Neutrosophic Fuzzy Research Articles

A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment

In this paper, we advance the study of plithogenic hypersoft set (PHSS). We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These four PHSS classifications cover most of the fuzzy and neutrosophic cases that can have neutrosophic applications in symmetry. We also make explanations with an illustrative example for demonstrating these four classifications. We then propose a novel multi-criteria decision making (MCDM) method that is based on PHSS, as an extension of the technique for order preference by similarity to an ideal solution (TOPSIS). A number of real MCDM problems are complicated with uncertainty that require each selection criteria or attribute to be further subdivided into attribute values and all alternatives to be evaluated separately against each attribute value. The proposed PHSS-based TOPSIS can be used in order to solve these real MCDM problems that are precisely modeled by the concept of PHSS, in which each attribute value has a neutrosophic degree of appurtenance corresponding to each alternative under consideration, in the light of some given criteria. For a real application, a parking spot choice problem is solved by the proposed PHSS-based TOPSIS under fuzzy neutrosophic environment and it is validated by considering two different sets of alternatives along with a comparison with fuzzy TOPSIS in each case. The results are highly encouraging and a MATLAB code of the algorithm of PHSS-based TOPSIS is also complied in order to extend the scope of the work to analyze time series and in developing algorithms for graph theory, machine learning, pattern recognition, and artificial intelligence.

Partner selection in Virtual enterprises using the Interval Neutrosophic fuzzy approach

With the rapid development of the Internet, information technology, and globalization of the economy, Some small and medium-sized companies know that they cannot compete with their limited capacity alone. As a result, they are beginning to seek collaboration and a collective approach to meet the dynamic needs of customers and increase their power for competition in the market. Virtual enterprise is a temporary platform for working with different companies that share their core tasks to meet customer’s demand. Partner selection is a major issue in the formation of a virtual organization. This is especially difficult due to the uncertainties regarding information, market dynamics, customer expectations, and rapidly changing technology, with highly random decision making. As a generalization of fuzzy sets and intuitionistic fuzzy sets, Neutrosophic sets are created to show the uncertain, and inconsistent information available in the real world. The main purpose of this paper is to identify and select partners in the formation of Virtual Enterprises under uncertainty and contradictory factors using the extended VIKOR group decision making technique using the Interval Neutrosophic fuzzy approach. For this purpose, after identifying the factors affecting partner selection, the factors are weighted using the Maximizing deviation method and the partners are ranked using this method. Finally, a sensitivity analysis for assessing the validity of the method is also presented. The results show that the Willingness to share information criterion is the most important partner selection criterion in this enterprise.

Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.

Segmentation Algorithm Based on Neutrosophic Fuzzy C-Means Clustering and Its Application

Segmentation Algorithm Based on Neutrosophic Fuzzy C-Means Clustering and Its Application

Neutrosophic Ideal layers Some Generalizations for GIS Topological Rules

This paper aims to introduce and study some new neutrosophic fuzzy pairwise notions via neutrosophic fuzzy ideals. We, also generalize the notion of FPL-open sets. In addition to generalizing the concept of FPL-closed sets and NPL-open function, the relationship between the above new neutrosophic Fuzzy pairwise notions and there other relevant classes are investigated. In Geographical information systems (GIS) there is a need to statistically model spatial regions with indeterminate boundary and under indeterminacy. Possible applications to GIS rules are touched upon.

Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

In this paper, we present and study some of the basic properties of the new class of sets called weakly b-closed sets and weakly b- open sets in fuzzy neutrosophic bi-topological spaces. We referred to some results related to the new definitions, which we taked the case of equal in the definition of b-sets instead of subset. Then, we discussed the relations between the new defined sets by hand and others fuzzy neutrosophic sets which were studied before us on the other hand on fuzzy neutrosophic bi-topological spaces. Then, we have studied some of characteristics and some relations are compared with necessary examples.

Risk Factors of Lifestyle Diseases – Analysis by Decagonal Linguistic Neutrosophic Fuzzy Cognitive Map

Lifestyle (LS) diseases are the outcomes of undesirable customs incorporated by the upcoming generation. The people of developed and developing nations are battling to procrastinate the epoch of mortality caused by LS diseases. The change in one’s health state is characterized by the extensive role of the respective internal and external environment. Contemporary social structure, occupational scenario, behavioural change, and recklessness of dietetics altogether have yielded a shallow health. This study considers the predominant lifestyle diseases and its risk factors in comprehensive perspective. Decagonal Linguistic Neutrosophic Fuzzy cognitive map facilitates the representation of indeterminacy and linguistic representation between the risk factors. This research work aims in developing a new methodology to determine the impact of one risk factor over the other by alleviating the indeterminacy.

