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Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decision-making problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives. The purpose of this paper is to propose single-valued trapezoidal neutrosophic preference relations (SVTNPRs) as a strategy for tackling multi-criteria decision-making problems. First, this paper briefly reviews basic concepts about neutrosophic sets and SVTNNs and defines a new comparison method and new operations for SVTNNs. Next, two aggregation operators, the single-valued trapezoidal neutrosophic weighted arithmetic average operator and the single-valued trapezoidal neutrosophic weighted geometric average operator, are proposed for applications in information fusion. Then, this paper discusses the definitions of completely consistent SVTNPRs and acceptably consistent SVTNPRs. Finally, we outline a decision-making method based on SVTNPRs to address green supplier selection problems, and we conduct a comparison study and discussion to illustrate the rationality and effectiveness of the decision-making method. [ABSTRACT FROM AUTHOR]

The selection of third-party logistics (TPL) providers can greatly influence the development of a company, and it has therefore become a hot topic for research. The process of selecting TPL providers is complicated because it includes fuzzy information that can be depicted by single-valued neutrosophic numbers (SVNNs). This paper establishes a new method for selecting TPL providers under single-valued neutrosophic environments. This method simultaneously takes into account the interrelationships among criteria and the different priority levels of criteria. To construct the method, we first introduce Frank operations of SVNNs, considering that extant operations for SVNNs lack flexibility and robustness. Then, we develop the single-valued neutrosophic Frank normalized prioritized Bonferroni mean (SVNFNPBM) operator utilizing the proposed Frank operations. The SVNFNPBM operator considers the interrelationships among criteria and their distinct priority levels by combining the Bonferroni mean and the prioritized average operators. Subsequently, we construct a method for selecting TPL providers based on the proposed operator. Finally, we describe a numerical example of selecting a TPL provider and conduct a comparative analysis to verify the applicability and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values. This paper focuses on developing an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is completely unknown and the evaluation values taking the form of probability multi-valued neutrosophic numbers (PMVNNs). First, the definition of PMVNSs is described. Second, an extended convex combination operation of PMVNNs is defined, and the probability multi-valued neutrosophic number weighted average operator is proposed. Moreover, two cross-entropy measures for PMVNNs are presented, and a novel qualitative flexible multiple criteria method (QUALIFLEX) is developed. Subsequently, an innovative MCGDM approach is established by incorporating the proposed aggregation operator and the developed QUALIFLEX method. Finally, an illustrative example concerning logistics outsourcing is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparison with other existing methods. [ABSTRACT FROM AUTHOR]

The personnel selection is a vital activity for companies, and multi-valued neutrosophic sets (MVNSs) can denote the fuzziness and hesitancy in the processes of the personnel selection. The extant fuzzy TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) methods take advantage of distance to denote the difference between two fuzzy sets (FSs). Nevertheless, the distance measurement, which ignores the included angle between two FSs, cannot comprehensively reflect the difference between two FSs. To cover this defect, a projection-based TODIM method with MVNSs for personnel selection is established to consider the risk preference of decision-makers and overcome the defect of the extant fuzzy TODIM methods. The proposed TODIM method makes use of an improved comparison method which overcomes the deficiency of extant comparison method. Furthermore, a projection-based difference measurement is defined and utilized in the projection-based TODIM method. We conduct a numerical example of the personnel selection to explain the application of the projection-based TODIM method and discuss the influence of the parameter. Finally, the proposed method is compared with several extant methods to verify its feasibility. [ABSTRACT FROM AUTHOR]

In this study, comprehensive multi-criteria decision-making (MCDM) methods are investigated under bipolar neutrosophic environment. First, the operations of BNNs are redefined based on the Frank operations considering the extant operations of bipolar neutrosophic numbers (BNNs) lack flexibility and robustness. Subsequently, the Frank bipolar neutrosophic Choquet weighted Bonferroni mean operator and the Frank bipolar neutrosophic Choquet geometric Bonferroni mean operator are proposed based on the Frank operations of BNNs. The proposed operators simultaneously consider the interactions and interrelationships among the criteria by combining the Choquet integral operator and Bonferroni mean operators. Furthermore, MCDM methods are developed based on the proposed aggregation operators. A numerical example of plant location selection is conducted to explain the application of the proposed methods, and the influences of parameters are also discussed. Finally, the proposed methods are compared with several extant methods to verify their feasibility. [ABSTRACT FROM AUTHOR]

With the popularity of online hotels booking, increasing attention has been paid to hotel recommendation methods. To provide personalized hotel recommendation for different types of consumers, a new hotel recommendation approach is proposed based on consumers' online reviews using interval neutrosophic linguistic numbers (INLNs). Meanwhile, this paper puts forward a distance formula of the interval neutrosophic linguistic numbers and the interval neutrosophic linguistic numbers power average (INLNPA) operator, making a further extension on the basis of the INLNs. Moreover, we develop a novel integration model utilizing the INLNPA operator that takes into consideration the relevance of the similar groups. And we apply the proposed approach to the hotel recommendation. In the case study, we have extracted 1902 online reviews of 10 hotels from TripAdvisor.com to verify the reliability of the proposed approach. The main conclusion of this paper is that the reliability of the hotel ordering can be improved by using the proposed approach. [ABSTRACT FROM AUTHOR]

