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Decision support is a vital function in electronic commerce (e-commerce). The purpose of this paper is to construct a review-based decision support model for items comparison in e-commerce. The proposed model uses probability multivalued neutrosophic linguistic numbers (PMVNLNs) to characterize online reviews. It overcomes the limitation of existing models by considering neutral information and hesitancy in text reviews. The fuzzy characterization of reviews (i.e., PMVNLN) can reflect similarities and differences in positive (negative) information. In addition, the model considers consumers’ bounded rational behaviors by combining the regret theory with an outranking method. We empirically compare the proposed model with models in http://PConline.com and four existing models with data from http://PConline.com. The performance of these models in terms of accuracy is measured by the total relative difference metric. Results indicate the good performance of the proposed model. Our model is a promising option for e-commerce to provide consumers with good decision support service. [ABSTRACT FROM AUTHOR]

For decision makers, expressing their opinions through subintervals of [0, 1] is sometimes easier than using crisp numbers. This study defines some outranking relations derived by ELECTRE III for hesitant interval-valued fuzzy sets (HIVFSs). The properties of these outranking relations are discussed in detail. The concordance and discordance indexes of HIVFSs are then proposed. Ranking approach is developed based on the outranking relations of HIVFSs to handle multi-criteria decision-making problems. Finally, we provide practical examples, as well as sensitivity analysis and comparison with other techniques. [ABSTRACT FROM AUTHOR]

The financial risk not only affects the development of the company itself, but also affects the economic development of the whole society; therefore, the financial risk assessment of company is an important part. At present, numerous methods of financial risk assessment have been researched by scholars. However, most of the extant methods neither integrated fuzzy sets with quantitative analysis, nor took into account the historical data of the past few years. To settle these defects, this paper proposes a novel financial risk assessment model for companies based on heterogeneous multiple-criteria decision-making (MCDM) and historical data. Subjective and objective indexes are comprehensively taken into consideration in the financial risk assessment index system of the model, which combines fuzzy theory with quantitative data analysis. Moreover, the assessment information obtained from historical financial information of company, credit rating agency and decision makers, including crisp numbers, triangular fuzzy numbers and neutrosophic numbers. Furthermore, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to determine the ranking order of companies according to their financial risk. Finally, an empirical study of financial risk assessment for companies is conducted, and the results of comparative analysis and sensitivity analysis suggest that the proposed model can effectively and reliably obtain the company with the lowest financial risk. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • We develop a comprehensive structure for weighting FMEA team members with respect to each risk factor based on proximity entropy weight and similarity entropy weight. • We develop a risk factor weighting approach based on fuzzy best-worst method. • The fuzzy VIKOR method is used to obtain the risk priorities of potential failure modes. Abstract In general, analysis of failure modes and their effects requires a group of experts to tackle substantial uncertainties associated with the risk evaluation process. To date, to overcome one or more of the uncertainty-related issues, an increasing number of failure mode and effects analysis (FMEA) models based on multi-criteria decision-making (MCDM) methods have been developed. However, most of the improvements have not cautiously considered the process of assigning importance weights to risk factors and FMEA team members during FMEA. This study aims to enhance the performance of the classic FMEA and to propose an integrated fuzzy MCDM approach for FMEA. First, a fuzzy best-worst method is used to obtain the weights of risk factors. Second, an integrated structure based on fuzzy proximity and fuzzy similarity entropy weights is developed to obtain the weights of FMEA team members with respect to different risk factors. Finally, a fuzzy VIKOR (VIsekriterijumska optimizacija i KOm-promisno Resenje) approach is employed to obtain the risk priorities of failure modes. The applicability and effectiveness of the proposed approach is validated through an illustrative example concerning risk analysis of a grinding wheel system. The results of sensitivity and comparative analyses show that the proposed approach is valid and can provide valuable and effective information in assisting risk management decision-making. [ABSTRACT FROM AUTHOR]

This paper proposes two extended projection-based preference ranking organization methods for enrichment evaluations for multi-criteria decision making with hesitant fuzzy linguistic term sets (HFLTSs). We first utilize three linguistic scale functions to solve linguistic information transformation with differences in semantics. Correspondingly, we define projection and normalized projection measurements for HFLTSs. We then propose a projection-based difference measurement for HFLTSs while considering the risk appetite of decision-makers. The effectiveness and robustness of the proposals are demonstrated by their application to a practical example of green supply chain management problem, which is followed by sensitivity and comparative analyses. Finally, conclusions and future research directions are drawn. [ABSTRACT FROM AUTHOR]

