Trapezoidal Neutrosophic Numbers Research Articles

Neutrosophic data envelopment analysis based on parametric ranking method

The use of fuzzy numbers and their extensions, especially neutrosophic fuzzy numbers, is inevitable to express the value of the parameters of optimization problems derived from the real world. In this regard, the comparison and ranking of neutrosophic fuzzy numbers as one of the main research topics that can provide a suitable decision to solve optimization problems is of interest to researchers. In this study, we introduce a parametric approach to rank single value trapezoidal neutrosophic numbers which are based on decision–maker aspiration level for degree of the truth membership function and selecting appropriate levels for non-indeterminacy and non-falsity–membership functions. A prominent feature of this method is its high flexibility, which is due to the consideration of acceptable levels for evaluation by the decision maker. Therefore, in most decision issues, it can be used to determine the preferred option. Also, some theorems and reasonable properties are given to demonstrate the effectiveness of our proposed parametric approach. Furthermore, in an example of data envelopment analysis model with neutrosophic information the validity and applicability of the suggested method are examined.

Applied Linguistics Driven Deceptive Content Recognition using Single Valued Trapezoidal Neutrosophic Number with Natural Language Processing

Single valued neutrosophic number is a special case of single valued neutrosophic set and are of importance for neutrosophic multi-attribute decision making problem. A single valued neutrosophic number seems to define an ill-known quantity as a generalization of intuitionistic number. Applied linguistics in the context of Natural Language Processing (NLP) comprises the practical applications of linguistic approaches for addressing real time language processing issues. Social media become indispensable components in many people’s lives and have been growing rapidly. In the meantime, social networking media have become a widespread source of identity deception. Several social media identity deception cases have appeared presently. The research was performed to detect and prevent deception. Identifying deceptive content in natural language is significant to combat misrepresentation. Leveraging forward-thinking NLP methods, our model contextual cues analyze linguistic patterns, and semantic inconsistencies to flag possibly deceptive contents. By assimilating complex procedures for parameter optimization, feature extraction, and classification, the NLP focused on precisely recognizing deceptive content through different digital platforms, which contributes to the preservation of data integrity and the promotion of digital literacy. This study presents a Single Valued Trapezoidal Neutrosophic Number with Natural Language Processing for Deceptive Content Recognition (STVNNLP-DCR) technique on Social Media. The presented technique includes four important elements: preprocessing, GloVe word embedding, STVN classification, and Chicken Swarm Optimization (CSO) for parameter tuning. The preprocessing stage includes tokenization and text normalization, preparing text information for succeeding analysis. Then, GloVe word embedding represents the word in a continuous vector space, which captures contextual relationships and semantic similarities. The STVN classifier deploys the embedding to discern deceptive patterns within the text, leveraging its capability to effectively manage high-dimensional and sparse datasets. Moreover, the CSO technique enhances the hyperparameter of the STVN classifier, improving its generalization capabilities and performance. Empirical analysis implemented on varied datasets validates the efficacy of the presented technique in precisely recognizing deceptive content. Comparative studies with advanced approaches demonstrate high efficiency. The presented technique shows robustness against different forms of deceptive content, such as clickbait, misinformation, and propaganda

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems

This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology.

Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Modified approaches to solve matrix games with payoffs of single-valued trapezoidal neutrosophic numbers

Trapezoidal neutrosophic assignment problem with new interval arithmetic costs

Due to present condition, the expenses of allocating a job to a specific person or scheduling transport with a precise value may result in ambiguity. To deal with this, neutrosophic sets which is an extended form of fuzzy sets, appear alongside membership, non-membership and indeterminacy. The assignment problem in a trapezoidal neutrosophic environment with cost as the trapezoidal neutrosophic numbers is discussed in this work. The paper’s motive is to convert the trapezoidal neutrosophic numbers into new interval arithmetic form and the efficiency of the same is shown by comparing the existing method with other assignment models using examples.

