Neutrosophic Set Environment Research Articles

Multi Criteria Decision Making Under Single-Valued Neutrosophic Set Environment for Supplier Selection

Multi Criteria Decision Making Under Single-Valued Neutrosophic Set Environment for Supplier Selection

An abstract approach to convex and concave sets under refined neutrosophic set environment

An abstract approach to convex and concave sets under refined neutrosophic set environment

Some applications of Weak-multiplication modules in Neutrosophic set environment

Some applications of Weak-multiplication modules in Neutrosophic set environment

Application of a Combined Approach of Text Mining and QFD Methodology Based on Single Valued Neutrosophic Numbers for Efficient Curriculum Design

In this study, an alternate curriculum design for an undergraduate program of Statistics is suggested carrying out a combined approach of the QFD methodology, text mining techniques under single valued neutrosophic set environment. To capture the employers’ expectations from their potential employees, 640 job advertisements, obtained from two of the most important career and job posting sites in Turkey, were analyzed using TF-IDF technique, which is one of the text mining methods. By using single-valued neutrophic set (SVNS) theory in QFD, the technical requirements representing the courses included in the curriculum were found their priorities. Hence, the technical characteristics that play a critical role in evaluating the curriculum quality of the undergraduate program were revealed. In addition, single valued neutrosophic sets have provided a flexible decision-making procedure to improve the quality of individuals’ subjective assessments. Consequently, this is expected to be a good reference for researchers working on these issues, both in terms of the proposed approach and the problem addressed.

VIKOR-Based MAGDM Strategy Revisited in Bipolar Neutrosophic Set Environment

VIKOR strategy was proposed to solve Multi-Attribute Group Decision Making ( MAGDM) in Bipolar Neutrosophic Set (BNS) environment, where compromise solutions were not identified. To overcome the shortcomings, the VIKOR strategy is revisited by incorporating compromise solutions in the BNS environment. Using the revisited VIKOR strategy, an MAGDM problem is solved. Sensitivity analysis is presented to reflect the impact of the decision-making mechanism coefficient on ranking of the alternatives.

Adaptive Autonomous Robot Navigation by Neutrosophic WASPAS Extensions

In this research, a novel adaptive frontier-assessment-based environment exploration strategy for search and rescue (SAR) robots is presented. Two neutrosophic WASPAS multi-criteria decision-making (MCDM) method extensions that provide the tools for addressing the inaccurate input data characteristics are applied to measure the utilities of the candidate frontiers. Namely, the WASPAS method built under the interval-valued neutrosophic set environment (WASPAS-IVNS) and the WASPAS method built under the m-generalised q-neutrosophic set environment (WASPAS-mGqNS). The indeterminacy component of the neutrosophic set can be considered as the axis of symmetry, and neutrosophic truth and falsity membership functions are asymmetric. As these three components of the neutrosophic set are independent, one can model the input data characteristics applied in the candidate frontier assessment process, while also taking into consideration uncertain or inaccurate input data obtained by the autonomous robot sensors. The performed experiments indicate that the proposed adaptive environment exploration strategy provides better results when compared to the baseline greedy environment exploration strategies.

Procedural Video Game Scene Generation by Genetic and Neutrosophic WASPAS Algorithms

The demand for automated game development assistance tools can be fulfilled by computational creativity algorithms. The procedural generation is one of the topics for creative content development. The main procedural generation challenge for game level layout is how to create a diverse set of levels that could match a human-crafted game scene. Our game scene layouts are created randomly and then sculpted using a genetic algorithm. To address the issue of fitness calculation with conflicting criteria, we use weighted aggregated sum product assessment (WASPAS) in a single-valued neutrosophic set environment (SVNS) that models the indeterminacy with truth, intermediacy, and falsehood memberships. Results are presented as an encoded game object grid where each game object type has a specific function. The algorithm creates a diverse set of game scene layouts by combining game rules validation and aesthetic principles. It successfully creates functional aesthetic patterns without specifically defining the shapes of the combination of games’ objects.

