\rm{min}}-{\rm{n}}{\rm{o}}{\rm{r}}{\rm{m}} $ and $ {\rm{max}}-{\rm{n}}{\rm{o}}{\rm{r}}{\rm{m}} $ are well-defined here for the first time to construct the intersection, union, difference, AND, OR operations. Then, the topology, open set, closed set, interior, closure, regularity concepts on NS-sets are introduced based on these just constructed operations. All the properties in the paper are stated in theorem form, which is proved convincingly and logically. In addition, we also elucidate the relationship between the topology on NS-sets and the fuzzy soft topologies generated by the truth, indeterminacy, falsity degrees by theorems and counterexamples.</p> </abstract>

Agriculture Production Decision Making using Generalized q-Rung Neutrosophic Soft Set Method

This paper introduces the generalized q-rung neutrosophic soft set (GqRNSSS) theory and its use to solve actual problems. We also define a few operations that make use of the GqRNSSS. The GqRNSSS is constructed by generalizing both the Pythagorean neutrosophic soft set (PyNSSS) and Pythagorean fuzzy soft set (PyFSS). We give a method for agricultural output that is based on the proposed similarity measure of GqRNSSS. If two GqRNSSS are compared, it can be determined whether or not a person produces good agricultural output. We support a strategy for dealing with the decision-making (DM) problem that makes use of the generalized qrung soft set model. In this article, we discuss the application of a similarity measure between two GqRNSSS in agricultural output. Show how they can be successfully applied to challenges with uncertainty.

Review of Generalized Neutrosophic Soft Set in Solving Multiple Expert Decision Making Problems

To manage issues with incompleteness, indeterminacy, and awareness of inconsistent information, Maji presented the idea of a neutrosophic soft set by merging the ideas of a neutrosophic set and a soft set. The generalized neutrosophic soft set (GNSS) is an extension of this idea, which has now been developed further. At the beginning of this paper, we describe the definition of a generalized neutrosophic soft set. Then, we focus on the concepts of GNSS operations, such as AND, OR, complement, intersection, and union, and provide illustrated examples to describe a number of associated properties. Finally, a description of an algorithm and an application that uses GNSS to address challenges that arise when making decisions that need the experience of more than one specialist is offered here.

Methods to find strength of job competition among candidates under single-valued neutrosophic soft model.

Neutrosophic soft set theory is one of the most developed interdisciplinary research areas, with multiple applications in various fields such as computational intelligence, applied mathematics, social networks, and decision science. In this research article, we introduce the powerful framework of single-valued neutrosophic soft competition graphs by integrating the powerful technique of single-valued neutrosophic soft set with competition graph. For dealing with different levels of competitive relationships among objects in the presence of parametrization, the novel concepts are defined which include single-valued neutrosophic soft k-competition graphs and p-competition single-valued neutrosophic soft graphs. Several energetic consequences are presented to obtain strong edges of the above-referred graphs. The significance of these novel concepts is investigated through application in professional competition and also an algorithm is developed to address this decision-making problem.

Time Q-Neutrosophic Soft Expert Set

This paper is a combination of time neutrosophic soft sets and Q- neutrosophic soft expert sets. We define the general concept of time Q-neutrosophic soft expert sets and study its properties. Some operations such as complement, union, and intersection are explored. Then a hypothetical application of this concept in the decision-making problem is given.

Heptapartitioned neutrosophic soft set

The aim of this paper is to introduce the concept of heptapartitioned neutrosophic soft set and to study some of its basic properties. This kind of set can be considered as a significant extension of the idea of neutrosophic set. In general, our research is based on the earlier study presented by Radha and Stanis Arul Mary in 2021. However, we combine their initial definition with the inspiring notion of soft set (which has been established by Molodtsov in 1999). We examine algebraic operations on our sets. Then we show that the particular choose of exactly seven neutrosophic logical values has an interesting interpretation in terms of ancient Jaina logic (which has been developed centuries ago in India to deal with imprecise knowledge and the matter of paraconsistency). Moreover, we exhibit some other potential practical applications of our theoretical concept. For example, it can be applied in widely understood social sciences.