Inventory model involving reworking of faulty products with three carbon policies under neutrosophic environment

The increasing in industry as well as usage of vehicles for transporting products generate many problems to the environment such as greenhouse gas emission and global warming. As nowadays environmental pollution has become a crucial problem, production companies have now shifted their attention to lower the carbon emission level along with their financial goal. In reality, the values of some parameters such as production cost, holding cost, demand rate, deterioration rate may not fixed due to several factors. Reworking of defective products reduces production cost. This study aims at developing a multi-objective supply chain inventory management by considering deteriorating products together with imperfect quality production under neutrosophic environment. Several carbon reduction policies such as carbon tax, carbon cap-and-trade and carbon cap-and-offset and green technology are implemented here to mitigate the influence of carbon emission by curbing amount of carbon emission. To reduce the deterioration rate, preservation technology is utilized. In real-world situations, all parameters related to an inventory management are not handled as a crisp value, a fuzzy number or an intuitionistic fuzzy number. To confrontation this issue, single valued trapezoidal neutrosophic number is chosen for investigating this type of an inventory problem. A ranking approach is designed to transform all uncertain parameters into deterministic values. A comparison between two types of reworking processes, and a comparison among crisp, intuitionistic fuzzy and neutrosophic models are drawn. A sensitivity analysis regarding important parameters is also taken into consideration to accentual managerial intuitions.

A novel method for solving neutrosophic data envelopment analysis models based on single-valued trapezoidal neutrosophic numbers

A novel method for solving neutrosophic data envelopment analysis models based on single-valued trapezoidal neutrosophic numbers

A risk assessment framework using neutrosophic theory for the halal supply chain under an uncertain environment

PurposeThe complex network structure causes several disruptions in the supply chain that make risk management essential for supply chain management including halal supply chain (HSM). During risk management, several challenges are associated with the risk assessment phase, such as incomplete and uncertain information about the system. To cater this, the authors propose a risk assessment framework that addresses the issues of uncertainty using neutrosophic theory and demonstrated the applicability of the proposed framework through the case of halal supply chain management (HSCM).Design/methodology/approachThe proposed framework is using the capabilities of the neutrosophic number which can handle uncertain, vague and incomplete information. Initially, the risk related to the HSC is identified through a literature review and expert’s input. Further, the probability and impact of each HSM-related risk are assessed using experts’ input through linguistic terms. These linguistic values are transformed into single-value trapezoidal neutrosophic numbers (SVTNNs). Finally, the severity of each HSM-related risk is determined through the multiplication of the probability and impact of each risk and prioritised the risks based on their severity.FindingsA comprehensive risk assessment framework is developed that could be used under uncertainty. Initially, 16 risks are identified related to the HSM. Further, the identified risks are prioritised using the severity of the risks. The high-priority risk is “raw material status”, “raw material wholesomeness” and “origin of raw material” while “information integrity” and “people integrity” are low-priority risks.Practical implicationsHSM risk can be effectively assessed through the proposed framework. The proposed framework applied neutrosophic numbers to represent real-life situations, and it could be used for other supply chains as well.Originality/valueThe proposed method is effectively addressing the issue of linguistic subjectivity, inconsistent information and uncertainty in the expert’s opinion. A case study of the HSC is adopted to illustrate the efficiency and applicability of the proposed risk framework.

A Neutrosophic differential equation approach for modelling glucose distribution in the bloodstream using neutrosophic sets

Neutrosophic sets are a generalization of fuzzy sets and intuitionistic fuzzy sets. They play an important role in addressing uncertainty, vagueness, and indeterminacy in problem-solving. Differential equations in a neutrosophic environment under Hukuhara differentiability are used to model the amount of glucose distribution and absorption rates in blood. Trapezoidal neutrosophic numbers are used to describe the initial conditions and equation parameters. Equilibrium points, along with their stability analysis, have been performed. Exact solutions are found, and corresponding numerical simulations for different (α,β,γ)-cut values of trapezoidal neutrosophic numbers are performed using MATLAB.