Decision-making method based on game theory and grey theory in a single-value neutrosophic environment and its application to typhoon disaster assessment

PurposeThe Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.Design/methodology/approachFirst, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.FindingsAn example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.Practical implicationsThe proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.Originality/valueThe proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision.

Bonferroni mean (BM) operators have been established as a powerful tool for handling the interrelationship between the input arguments under various decision-making information. However, the existing BM operators do not take into account the overall interaction among decision makers or criteria. To overcome this limitation, this study considers the Shapley fuzzy measure (SFM) with the normalized weighted BM (NWBM) operator under a neutrosophic environment. In addition, the current research ignores the bipolarity and hesitancy during decision elicitations, resulting in the imprecise decision results. In this paper, the hesitant bipolar-valued neutrosophic set (HBNS) which is the extension of hesitant fuzzy set and bipolar neutrosophic set is employed. The main focus of this paper is in the development of an aggregation operator for HBNS. Based on the literature review, we would like to fill in the gaps by developing a hesitant bipolar-valued neutrosophic Shapley NWBM (HBN-SNWBM) operator where the overall interaction among decision makers can be considered. Besides that, a three-phase decision making framework is also proposed to show the applicability of the proposed aggregation operator to the real-world decision problems. The HBN-SNWBM operator and the decision making framework are applied to two examples of investment selection where evaluations are implemented using the proposed aggregations that based upon hesitant bipolar-valued neutrosophic sets. In the first example, it is found that a weapon company is the best alternative for investment followed by a food company. Sensitivity of parameters of the aggregation operator is also analysed and it is found that the ranking results are consistent despite of different parameter values used. This verifies the insensitivity of p,q parameters in the developed aggregation operator. The proposed decision making framework and hesitant bipolar-valued neutrosophic sets would be a great significance for the practical implementation of the aggregation operators.

Decision-making method based on new entropy and refined single-valued neutrosophic sets and its application in typhoon disaster assessment

This study proposes a multi-attribute decision-making method for the decision-making problems with attributes and sub-attribute where the attribute weight is unknown, based on information entropy and the evaluation based on distance from average solution (EDAS) method under a refined single-valued neutrosophic set environment. First, the new distance measure, similarity measure, and neutrosophic entropy based on refined single-valued neutrosophic sets are defined. Further, the relationship between them is discussed and the attribute weights are determined based on the new neutrosophic entropy. Then, the EDAS method is used to rank and select the best alternative. Finally, two illustrative examples of typhoon disaster assessment (typhoon disaster assessment with multi-layer indicators and dynamic assessment of typhoon disaster) are presented to demonstrate the feasibility, effectiveness, and practicality of the proposed method. The advantages of the proposed method are illustrated by sensitive analysis and comparative analysis with other methods.

Multiple attribute decision making based on immediate probabilities aggregation operators for single-valued and interval neutrosophic sets

The objective of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the neutrosophic set environment. Single-valued and interval neutrosophic sets are the important mechanisms for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Also, to describe the behavior of the decision-maker objectively (in terms of probability) and subjectively (in terms of weights), a concept of probabilistic information plays a dominant role in the investigation. Keeping these features in mind, this paper presents several probabilistic and immediate probability-based averaging and geometric aggregation operators for the collection of the single-valued and interval neutrosophic sets. The advantage of these proposed operators is that it simultaneously combines the objective and subjective behavior of the decision-maker during the process. The various salient features of the proposed operators are studied. Later, we develop two new algorithms based on the aggregation operators to solve multiple attribute decision-making problems with single-valued and interval neutrosophic sets features. A numerical example related to the demonetization is given to demonstrate the presented approaches, and the advantages, as well as comparative analysis, are given to shows its influence over existing approaches.