Bipolar Neutrosophic Dombi Aggregation Operators With Application in Multi-Attribute Decision Making Problems

In this paper, Dombi t-norm (TN) and Dombi t-conorm (TCN) are used to generate more complex, flexible and feasible operation rules by managing a parameter in bipolar neutrosophic fuzzy (BNF) environment. We introduce the notion of bipolar neutrosophic Dombi weighted geometric aggregation (BNDWGA) and bipolar neutrosophic Dombi ordered weighted geometric aggregation (BNDOWGA) operators. We discuss their different properties along with proofs and also investigate multi-attribute decision making (MADM) methods on basis of propose aggregation operators under bipolar neutrosophic fuzzy (BNF) environment. We propose an algorithm of selection of cultivating crop to explain the proposed methods under bipolar neutrosophic fuzzy (BNF) environment. The effect of parameter on our proposed bipolar neutrosophic Dombi aggregation operators are discussed graphically. Moreover, the comparison of our proposed methods with existing methods to test their suitable preferences are discussed in detail.

Decision-Making Method Based on Grey Relation Analysis and Trapezoidal Fuzzy Neutrosophic Numbers Under Double Incomplete Information and its Application in Typhoon Disaster Assessment

Multi-attribute decision-making problems under the trapezoidal fuzzy neutrosophic numbers environment are complex, particularly when the attribute value data are incomplete, and the attribute weight is completely unknown. As a solution, this study proposes a decision-making method based on information entropy and grey theory. First, regarding the problem of attribute value incompleteness in the decision matrix, a method of defining the missing information using trapezoidal fuzzy neutrosophic numbers is proposed, which is simpler and more reasonable than the traditional method of complements. Regarding the problem of completely unknown attribute weights, the definition of new trapezoidal fuzzy neutrosophic entropy is proposed and used to determine the attribute weight. Thereafter, the grey relation analysis method of grey theory is used to rank alternatives and select the best one. Finally, an illustrative example about typhoon disaster assessment is presented to show the feasibility and effectiveness of the proposed method. Finally, the advantages of the proposed method are illustrated by comparison with other methods from multiple aspects.

Generalized b Closed Sets and Generalized b Open Sets in Fuzzy Neutrosophic bi-Topological Spaces

Generalized b Closed Sets and Generalized b Open Sets in Fuzzy Neutrosophic bi-Topological Spaces

Neutrosophic Transportation Problems Using Zero Suffix Method

The aim of this paper is to propose a method for finding an optimal solution for Neutrosophic Fuzzy Transportation Problem (TP). Here, a new ranking approach to solve fuzzy Neutrosophic transportation problems under the approach of zero suffix method together with the scalar division of fuzzy numbers is introduced. The solution of the given problem which satisfies the conditions of optimality and feasibility by proposing the method together with scalar division and triangular ranking technique.

Adaptive Region Growing Image Segmentation Algorithms for Breast MRI

Early detection and characterization of breast lesion are important for a better and effective treatment of breast cancer. In this paper, four different adaptive region growing image segmentation algorithms are compared. In fact, seed selection was a vital step in the success of region growing methods, so, better schemes for seed selection methods are proposed, namely, joint probabilistic seed selection (JPSS) and Generalised simulated annealing (GSA) based seed selection. The proposed region growing methods namely Fuzzy Region Growing (FRG) and Neutrosophic Region Growing (NRG) are integrated as JPSS-FRG and GSA-NRG frameworks. Another two methods are Scale Invariant Region growing (SiRG) and Fuzzy Neutrosophic Confidence Region growing (FNCRG). The results showed that FNCRG algorithm increases breast cancer detection rate on MRI breast images with the maximum of 93% is achieved. SiRG algorithm improves the true positive rate by 13% compared to existing methods. Further, GSA-NRG makes better segmentation accuracy by 9% and true positive rate by 12%. Also, JPSS-FRG algorithm enhances segmentation accuracy by 24% and improving the true positive rate by 27% compared to Region Growing-Cellular Neural Network (RG-CNN) and Seeded Region Growing-Particle swarm optimization (SRG-PSO) methods respectively.

Triangular Fuzzy Neutrosophic Preference Relations and Their Application in Enterprise Resource Planning Software Selection

