Triangular Neutrosophic Numbers Research Articles

Valuation of Internet of Energy (IoE) Platforms in Smart Cities: A Hybrid Multi-Criteria Decision Making Approach

A smart city is a place where people live using computing, sensing, and networking technology in a variety of ways, including smart buildings, smart homes, smart transportation, smart workplaces, smart offices, smart industries, and smart agriculture. These smart technologies need to connect so; we need to use the Internet of Things (IoT) that has applications in many areas of our smart lives. IoT has been used due to the growing usage of renewable energy sources and the challenges of network management. Internet of Energy (IoE) integrates the IoT and smart grid capabilities. The basic role of smart grids or IoE is an essential element in creating smart cities. In this work, we present some IoE platforms that represent the alternatives and their criteria. The proposed study treats the uncertainty of multi-criteria decision-making (MCDM) modified by single value triangular neutrosophic number (SVTrN) by choosing the optimal IoE platform based on the criteria importance through inter-criteria correlation (CRITIC) method and multi-attributive ideal-real comparative analysis (MAIRCA). The proposed model proved its effectiveness by applying it to an experimental case. The results show that the DCC (A3) platform is the best one.

A Direct Method to Solve Double Refined Indeterminate Triangular Neutrosophic Linear Programming Problem

Double Refined Indeterminate Triangular Neutrosophic Number (DRITrNN) provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete and inconsistent information. In this article a Linear programming problem is considered in DRITrNN situation and an efficient novel algorithm is proposed to solve the LPP with variables in the form of DRITrNN and its efficiency is validated with Numerical illustration. Keywords: Single valued triangular neutrosophic number , Double Refined Indeterminate Triangular Neutrosophic Number , Linear Programming Problem, Algorithm.

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

Profit maximizing business model for electric vehicle industry incorporating fuzziness in the environment: Encompassing a case study from silicon valley of India

Electric vehicles (EVs) are among the most revolutionary breakthroughs by the context of decarbonization of road transport. The adoption of EVs has drawn increasing attention and is currently considered a potential route towards sustainable transportation. Businesses approaching the EV market must establish lucrative business models that overcome the adoption obstacles for EVs while assuring long-term growth. The intent of the current research exploration is to create a cutting-edge framework for EV enterprises that aims to maximize profit and save delivery time leading to high customer satisfaction. The volume discount strategy is used for profit escalation. The model presented in this paper is highly adaptable for a real-world problem as it incorporates uncertainty in the EV industry through generalized triangular neutrosophic numbers, an extension of fuzzy numbers. A modified version of the neutrosophic compromise programming approach is proposed in this paper. The results from this approach are validated using genetic algorithm. The proposed optimization-based framework is encapsulated in the form of study of a case from Bangalore city, in India. An in-depth exploration of two cases along with sensitivity analysis is carried out that helped in prioritizing some discrete customers and gave insights on which manufacturing site should be designated more focus.

A novel method for solving “Entrepreneurship and Entrepreneurship” career ability evaluation of local college students with triangular neutrosophic numbers

With the proposal of the “Double First Class” construction concept in Chinese universities, cultivating high-quality talents has become the main direction of university education. At present, local universities in China are actively adapting to the changes of the times, taking the construction of the Double First Class as an opportunity, continuously adjusting and deepening the reform of the double innovation and innovation talent cultivation mode, further improving the curriculum system, increasing investment in professional practical teaching, stimulating students’ enthusiasm for innovation and entrepreneurship (IAE), and focusing on improving students’ comprehensive abilities, achieving significant results in talent cultivation. The “Entrepreneurship and Entrepreneurship” career ability evaluation of local college students could be considered as multiple attribute decision-making (MADM). Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method was employed to deal with MADM. The triangular fuzzy neutrosophic sets (TFNSs) are employed as a better tool for expressing uncertain information during the “Entrepreneurship and Entrepreneurship” career ability evaluation of local college students. In this paper, the triangular fuzzy neutrosophic number CoCoSo (TFNN-CoCoSo) based on the Hamming distance and Euclid distance is constructed to cope with the MADM under TFNSs. The information entropy method is employed to compute the weight values based on the Hamming distance and Euclid distance under TFNSs. Finally, a numerical example of “Entrepreneurship and Entrepreneurship” career ability evaluation of local college students is constructed and some decision comparisons are constructed to verify the TFNN-CoCoSo method.