Some hybrid weighted aggregation operators under neutrosophic set environment and their applications to multicriteria decision-making

A single-valued and an interval neutrosophic sets are two instances of the neutrosophic set(NS), which can efficiently deal with uncertain, imprecise and inconsistent information. In the present work, the work has been done under this environment to develop some novel hybrid aggregation operators based on arithmetic and geometric aggregation operators. The preferences related to the attributes are made in the form of single-valued and interval neutrosophic numbers. Their desirable properties such as idempotency, boundedness and monotonicity are also investigated. Furthermore, a decision-making approach presents to investigate the multi-criteria decision-making problem. The effectiveness of the approach is demonstrated through a case study and a comparison analysis with some other existing methods has been done to validate the results.

Study of Decision Framework of Shopping Mall Photovoltaic Plan Selection Based on DEMATEL and ELECTRE III with Symmetry under Neutrosophic Set Environment

Rooftop distributed photovoltaic projects have been quickly proposed in China because of policy promotion. Before, the rooftops of the shopping mall had not been occupied, and it was urged to have a decision-making framework to select suitable shopping mall photovoltaic plans.

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems.

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

Study of Decision Framework of Shopping Mall Photovoltaic Plan Selection Based on DEMATEL and ELECTRE III with Symmetry under Neutrosophic Set Environment

Rooftop distributed photovoltaic projects have been quickly proposed in China because of policy promotion. Before, the rooftops of the shopping mall had not been occupied, and it was urged to have a decision-making framework to select suitable shopping mall photovoltaic plans. However, a traditional multi-criteria decision-making (MCDM) method failed to solve this issue at the same time, due to the following three defects: the interactions problems between the criteria, the loss of evaluation information in the conversion process, and the compensation problems between diverse criteria. In this paper, an integrated MCDM framework was proposed to address these problems. First of all, the compositive evaluation index was constructed, and the application of decision-making trial and evaluation laboratory (DEMATEL) method helped analyze the internal influence and connection behind each criterion. Then, the interval-valued neutrosophic set was utilized to express the imperfect knowledge of experts group and avoid the information loss. Next, an extended elimination et choice translation reality (ELECTRE) III method was applied, and it succeed in avoiding the compensation problem and obtaining the scientific result. The integrated method used maintained symmetry in the solar photovoltaic (PV) investment. Last but not least, a comparative analysis using Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method and VIKOR method was carried out, and alternative plan X1 ranks first at the same. The outcome certified the correctness and rationality of the results obtained in this study.

VIKOR Based MAGDM strategy under Bipolar Neutrosophic Set Environment

In this paper, we extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) strategy to multiple attribute group decision-making(MAGDM) with bipolar neutrosophic set environment. In this paper, we first define VIKOR strategy in bipolar neutrosophic set environment to handle MAGDM problems, which means we combine the VIKOR with bipolar neutrosophic number to deal with MAGDM. We propose a new strategy for solving MAGDM. Finally, we solve MAGDM problem using our newly proposed VIKOR strategy under bipolar neutrosophic set environment. Further, we present sensitivity analysis to show the impact of different values of the decision making mechanism coefficient on ranking order of the alternatives.

NS-Cross Entropy-Based MAGDM under Single-Valued Neutrosophic Set Environment

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is capable of dealing with an unknown weight of attributes and an unknown weight of decision-makers. Finally, a numerical example of multi-attribute group decision-making problem of investment potential is solved to show the feasibility, validity and efficiency of the proposed decision-making strategy.

Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment

Interval neutrosophic sets (INSs) capturing the uncertainties by characterizing into the intervals of the truth, the indeterminacy, and the falsity membership degrees, is a more flexible way to explore the decision-making applications. In this paper, we develop a nonlinear programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve decision-making problems in which criterion values and their importance are given in the form of interval neutrosophic numbers (INNs). Based on the concept of closeness coefficient, we firstly construct a pair of the nonlinear fractional programming model and then transform it into the linear programming model. Furthermore, to determine the ranking of considered alternatives, likelihood-based comparison relations are constructed. Finally, an illustrative example demonstrates the applicability of the proposed method for dealing with decision making problems with incomplete knowledge.