Complex Neutrosophic Set Research Articles

A soft set based VIKOR approach for some decision-making problems under complex neutrosophic environment

Applications in various fields of neutrosophic soft set theory enhance its appreciation to the researchers. Although, this uncertain solving tool can accomplish several types of real-life problems, but not able to deal with the decision-making problems in which considering an additional information of a corresponding parameter is needed to get a proper decision from a problem. But, complex neutrosophic soft sets can handle such type of decision-making problems. Consequently, in this study, we have given concentration on solving soft set based decision-making problems in the field of complex neutrosophic environment. Firstly, we have introduced some basic set-theoretic operations of complex neutrosophic sets including different types of unions, intersections and aggregations. Then, a new definition of score function of a complex neutrosophic number has been proposed. Additionally, the above-defined unions and intersections of complex neutrosophic sets have been stated for complex neutrosophic soft sets. Finally, by utilizing these proposed notions, we have offered a complex neutrosophic soft VIKOR approach to get a compromise optimal solution for single as well as multiple decision-maker based problems. Our proposed approach has been clarified by several real life-related problems including medical diagnosis problem, sustainable manufacturing material selection problem, company’s manager selection problem, etc. The feasibility and effectiveness of our proposed approach have also been included in the article.

Complex Neutrosophic Hypergraphs: New Social Network Models

A complex neutrosophic set is a useful model to handle indeterminate situations with a periodic nature. This is characterized by truth, indeterminacy, and falsity degrees which are the combination of real-valued amplitude terms and complex-valued phase terms. Hypergraphs are objects that enable us to dig out invisible connections between the underlying structures of complex systems such as those leading to sustainable development. In this paper, we apply the most fruitful concept of complex neutrosophic sets to theory of hypergraphs. We define complex neutrosophic hypergraphs and discuss their certain properties including lower truncation, upper truncation, and transition levels. Furthermore, we define T-related complex neutrosophic hypergraphs and properties of minimal transversals of complex neutrosophic hypergraphs. Finally, we represent the modeling of certain social networks with intersecting communities through the score functions and choice values of complex neutrosophic hypergraphs. We also give a brief comparison of our proposed model with other existing models.

RETRACTED ARTICLE: Extentions of neutrosophic cubic sets via complex fuzzy sets with application

In this paper, we propose that the complex neutrosophic cubic set (internal and external) show, which is a blend of complex fuzzy sets, neutrosophic sets, and cubic sets. We characterize a few set theoretic activities of internal complex neutrosophic sets, for example, union, intersection and complement, and a while later the operational principles. A few ideas identified with the structure of this model are clarified. We present some accumulation administrators and talk about some basic leadership issue with genuine model.

Relations between the Complex Neutrosophic Sets with Their Applications in Decision Making

Relations between the Complex Neutrosophic Sets with Their Applications in Decision Making

An application of complex neutrosophic sets to the theory of groups

An application of complex neutrosophic sets to the theory of groups

Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making

Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making

Some Results on the Graph Theory for Complex Neutrosophic Sets

Some Results on the Graph Theory for Complex Neutrosophic Sets

Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making

One of the most efficient tools for modeling uncertainty in decision-making problems is the neutrosophic set (NS) and its extensions, such as complex NS (CNS), interval NS (INS), and interval complex NS (ICNS). Linguistic variables have been long recognized as a useful tool in decision-making problems for solving the problem of crisp neutrosophic membership degree. In this paper, we aim to introduce new concepts: single-valued linguistic complex neutrosophic set (SVLCNS-2) and interval linguistic complex neutrosophic set (ILCNS-2) that are more applicable and adjustable to real-world implementation than those of their previous counterparts. Some set-theoretic operations and the operational rules of SVLCNS-2 and ILCNS-2 are designed. Then, gather classifications of the candidate versus criteria, gather the significance weights, gather the weighted rankings of candidates versus criteria and a score function to arrange the candidates are determined. New TOPSIS decision-making procedures in SVLCNS-2 and ICNS-2 are presented and applied to lecturer selection in the case study of the University of Economics and Business, Vietnam National University. The applications demonstrate the usefulness and efficiency of the proposal.