A new approach to neutrosophic soft set minimal structure spaces

This chapter is an introduction of neutrosophic soft set minimal structure space and addresses properties of neutrosophic soft set minimal structure space. Neutrosophic set has plenty of applications. Moreover, we introduced neutrosophic soft set minimal closed set , neutrosophic soft set minimal open set, neutrosophic soft set minimal interior of (Fe, E), neutrosophic soft set minimal closure of (Fe, E), NSSm(Fe, E)-continuous, NSSm(Fe, E)-T0, NSSm(Fe, E)-T1, NSSm(Fe, E)-T2, NSSm(Fe, E)-compact, almost NSSm(Fe, E)-compact. We also present some of their basic properties.

Mapping on Interval Complex Neutrosophic Soft Sets

The neutrosophic idea is a fertile environment adaptable to different mathematical tools. This paper aims to introduce the mapping of complex interval neutrosophic soft sets (MI-CNSSs). Further, the images and inverse images of complex interval neutrosophic soft sets and their properties are explored. These will be supported by concrete examples, and this paper will present some theorems about complex interval neutrosophic soft images and inverse images.

A look at soft neutrosophic spaces

In this article, new definition of neutrosophic soft ** b-open set is introduced with the help of neutrosophic soft α-open set and neutrosophic soft β-open set. With the application of this new definition some neutrosophic soft separation axioms and neutrosophic soft other separation axioms are addressed with respect to soft points of the spaces. Suitable examples are provided for the clarification of different results. Soft countability results and its engagements with different other neutrosophic soft results are studied. In continuation, characterization of Bolzano Weirstrass Property with respect to neutrosophic soft results and neutrosophic soft compactness results are inaugurated.

Similarity Measure for m-Polar Interval Valued Neutrosophic Soft Set with Application for Medical Diagnoses

Similarity Measure for m-Polar Interval Valued Neutrosophic Soft Set with Application for Medical Diagnoses

Complex Bipolar- Valued Neutrosophic Soft Set and its Decision Making Method

Complex Bipolar- Valued Neutrosophic Soft Set and its Decision Making Method

Impact of Complex Interval Neutrosophic Soft Set Theory in Decision making By Using Aggregate Operator

The main purpose of the paper is to introduce the notion of complex interval neutrosophic soft set (CIVNSS) theory, which is the generalization of the soft set, fuzzy soft set, interval-valued fuzzy soft set, interval neutrosophic soft set, etc. to describe the uncertain time-periodic phenomena in the form of an interval. After that, some important properties, and operations on CIVNSSs have been discussed. Also, we study the similarity measures on CIVNSSs. Then, an algorithm has been constructed by using the CIVNSS aggregate operator. Finally, to show the impact of CIVNSS in solving real decision-making problems, an example, whichis suitable to the current theory, is chosen, which ensures the effectiveness of the proposed theory in group decision-making problem.

Complex Neutrosophic Soft Matrices Framework: An Application in Signal Processing

In this paper, we introduce the concept of complex neutrosophic soft matrices. We define some basic operations including complement, union, and intersection on these matrices. We extend the concept of complex neutrosophic soft sets to complex neutrosophic soft matrices and prove related properties. Moreover, we develop an algorithm using complex neutrosophic soft matrices and apply it in signal processing.

On the neutrosophic soft set with rough set theory.

Rough set is a very powerful invention to the whole world for dealing with uncertain, incomplete and imprecise problems. Also soft set theory and neutrosophic set theory are advance mathematical tools to handle these uncertain, incomplete, inconsistent information in a better way. The purpose of this article is to expand the scope of rough set, soft set and neutrosophic set theory. We have introduced the concept of neutrosophic soft set with roughness without using full soft set. Some definitions, properties and examples have been established on neutrosophic soft rough set. Moreover, dispensable and equalities are written on roughness with neutrosophic soft set.

Application of interval-valued neutrosophic soft sets in decision making based on game theory

Application of interval-valued neutrosophic soft sets in decision making based on game theory