A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers

In general, a fuzzy set can’t handle situations of inconsistencies and inexact data, however, the Neutrosophic Set (NS) has been used to address such types of issues in all real world problems. The neutrosophic set is an extension of the fuzzy set and the intuitionistic fuzzy set, that can deal with imperfect, inconsistent, and indeterminate data in all the related problems. This article proposed a conventional neutrosophic approach using a ranking function for the transportation problem. This approach has considered a single-valued neutrosophic set for the entire transportation problem with the numerical illustration. Single valued trapezoidal neutrosophic numbers are well-known and used in solving the transportation problem and its extension. Besides, a novel ranking function is proposed with the help of membership functions, which gives the best optimal solution. Moreover, the obtained optimal solution has been compared with recent new approaches. This research will help to get the best optimal solution for the transportation problem under uncertainty.

Optimal Site Selection for Women University Using Neutrosophic Multi-Criteria Decision Making Approach

Site selection for an institute or a university is a challenging task. The selection of sites for setting up a new university depends on multiple criteria. In backward, under privileged area people’s perception towards the co-educational universities and women universities are different. Poor families with their conservative mentality possess inhibitions while sending their girl child to co-educational universities as they have concerns about safety, security and family honor. Hence many attributes which are not so important for co-educational universities are more pertinent for women university. In this research paper, we have considered a model for selecting women’s university sites in different backward locations in the state of West Bengal, India. This model incorporated different types of uncertainty related to site selection. Ten important criteria are chosen for the selection of sites. To capture the uncertainty of the problem, trapezoidal neutrosophic numbers are used along with the Multi-criteria Decision Making tool Analytic Hierarchy Process (AHP) for obtaining criteria weights. Finally, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and COmplex PRoportional ASsessment (COPRAS) are applied for ranking of the sites. Comparative and sensitivity analyses are conducted to check the steadiness of the techniques used.

Neutrosophic data envelopment analysis based on the possibilistic mean approach

Data envelopment analysis (DEA) is a non-parametric approach for the estimation of production frontier that is used to calculate the performance of a group of similar decision-making units (DMUs) which employ comparable inputs to produce related outputs. However, observed values might occasionally be confusing, imprecise, ambiguous, inadequate, and inconsistent in real-world applications. Thus, disregarding these factors may result in incorrect decision-making. Thus neutrosophic sets have been created as an extension of intuitionistic fuzzy sets to represent ambiguous, erroneous, missing, and inaccurate information in real-world applications. In this study, we have proposed a technique for solving the neutrosophic form of the Charnes–Cooper–Rhodes (CCR) model based on single-value trapezoidal neutrosophic numbers (SVTrNNs). The possibilistic mean for SVTrNNs is redefined and applied the Mehar approach to transforming the neutrosophic DEA (Neu-DEA) model into its corresponding crisp DEA model. As a result, the efficiency scores of the DMUs are calculated using different risk parameter values lying in [0, 1]. A numerical example is given to analyze the performance of the all India institutes of medical sciences and compared it with Abdelfattah’s ranking approach.

Integrated Multi-Criteria Decision Making Via Trapezoidal Neutrosophic Sets to Evaluate the Risks of Failure Mode

The purpose of a failure mode and effect analysis (FMEA) is to improve the safety and dependability of a system, product, procedure, or facility by identifying potential points of failure and determining the consequences of such failures. The assessment of failure modes, the weighting of risk factors, and the ranking of failure modes are all areas where the conventional FMEA falls short when put to use in the real world. To assess the hazard of failure modes in a trapezoidal neutrosophic sets environment, this research proposes a model that combines the neutrosophic sets and MCDM technique such as WASPAS. The WASPAS MCDM method is used to calculate the weights of standards and order the alternatives. Advantages of trapezoidal neutrosophic numbers in dealing with uncertainty, ambiguity, and incompleteness are combined with the benefits of WASPAS to create the suggested risk prioritization strategy.