An application of complex neutrosophic sets to the theory of groups

In this article we introduce the concept of complex neutrosophıc subgroups (normal subgroups). We define the notion of alpha-cut of complex neutrosophıc set, give examples and study some of its related results. We also define the Cartesian product of complex neutrosophic subgroups. Furthermore, we introduce the concept of image and preimage of complex neutrosophic set and prove some of its properties.

Relations between the Complex Neutrosophic Sets with Their Applications in Decision Making

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.

Some Results on the Graph Theory for Complex Neutrosophic Sets

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept.

Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making

Neutrosophic set is a powerful general formal framework which generalizes the concepts of classic set,fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set,etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications.

Some Results on the Graph Theory for Complex Neutrosophic Sets

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1) and generalized single-valued neutrosophic graphs of type 1 (GSVNG1). The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection.

Complex neutrosophic concept lattice and its applications to air quality analysis

In the current year, the precise measurement of uncertainty and fluctuation exists in a complex fuzzy attributes is addressed as computationally and mathematically expensive tasks with regard to its graphical analytics. To deal with this problem the calculus of complex neutrosophic sets are recently introduced to characterize the uncertainty and its changes based on its truth, indeterminacy, and falsity membership–value, independently. This given a way to represent the given data sets in form of complex neutrosophic matrix for further analysis towards knowledge processing tasks. In this process, a major problem arises when an expert wants to find some of the interesting patterns in the given complex neutrosophic data sets to solve the particular problem. To resolve this issue, the current paper proposes a method for step by step demonstration to investigate the complex neutrosophic concepts and their graphical structure visualization based on their Lower Neighbors. One of the suitable examples of the proposed method is also given for precise measurement of uncertainty exists in Air Quality Index (AQI) and its pattern at given phase of time.

Complex Neutrosophic Subsemigroups and Ideals

In this article we study the idea of complex neutrosophic subsemigroups. We define the Cartesian product of complex neutrosophic subsemigroups, give some examples and study some of its related results. We also define complex neutrosophic (left, right, interior) ideal in semigroup. Furthermore, we introduce the concept of characteristic function of complex neutrosophic sets, direct product of complex neutrosophic sets and study some results prove on its.

Analysis of Handwritten Text Recognition System using EDAS Method

The recognition of sloppy handwriting for Using hybrid Hidden Markov Model (HMM)/Artificial Neural Network (ANN) models This article proposes that Text Recognition System. A single-valued complex neutrosophic EDAS (estimation based on distance from average temptation) model was established and used in green supplier selection. First, the definition and relatedness of a single-valued complex neutrosophic set Functional laws are briefly introduced. The handwritten text recognition system, Integration of Fuzzy AHP and Estimation Based on Distance from Average Solution (EDAS) presented a new unified model, in which Fuzzy AHP is used to calculate the priority weight of each criterion and is EDAS. Handwritten Text Recognition System was used to arrive at the final ranking. The alternatives are B-HTR, LM-HTR, ALIGN-HTR, HMM, EMAC, LSTM, MDLSTM, BLSTM and GMM. Evaluation parameter is WER and CER. The Handwritten Text Recognition System using EDAS method final result is given to by first rank is EMAC and LSTM is lowest rank.

Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making

Neutrosophic set is a powerful general formal framework which generalizes the concepts of classic set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications. The single-valued complex neutrosophic set, which is an extended form of the single-valued complex fuzzy set and of the single-valued complex intuitionistic fuzzy set, presents difficulties to defining a crisp neutrosophic membership degree as in the single-valued neutrosophic set. Therefore, in this paper we propose a new notion, called interval complex neutrosophic set (ICNS), and examine its characteristics. Firstly, we define several set theoretic operations of ICNS, such as union, intersection and complement, and afterward the operational rules. Next, a decision-making procedure in ICNS and its applications to a green supplier selection are investigated. Numerical examples based on real dataset of Thuan Yen JSC, which is a small-size trading service and transportation company, illustrate the efficiency and the applicability of our approach.

Complex neutrosophic set

Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and ź-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.