An Efficient Technique for Algebraic System of Linear Equations Based on Neutrosophic Structured Element

Neutrosophic logic is frequently applied to the engineering technology, scientific administration, and financial matters, among other fields. In addition, neutrosophic linear systems can be used to illustrate various practical problems. Due to the complexity of neutrosophic operators, however, solving linear neutrosophic systems is challenging. This work proposes a new straightforward method for solving the neutrosophic system of linear equations based on the neutrosophic structured element (NSE). Here unknown and right-hand side vectors are considered as triangular neutrosophic numbers. Based on the NSE, analytical expressions of the solution to this equation and its degrees are also provided. Finally, several examples of the methodology are provided.

An extended ISM and MICMAC method under neutrosophic environment

PurposeISM technique is one of the tools of interest in soft operations research. The soft nature of this technique has made inevitable use of indeterminacy theories. The present research attempts to develop ISM technique and MICMAC analysis in a neutrosophic space due to the complexity and uncertainty of the decision-making environment.Design/methodology/approachIn this study, single-valued triangular neutrosophic numbers is used to develop Neutrosophic ISM (NISM) and Neutrosophic MICMAC (NMICMAC). First, the general algorithm of NISM and NMICMAC is provided. In the following, the complete description of NISM steps including level value determination, Factor Leveling Algorithm and NISM digraph algorithm are presented. Finally, a description of the NMICMAC steps is described.FindingsAn illustrative example – supplier selection problem – is given to verify the effectiveness of the proposed method and in the discussion section; the comparison and analysis of different aspects of the NISM with the previous methods are discussed.Originality/valueIn this study, NISM and NMICMAC are presented for the first time, so that each pairwise comparison judgment is provided as single valued triangular neutrosophic numbers. The development of the model is continued until the final stages of calculations with neutrosophic numbers, and only in the final stage the results are crispy presented. In addition, not only the factors of process are leveled, but at each level the factors are lined up and their importance is determined.

A New Perspective for Solving the System of Differential Equations Describing Arm Race Model in Neutrosophic Environment

The term “arms race” literally refers to competitions between nations for military superiority during times of peace. For a number of reasons, arms races have attracted a lot of attention. They are widely meant to have important repercussions for national security. The best course of action for a nation facing an aggressive foe is to engage in an armaments race. If one nation raises its arsenal, another will follow suit, in order the first nation responds by increasing its arsenal. Differential equations can be used to model this type of arms race. Both Engineering and Science rely only on differential equations. Modeling the problems in this field include some parameters that are uncertain or imprecise. To resolve this, neutrosophic differential equations are evolved. In this article, the arms race is modeled using a differential equation with a triangular neutrosophic number as the initial value. The system of neutrosophic differential equation is then solved using the MATLAB tool and the results are visualised graphically. The solution is compared by finding the value, ambiguity, and rank of neutrosophic numbers.

Prioritizing Factors of Panic Buying Behaviour: A Neutrosophic Analytical Approach

In a crisis, panic buying (PB) has negative ramifications for manufacturers, suppliers, retailers, consumers and the overall economy. There is a plethora of research in extant literature identifying the factors causing PB, but none has prioritized them so that firms can devise focused strategies to tackle the situation of PB. In this research, through extant literature and experts’ opinion, 18 PB factors (PBFs) are identified. The neutrosophic analytical hierarchy process is used for prioritizing the factors based on single-valued triangular neutrosophic numbers. From the 18 PBFs, on the basis of ranking received from results, top 50% most influencing factors are social media, fear of missing out, peer influence, social learning, product importance, cultural values, rumours, sense of security and government regulations. Thereafter, in close conjunction with these factors, most significant interventions/measures to curb PB are presented in the form of a PB prevention and control framework. The knowledge of the top influencing factors of PB is vital for policymakers, administrators, marketers, retailers and consumers so that they can devise appropriate interventions when required.

Neutrosophic MARCOS in Decision Making on Smart Manufacturing System

Business firms prefer software-based smart manufacturing systems to monitor and supervise all production activities in a decentralized manner. The choice of software decides the degree of manufacturing robustness. This paper proposes a neutrosophic-based MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) method of MCDM with single-valued triangular neutrosophic numbers to solve the software selection problem. The proposed neutrosophic method is applied to hypothetical data to test the efficacy of the method. The results obtained using the proposed method are compared with crisp, fuzzy, and intuitionistic data representations, and suitable inferences are acquired. The proposed method has several industrial implications and it has several scopes of applying to other decision-making scenarios with real data sets.