A neutrosophic application to the transportation problem with Mixed Constraints using single-valued trapezoidal neutrosophic numbers

A neutrosophic application to the transportation problem with Mixed Constraints using single-valued trapezoidal neutrosophic numbers

A Novel Approach by using Interval-Valued Trapezoidal Neutrosophic Numbers in Transportation Problem

A Novel Approach by using Interval-Valued Trapezoidal Neutrosophic Numbers in Transportation Problem

A Note on “Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers”

A Note on “Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers”

Mehar approach to solve neutrosophic linear programming problems using possibilistic mean

Khatter (Soft Comput 24:6847–16,867, 2020) pointed out that although several approaches are proposed in the literature to solve single-valued neutrosophic linear programming problems (SVNLPPS) (linear programming problems in which all the parameters except decision variables are either represented by single-valued triangular neutrosophic numbers (SVTNNS) or single-valued trapezoidal neutrosophic numbers (SVTrNNS)). However, all the methods for comparing single-valued neutrosophic numbers (SVNNS), used in existing approaches, are independent from the attitude of the decision-maker towards the risk. To fill this gap, Khatter (2020), firstly, proposed a method for comparing two SVNNS by considering the attitude of the decision-maker towards the risk. Then, using the proposed comparing method, Khatter (2020) proposed an approach to solve SVNLPPS. In this paper, it is pointed out that a mathematical incorrect result is considered in Khatter’s approach. Hence, it is inappropriate to use Khatter’s approach. Also, it is pointed out that some mathematical incorrect results are considered in other existing approaches for solving SVNLPPS. Hence, it is inappropriate to use other existing approaches for solving SVNLPPS. Furthermore, to resolve the inappropriateness of Khatter’s approach and other existing approaches, a new approach (named as Mehar approach) is proposed to solve SVNLPPS. Finally, correct optimal solution of some existing SVNLPPS is obtained by the proposed Mehar approach.

Intelligent model for contemporary supply chain barriers in manufacturing sectors under the impact of the COVID-19 pandemic

The COVID-19 pandemic has cast a shadow on the global economy. Since the beginning of 2020, the pandemic has contributed significantly to the global recession. In addition to the health damages of the pandemic, the economic impacts are also severe. The consequences of such effects have pushed global supply chains toward their breaking point. Industries have faced multiple obstacles, threatening the fragile flow of raw materials, spare parts, and consumer goods. Previous studies showed that supply chain barriers have multi-faceted impacts on industries and supply chains, which demand appropriate measures. In this regard, seven major barriers that directly impact industries have been identified to determine which industry is most affected by the COVID-19 pandemic. This paper utilized a hybrid multi-criteria decision-making (MCDM) approach under a neutrosophic environment using trapezoidal neutrosophic numbers to rank those barriers. The Analytical Network Process (ANP) quantifies the effects and considers the interrelationships between the determined barriers (criteria) involved in decision-making. Subsequently, the Measurement Alternatives and Ranking according to the COmpromise Solution (MARCOS) method was adopted to rank six industries according to the impact of those barriers. Results show that the lack of inventory is the largest barrier to influencing industries, followed by the lack of manpower. Sensitivity analysis is performed to detect the change in the rank of industries according to the change in the relative importance of the barriers.

Multiple Attribute Decision Making Based on Interval-Valued Neutrosophic Trapezoidal Fuzzy Numbers and its Application in the Diagnosis of Viral Flu

Decision-making technique (DMT) is mostly used in artificial intelligence and cognitive sciences to elaborate individual and social perception. So, one of the most important strategies in DMT evolved in medical diagnosis scrutiny regarding the connection of symptoms and diagnosis of diseases due to uncertainty and fuzziness in the relevant information. The focus of this article is to develop a diagnostic decision making strategy for the diagnosis of Viral diseases with close related symptoms using the Interval-valued trapezoidal neutrosophic fuzzy Numbers (IVTrNFN) w.r.t multiple attribute decision making (MADM) strategy where, the attribute value is evolved to Interval-valued trapezoidal neutrosophic fuzzy number and the attribute weight is unknown and can be related to the GRA (Grey relational analysis projection) technique. In this research several operational laws are developed as well as the expected value and the hamming distance between two IVTrFNs are introduced. Moreover, the information entropy method is used to determine the attributes weights and the grey relational analysis as well as the projection method are involved too in the proposed framework. The ranks of the alternative decisions are evaluated by their relative closeness to PIS (Positive Ideal Solutions), which combine the grey relational projection values from positive and negative ideal solutions associated with each alternative. Finally, a Viral disease example is given to verify the developed approach and to demonstrate its practicality and effectiveness.