Search engines are as important as recommender systems for hotel selections. However, the recommended lists of search engines are usually non-personalized and low accuracy. In order to deal with these issues in search engines, a comprehensive mechanism for hotel recommendation is proposed. In this mechanism, we consider users' personalized preferences by identifying users' attributes about interest, trust and consumption capacity. Meanwhile, the quantification method for each attribute is presented by using fuzzy theory. Moreover, this paper improves the method to evaluate the hotel, which respects to the criteria price, rating, and online review by using fuzzy theory. In addition, this proposed approach uses TOPSIS, a classical multi-criteria decision making method, to improve the accuracy further. Finally, a case study is conducted based on Tripadvisor.com to illustrate the validity of the proposed method for hotel recommendation in search engines. The results of the case study indicate that it not only solves the problem of non-personalization, but also improves the accuracy in search engine. [ABSTRACT FROM AUTHOR]

Linguistic hesitant fuzzy sets (LHFSs), which can be used to both represent decision-makers’ qualitative preferences and reflect their hesitancy and inconsistency, have attracted much attention due to their flexibility and efficiency. In this paper, some distance-based approaches for resolving multi-criteria decision-making (MCDM) problems with linguistic hesitant fuzzy information are introduced. To begin, a new order relationship between LHFSs, based on the defined LHFSs, is presented. Then, distance measures for LHFSs are proposed, which include the generalised, Hamming, and Euclidean distance measures. Additionally, some approaches for handling MCDM problems with linguistic hesitant fuzzy information are proposed, which are based on the TOPSIS, VIKOR, and TODIM methods, as well as the proposed distance measures. Finally, an illustrative example is provided to show the feasibility and usability of the methods, which are then compared with the existing method. [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]

Decision support models for satisfactory restaurants have attracted numerous researchers' attention. Many extant models do not consider the active, neutral and passive information in online reviews all at once. Moreover, they ignore the effect of interdependence among criteria on tourists' decision-making. To cover these defects, this study proposes a restaurant decision support model using social information for tourists on TripAdvisor.com . The model introduces fuzzy sets to denote online reviews and utilizes Bonferroni mean to consider interdependence among criteria. Furthermore, it uses a novel similarity measurement which can handle sparse data in fuzzy environments. To validate the model, we conduct a case study of TripAdvisor.com which compares the proposed model with four other models. The performance of each model is evaluated by the metric called the mean absolute error. The study shows that the proposed model can effectively support tourists' decision-making and it performs better than the other four models. [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]

A hesitant fuzzy linguistic set is an extension of both a linguistic term set and a hesitant fuzzy set. It combines a quantitative evaluation with a qualitative evaluation, which can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency. The focus of this paper is those multi-criteria decision-making (MCDM) problems in which the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). Having reviewed the relevant literature, the Hausdorff distance for HFLNs is provided and some linguistic scale functions are applied. Subsequently, two hesitant fuzzy linguistic MCDM methods are proposed, which are based on the proposed distance measure and the TOPSIS and TODIM methods. The first of these MCDM methods is based on complete rationality, whilst the second is based on bounded rationality. Finally, an illustrative example is provided to verify the proposed methods, which are then compared to the existing approaches. [ABSTRACT FROM AUTHOR]

In practice, when the frequency of a linguistic term in evaluation information is greater than one, a consensus has been reached and this frequency is regarded to be one by default. However, in case that the frequencies of several elements in a dataset are not identical, their respective importance that was initially distinguishable will become indifferent in a routine processing, which may distort the original intention of decision-makers. As an extension of hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic sets (HFLSs), multi-hesitant fuzzy linguistic term sets (MHFLTSs) are thus proposed on the basis of multi-hesitant fuzzy sets (MHFSs) in this paper, and each multi-hesitant fuzzy linguistic term element (MHFLTE) can contain inconsecutive and repeatable linguistic terms. Besides, inspired by the 2-tuple linguistic model and linguistic scale functions, the transformation functions among linguistic terms, 2-tuples, and numerical data are constructed in a generalized form to cope with different semantics. According to practical conditions, decision-makers' preferences, or experts' suggestions, various functions can be chosen after some necessary adjustments. In this way, the original essence of vague evaluations can be retained properly and the accuracy and reliability of final results could be further improved. Furthermore, the basic operations and comparison method of MHFLTEs are given on the basis of the transformation functions, and some 2-tuple linguistic aggregation operators of MHFLTEs are also provided to deal with problems where the criteria weights are known or unknown. Based on these prerequisites, a multi-criteria group decision-making approach is established to process multi-hesitant fuzzy linguistic information. The validity and effectiveness of the proposed approach are finally demonstrated through illustration and comparison analysis. [ABSTRACT FROM AUTHOR]

Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made. [ABSTRACT FROM AUTHOR]