An Intelligent Decision Support Model for Optimal Selection of Machine Tool under Uncertainty: Recent Trends

Many scholars have been interested in the subject of machine tool selection as a result of the growing number of different machines and the continuous advancement of technology associated with these machines. The selection of an unsuitable machine tool may lead to a variety of issues, including limitations on production capacities and productivity indicators when taking into account both time and money from an industrial and practical perspective. The present strategy of selecting machine tools, known as multi-criteria decision-making (MCDM), relies on the subjective viewpoint the vast majority of the time. When selecting an appropriate machining tool, however, it is necessary to take both the subjective and objective points of view into consideration. This is due to the fact that the objective assessment accurately reflects the performance of the machine tools. As a result, the purpose of this work is to provide a strategy for selecting machine tools that are based on an innovative hybrid MCDM framework. The study was conducted under a neutrosophic environment and using triangular neutrosophic numbers (TNNs). In the beginning, the CRiteria Importance through Intercriteria Correlation (CRITIC) method is used to assess and prioritize the criteria set for the study. Then, the Additive Ratio Assessment (ARAS) method is applied to evaluate and rank four machine tools that were selected and used as alternatives in the study. The results indicate that the criteria of maximum spindle speed and linkage accuracy are the most important in determining the best machine tool. Also, the results indicate that the best alternative among the four tools used is FIDLA GTF-28. As a result, the requirements and priorities for research in the future are highlighted.

Solving shortest path problems using an ant colony algorithm with triangular neutrosophic arc weights

Indeed, one of the most well-known topics in the area of graph theory is the shortest path (SP) problem, which has practical applications in various areas of research, including transportation, communication via networks, life-saving services, fire department services, etc. The edges of the connected SP problems are typically characterized by various numbers in practical applications. In this research paper, we calculate the shortest path using an ant colony optimization (ACO) algorithm with single value triangular neutrosophic numbers as arc weights. The method is used to estimate the shortest path of a neutrosophic network. One numerical example is used to test the suggested method, and outcomes are provided.

Neutrosophic multi-item inventory control models with constraints

Inventory managers are expected to handle a large number of items in their inventory while adhering to budgetary and space limits, as well as the number of items bought from vendors. Multi-item inventory models with one or more resource constraints, such as budget, space, or number of orders. This paper talks about an EOQ model in neutrosophic multi-item inventory control models with constraints. The ordering costs, the holding costs, demands, storage area, investment amount, and the maximum average number of units are considered as triangular neutrosophic numbers, as opposed to crisp values, to make the inventory model more realistic. This idea is used to decide the neutrosophic optimal order quantities with the assistance of the Lagrange multiplier. Eventually, the proposed method is delineated with a numerical instance and the results are analysed briefly.

A Newly Proposed and Comparative Study on Multi - Criteria Decision Making in Interval Valued Bipolar Triangular Neutrosophic Set by PROMETHEE II

Objectives: To propose the operational laws and operators in interval valued bipolar triangular neutrosophic sets and also to resolve multi criteria decision making problem using PROMETHEE II. Methods: Based on the combination of bipolar neutrosophic sets and interval valued triangular neutrosophic sets, an interval valued bipolar triangular neutrosophic set is proposed followed by its operational laws, score function, accuracy and certainty function. Findings: The arithmetic operators, operational laws and also the score function, accuracy and certainty functions have been proposed for interval valued bipolar triangular neutrosophic sets. The PROMETHEE II technique discovered and employed an aggregated weighted arithmetic operator to address the multi-criterion decision-making problem. Novelty: By the concept of interval valued bipolar triangular neutrosophic set, the results can be viewed with more accuracy for the linguistic variables rather than the crisp values. An illustrative example has been explained for the interval valued bipolar triangular neutrosophic numbers by which the effectiveness is tested with the comparative approach by using PROMETHEE II method. Keywords : Interval valued neutrosophic numbers, Bipolar neutrosophic numbers, Interval valued bipolar triangular neutrosophic numbers, Score function, PROMETHEE II method.

A parametric neutrosophic model for the solid transportation problem

PurposeThis research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels.Design/methodology/approachDue to the lack of reliable information, changeable economic circumstances, uncontrolled factors and especially variable conditions of available resources to adapt to the real situations, the authors are faced with a kind of uncertainty and indeterminacy in constraints and the nature of the parameters of STP. Therefore, an approach based on neutrosophic logic is offered to make it more applicable to real-world circumstances. In this study, the triangular neutrosophic numbers (TNNs) have been utilized to represent demand, transportation capacity, accessibility and cost. Then, the neutrosophic STP was converted into an interval programming problem with the help of the variation degree concept. Then, two simple linear programming models were extracted to obtain the lower and upper bounds of the optimal solution.FindingsThe results reveal that the new model is not complicated but more flexible and more relevant to real-world issues. In addition, it is evident that the suggested algorithm is effective and allows decision makers to specify their acceptance, indeterminacy and falsehood thresholds.Originality/valueUnder the transportation literature, there are several solutions for TP and STP in crisp, fuzzy set (FS) and intuitionistic fuzzy set (IFS) conditions. However, the STP has never been explored in connection with neutrosophic sets to the best of the authors’ knowledge. So, this work tries to fill this gap by coming up with a new way to solve this model using NSs.