Market segment evaluation and selection (MSE/MSS) become one of the most essential elements in marketing practices of enterprises, since they assist enterprises in developing homogeneous market segments. In this paper, a hybrid single-valued neutrosophic multi-criteria group decision-making (MCGDM) approach with quality function deployment (QFD) is used to support theMSE/MSSprocess. Firstly, single-valued neutrosophic numbers are used to represent the decisionmakers' qualitative assessments. Secondly, an extended QFD is used to translate the customer requirements (CRs) into relevant design requirements (DRs), and a single-valued neutrosophic DEMATEL (DEcision-MAking Trial and Evaluation Laboratory) is used to determine the importance weights of CRs and DRs. Thirdly, a single-valued neutrosophic TODIM (An acronym in Portuguese of interactive and multi-criteria decision-making) is employed to rank all the alternatives. Subsequently, a case study of MSE/MSS of a smart bike-sharing company is presented. Finally, some valuable managerial suggestions are provided through the results of sensitivity analysis and comparative analysis. [ABSTRACT FROM AUTHOR]

Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the flexibility and robustness it introduces into the decision process. This paper defines several simplified neutrosophic linguistic distance measures and employs a distance-based method to determine criterion weights. Then, an improved MULTIMOORA approach is presented by integrating the simplified neutrosophic linguistic normalized weighted Bonferroni mean and simplified neutrosophic linguistic normalized geometric weighted Bonferroni mean operators as well as a simplified neutrosophic linguistic distance measure. This approach ranks alternatives according to three ordering methods, and then, uses dominance theory to combine the three rankings into a single ranking. Finally, this paper presents a practical case example and conducts a comparative analysis between the proposed approach and existing methods in order to verify the feasibility and effectiveness of the developed methodology. [ABSTRACT FROM AUTHOR]

For many companies, green product development has become a key strategic consideration due to regulatory requirements and market trends. In this paper, the life cycle assessment technique is used to develop an innovative multi-criteria group decision-making approach that incorporates power aggregation operators and a TOPSIS-based QUALIFLEX method in order to solve green product design selection problems using neutrosophic linguistic information. Differences in semantics as well as the risk preferences of decision-makers are considered in the proposed method. The practicality and effectiveness of the proposed approach are then demonstrated through an illustrative example, in which the proposed method is used to select the optimum green product design, followed by sensitivity and comparative analyses. [ABSTRACT FROM AUTHOR]

In this paper, two optimisation models are established to determine the criterion weights in multi-criteria decision-making situations where knowledge regarding the weight information is incomplete and the criterion values are interval neutrosophic numbers. The proposed approach combines interval neutrosophic sets and TOPSIS, and the closeness coefficients are expressed as interval numbers. Furthermore, the relative likelihood-based comparison relations are constructed to determine the ranking of alternatives. A fuzzy cross-entropy approach is proposed to calculate the discrimination measure between alternatives and the absolute ideal solutions, after a transformation operator has been developed to convert interval neutrosophic numbers into simplified neutrosophic numbers. Finally, an illustrative example is provided, and a comparative analysis is conducted between the approach developed in this paper and other existing methods, to verify the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made. [ABSTRACT FROM AUTHOR]

In this paper, a new outranking approach for multi-criteria decision-making (MCDM) problems is developed in the context of a simplified neutrosophic environment, where the truth-membership degree, indeterminacy-membership degree and falsity-membership degree for each element are singleton subsets in [0,1]. Firstly, the novel operations of simplified neutrosophic sets (SNSs) and relational properties are developed. Then some outranking relations for simplified neutrosophic number (SNNs) are defined, based on ELECTRE, and the properties within the outranking relations are further discussed in detail. Additionally, based on the outranking relations of SNNs, a ranking approach is developed in order to solve MCDM problems. Finally, two practical examples are provided to illustrate the practicality and effectiveness of the proposed approach. Moreover, a comparison analysis based on the same example is also conducted. [ABSTRACT FROM AUTHOR]

This study introduces simplified neutrosophic linguistic numbers (SNLNs) to describe online consumer reviews in an appropriate manner. Considering the defects of studies on SNLNs in handling linguistic information, the cloud model is used to convert linguistic terms in SNLNs to three numerical characteristics. Then, a novel simplified neutrosophic cloud (SNC) concept is presented, and its operations and distance are defined. Next, a series of simplified neutrosophic cloud aggregation operators are investigated, including the simplified neutrosophic clouds Maclaurin symmetric mean (SNCMSM) operator, weighted SNCMSM operator, and generalized weighted SNCMSM operator. Subsequently, a multi-criteria decision-making (MCDM) model is constructed based on the proposed aggregation operators. Finally, a hotel selection problem is presented to verify the effectiveness and validity of our developed approach. [ABSTRACT FROM AUTHOR]