Enterprise resource planning (ERP) system selection is one of the most important topics in an ERP implementation program that ensures the success of the system. Because of the inherent complexity of ERP systems, it is difficult and time consuming for the organization to select the suitable ERP software. This paper employs triangular fuzzy neutrosophic preference relations (TFNPRs) to express the recognitions of decision-makers (DMs) for the choice of ERP software. Preference relation is a powerful tool to express complex decision problems, and the triangular fuzzy neutrosophic number (TFNN) is a good choice to represent the recognitions of the DMs; this paper combines preference relation with TFNN to define the concept of triangular fuzzy neutrosophic preference relations (TFNPRs). To rank the evaluated ERP systems logically, a multiplicative consistency concept for TFNPRs is defined. Then, several multiplicative consistency-based 0–1 mixed programming models are established for estimating missing values in incomplete TFNPRs and for deriving multiplicatively consistent TFNPRs from inconsistent ones, respectively. For group decision-making (GDM), a Manhattan distance measure-based consensus index is defined to measure the agreement degrees of the DMs’ opinions. A multiplicative consistency and consensus-based algorithm to GDM with TFNPRs is provided that can cope with incomplete and inconsistent TFNPRs. Meanwhile, an illustrative example about the selection of ERP software is offered to show the utilization of the new method, and comparison analysis is performed with several previous methods about ERP software selection. The new method adopts TFNPRs that can express the fuzzy truth-membership degree, the fuzzy indeterminacy-membership degree and the fuzzy falsity-membership degree of the recognitions of the DMs. It extends the application of preference relations and endows the DMs with more flexibility to denote their recognitions. Furthermore, the new method is based on the multiplicative consistency and consensus analysis that ensures the rational and representative ranking of the considered objects.

Uncertainty Aware Resource Provisioning Framework for Cloud Using Expected 3-SARSA Learning Agent: NSS and FNSS Based Approach

Abstract Efficiently provisioning the resources in a large computing domain like cloud is challenging due to uncertainty in resource demands and computation ability of the cloud resources. Inefficient provisioning of the resources leads to several issues in terms of the drop in Quality of Service (QoS), violation of Service Level Agreement (SLA), over-provisioning of resources, under-provisioning of resources and so on. The main objective of the paper is to formulate optimal resource provisioning policies by efficiently handling the uncertainties in the jobs and resources with the application of Neutrosophic Soft-Set (NSS) and Fuzzy Neutrosophic Soft-Set (FNSS). The performance of the proposed work compared to the existing fuzzy auto scaling work achieves the throughput of 80% with the learning rate of 75% on homogeneous and heterogeneous workloads by considering the RUBiS, RUBBoS, and Olio benchmark applications.

Modeling the Performance Indicators of Financial Assets with Neutrosophic Fuzzy Numbers

This research sets the basis for modeling the performance indicators of financial assets using triangular neutrosophic fuzzy numbers. This type of number allows for the modeling of financial assets performance indicators by taking into consideration all the possible scenarios of their achievement. The key performance indicators (KPIs) modeled with the help of triangular fuzzy neutrosophic numbers are the return on financial assets, the financial assets risk, and the covariance between financial assets. Thus far, the return on financial assets has been studied using statistical indicators, like the arithmetic and geometric mean, or using the financial risk indicators with the help of the squared deviations from the mean and covariance. These indicators are well known as the basis of portfolio theory. This paper opens the perspective of modeling these three mentioned statistical indicators using triangular neutrosophic fuzzy numbers due to the major advantages they have. The first advantage of the neutrosophic approach is that it includes three possible symmetric scenarios of the KPIs achievement, namely the scenario of certainty, the scenario of non-realization, and the scenario of indecision, in which it cannot be appreciated whether the performance indicators are or are not achieved. The second big advantage is its data series clustering, representing the financial performance indicators by which these scenarios can be delimitated by means of neutrosophic fuzzy numbers in very good, good or weak performance indicators. This clustering is realized by means of the linguistic criteria and measuring the belonging degree to a class of indicators using fuzzy membership functions. The third major advantage is the selection of risk mitigation analysis scenarios and the formation of financial assets’ optimal portfolios.

An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers

An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers

Fuzzy Neutrosophic Weakly-Generalized Closed Sets in Fuzzy Neutrosophic Topological Spaces

Fuzzy Neutrosophic Weakly-Generalized Closed Sets in Fuzzy Neutrosophic Topological Spaces

A New Failure-Censored Reliability Test Using Neutrosophic Statistical Interval Method

The failure-censored reliability tests available in the literature are applied when under the assumption that all failure data/observations are precise, clear and determinate. But, in practice, when the variable failure data/observations obtained from the measurement process are not precise, clear and determinate, the failure-censored reliability tests using classical statistics cannot be applied for the reliability testing. A more generalized form of the classical statistics is known as neutrosophic statistics which can be applied when the measurable failure data/observations are indeterminate, unclear, incomplete and vague. In this manuscript, we will originally design failure-censored reliability tests using the neutrosophic fuzzy approach. The neutrosophic plan parameters of the proposed neutrosophic fuzzy failure-censored reliability plan assume that the failure time follows the neutrosophic Weibull distribution. The neutrosophic fuzzy optimization problem is used to determine the neutrosophic plan parameters for given producer’s risk and consumer’s risk. Some tables are given for the practical use and exampled with the help of an example.