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.

New multi-criteria decision-making technique based on neutrosophic axiomatic design

There are several multicriteria decision-making (MCDM) approaches presented in the literature with their characteristics. Although traditional MCDM approaches are considered a proper implementation to select the best alternative from available types, they failed to consider uncertainty which is quite high and desires to be thoughtfully measured in the selection process. This research focuses on extending MCDM in the neutrosophic environment using axiomatic design (AD) as a novel contribution to selecting appropriate Computed Tomography (CT) devices. We present a new linguistic scale for evaluating criteria and alternatives based on single-valued triangular neutrosophic numbers (SVTrN). The proposed approach is superior to other existing approaches due to its simplicity and ability to simulate natural human thinking via considering truth, indeterminacy, and falsity degrees. Then, applying it will increase the value of imaging for medical decision-making and decrease needless costs. So, this study can be valuable to researchers by helping them consider the appropriate medical imaging system selection problem theoretically under uncertainty, and for governments and organizations to design better satisfying medical imaging evaluation systems.

New extension of ordinal priority approach for multiple attribute decision-making problems: design and analysis

The selection and assessment process of appropriate robots became a more complex and complicated task due to various available alternatives and conflicting attributes which must take into consideration. Also, uncertainty which exists usually in the selection process is an unavoidable component that needs to be thoughtfully measured and traditional multi-attribute decision-making approaches failed to deal precisely with it. Since almost all decisions originate from subjective ordinal preferences, handling uncertainty using linguistic variables is also not enough. Thus, the objective of the current study is to present a new extended ordinal priority approach in the neutrosophic environment for the first time to select an appropriate robot. Since neutrosophic is one of the most effective and accommodating tools for handling uncertainty, thus, this method goes to transform linguistic information into triangular neutrosophic numbers using a new presented scale. This scale was used to determine the importance degree of attributes and alternatives regarding experts' opinions. Also, the score function of the triangular neutrosophic number is used for prioritizing attributes and alternatives. The experts in our proposed method have the same degree of importance, since each expert is a person with special skills and knowledge representing mastery of a particular subject. To measure the applicability and efficiency of the proposed approach, an experimental case study has been established for the robot selection problem of a new pharmaceutical city in Egypt for the first time. The source of data in this case study is experts, interviews, and questionnaires. Also, sensitivity and comparative analysis are further made for verifying the power of the proposed approach. The outcome of this study shows that the suggested approach for robot selection is quite helpful and has a great performance under uncertainty over classical and fuzzy ordinal priority approaches. Also, the suggested approach is less consumption of time and simpler than the fuzzy ordinal priority approach. Therefore, we recommend firms and governments to apply it for increasing product quality, hence the profitability of manufacturing industries and decrease needless costs.

Experts' Selection for Neutrosophic Delphi Method. A Case Study of Hotel Activity

This investigation aims to model experts’ selection for neutrosophic Delphi method. The phase of selecting experts is essential to obtain adequate results in Delphi method, thus this phase deserves a major attention. The proposed method considers the complexity of the subject, according to experts’ criteria to fix the number of experts necessary to apply the neutrosophic Delphi method. Single-valued triangular neutrosophic numbers are used to measure experts’ self-evaluations and the weights of expertise criteria. Neutrosophy allows us to include indeterminacy, which is typical in any decision-making problem, as well as the calculation based on linguistic terms. Hotel activity serves as a case study for illustrating the applicability of the method in a real life situation.

Neutrosophic Cognitive Maps for Violence Cause Analysis

Among the most valuable AI methods for modeling complicated things at the moment is the use of fuzzy cognitive mapping (FCMs). Conventional FCMs, on the other hand, can't handle the ambiguity that often arises in decision-making scenarios. A novel expansion of conventional FCMs called neutrosophic cognitive mapping (NCMs) was developed to address this shortcoming. However, the indeterminacy is not well handled by the NCMs stated in the citations since the level of indeterminacy is not quantified. In certain cases, choices should be seen as a series of steps that are only loosely related to one another. This occurs in project assessment when several activities depend on one another. Another difficult aspect of FCMs is that there isn't an appropriate topology for representing these types of decision-making difficulties. To aid in making decisions over several time periods, this research introduces a neutrosophic cognitive map built on triangular neutrosophic values (MS-TrNCM) for violence analysis. Through the use of triangular neutrosophic numbers, the suggested model allows experts to express their choices while considering various extents of truth, indeterminacy, and falsity in the underlying map linkages.