In this paper, the cross-entropy of intuitionistic hesitant fuzzy sets (IHFSs) is developed by integrating the cross-entropy of intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). First, several measurement formulae are discussed and their properties are studied. Then, two approaches, which are based on the developed intuitionistic hesitant fuzzy cross-entropy, are proposed for solving multi-criteria decision-making (MCDM) problems within an intuitionistic hesitant fuzzy environment. For both methods, an optimisation model is established in order to determine the weight vector for MCDM problems with incomplete information on criteria weights. Finally, an example is provided in order to illustrate the practicality and effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attention in multicriteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds, as well as several new aggregation operators: the trapezium cloud weighted arithmetic averaging operator, the trapezium cloud ordered weighted arithmetic averaging operator, and the trapezium cloud hybrid arithmetic operator. Moreover, a method with Atanassov's interval-valued intuitionistic linguistic numbers (AIVILNs) based on trapezium clouds is presented, which can provide solutions to multicriteria group decision-making problems with Atanassov's interval-valued intuitionistic linguistic information. In this method, AIVILNs are first converted into trapezium clouds and aggregated by trapezium cloud aggregation operators. Then, the ranking of alternatives is determined by the possibility degree matrix of trapezium clouds. Finally, an illustrative example confirming the validity and feasibility of the proposed method is given. [ABSTRACT FROM AUTHOR]

Considering that interval 2-tuple linguistic model can solve the interval linguistic multi-criteria decision-making problems, and Choquet integral can deal with the multi-criteria group decision-making problems with correlated criteria, in the revelation of these two methods, this paper combined them together to cope with the interval linguistic multi-criteria group decision-making problems with correlated criteria. Because of the limitations of 2-tuple linguistic representation model, a modified composite scale based on 2-tuple linguistic model was proposed which can better improve the accuracy of decision-making. First, using Choquet integral and interval 2-tuple linguistic model, two aggregation operators with their properties were introduced to better reflect correlations among criteria, i.e., the interval 2-tuple correlated averaging operator and the interval 2-tuple correlated geometric operator. Then, a multi-criteria group decision-making method based on the above operators was proposed. Finally, the proposed method was compared with the existing ones based on the same illustrative example to confirm its feasibility and rationality. [ABSTRACT FROM AUTHOR]

In this paper, after analyzing on shortcomings of the existing score functions of intuitionistic fuzzy set (IFS), a new score function based on relative entropy is presented. The risk attitudes of the decision makers are also defined. Examples have been given to show the validity of this score function. Meanwhile, the definition of the intuitionistic normal fuzzy number and their operational laws and intuitionistic normal fuzzy weighted arithmetic averaging operator are proposed. As for the intuitionistic normal fuzzy multi-criteria decision-making problems in which criteria weights remain fixed and the criteria values of alternatives are in the form of intuitionistic normal fuzzy numbers. An intuitionistic normal fuzzy multi-criteria decision-making approach based on the relative score function is proposed. Finally, an example is provided to show the feasibility and validity of the approach. [ABSTRACT FROM AUTHOR]

To handle multicriteria fuzzy decision-making problems, a new multicriteria decision-making method is proposed in which the information about criteria's weights is not completely certain, and the criteria values of alternatives are Atanassov's intuitionistic fuzzy sets (A-IFSs). Using evidential reasoning algorithms, the criteria values are aggregated; receiving the overall A-IFS for alternatives and the distances between each alternative and the ideal, as well as anti-ideal alternative, are computed. Combining the incomplete certain information of weights, a nonlinear programming model is developed and resolved by particle swarm optimization algorithms to obtain the optimal criteria's weights. The corresponding decision-making procedure is given in detail. Finally, two examples are given to show the feasibility and availability of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper analyzes the limitations of existing score functions of intuitionistic fuzzy set. A new score function is defined based on the prospect value function, and examples are given to demonstrate the validity of this score function. As for the interval-valued intuitionistic fuzzy multi-criteria decision-making problems in which criteria weights are fixed, and the criteria values of alternatives are in the form of interval intuitionistic fuzzy numbers, an interval-valued intuitionistic fuzzy multi-criteria decision-making approach is proposed based on the prospect score function. This approach gives a matrix of score function values and a comprehensive evaluation value of each alternative. And the order of alternatives is listed by comparing the projection values of each alternative to the positive ideal solution. Finally, an example shows the feasibility and validity of this approach. [Copyright &y& Elsevier]

The smart bike-sharing program (BSP), which is a novel bike-sharing mode of traditional BSP, has become popular in many cities in China. However, most BSP studies focus only on the socio-economic characteristics of the users, bike-sharing patterns, and impacts that influence bike-sharing demand. This study increases the knowledge on BSPs by presenting a hybrid fuzzy multi-criteria decision-making approach that is based on multi-phase quality function deployment. This approach covers the performance evaluation of smart BSPs allowing for customer voices under uncertain conditions. This method combines the fuzzy best-worst method (BWM), fuzzy maximizing deviation method (MDM), and fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA). It uses fuzzy BWM to determine priorities of customer requirements and company strategies and to obtain subjective importance coefficients of criteria. Fuzzy MDM is used to derive objective importance coefficients of criteria and fuzzy MULTIMOORA is used to rank alternatives in terms of each criterion. An empirical case in Changsha, which is one of the pilot areas for comprehensively supporting the reform for an environment-friendly and resource-conserving society ("two-oriented society") in China, is provided to illustrate the application of the proposed framework. Results can help enterprises and organizations improve their performance and provide high-quality products and services for customers. [ABSTRACT FROM AUTHOR]