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Analytical hierarchy process (AHP) has been prevailing in multicriteria decision-making (MCDM) problems. Meanwhile, the fuzzy sets family has shown great power in representing vagueness and advancing the decision quality under uncertainties. The literature well documented the foundation and advantages of their integration, such as Fuzzy AHP. However, under what conditions do such integrations surely perform better than AHP in the MCDM process is still unclear. In this paper, we pick intuitionistic fuzzy (IF) sets—one of the advanced and most prevailing members of the fuzzy sets family, and further investigate when and how to integrate IF and AHP (IF-AHP) to the best advantage. We illustrate the formulated quantitative differences between the weight of AHP and the normalized defuzzified weight of IF-AHP. We uncover the qualitative and quantitative differences between AHP and IF-AHP, and identify the conditions and strategies of using IF-AHP instead of AHP. We use data experiments to illustrate our findings and further implement two case studies based on the real scenarios of supplier selection for validation and explanation.

The aggregation of fuzzy information is a key process of MCDM methods used to deal with uncertainties. A class of aggregation methods for fuzzy information is fuzzy distance aggregation operators in which distance values are argument variables. This class of aggregation operators permits us to consider an ideal alternative in the aggregation process. But these operators fall in dealing with situations among which distance values cannot be aggregated directly. Therefore, we proposed some distance induced fuzzy operators in which distance values are order-inducing variables so that we can also consider an ideal alternative but take other parameters, also including distance values, as argument variables in an aggregation process. We analyzed the concepts, properties, and generalized forms of proposed distance induced fuzzy operators in this paper. Moreover, aiming at multi-criteria group decision-making (MCGDM), three frameworks of MCGDM methods with the proposed distance induced fuzzy operators are constructed for three different MCGDM situations, respectively. At the end of this paper, an example is used to explain the detailed processes of using the proposed frameworks to make a decision.

The problem of hotel selection involves lots of uncertain information and multiple factors and can be identified as a multi-criteria decision-making problem. Aiming at the information description, measure, and fusion of hotel selection problems, this study develops multi-criteria decision-making methods based on Z-numbers and their projection measure and fusion techniques. To manage the three-dimensional structure of Z-numbers effectively, an optimization model is introduced to determine the potential probability distributions involved in Z-numbers. Then, the module, inner product, and cosine of Z-numbers are defined, and the projection measure of Z-numbers is presented by dealing with the three-dimensional structure of Z-numbers directly. Moreover, some Z-number Choquet integral projection operators are proposed for fusing Z-number evaluation information. Subsequently, an improved Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative Form method and an innovative pairwise evaluation-based multi-criteria decision-making method are developed. Based on the ideas of content-based recommendation and collaborative filtering recommendation, the above two methods are applied to solve hotel selection problems. And the sensitivity analysis and comparison discussion are conducted to demonstrate the applicability and validity of the two methods.

In the era of uncertain information everywhere, the Probabilistic Hesitant Fuzzy sets (PHFs), utilizing the possible numbers and its possible membership degrees to descript decision-makers’ behavior, has been brought about widespread attention. Scholars from all over the world applied numerous approaches in this environment since Probabilistic Hesitant Fuzzy sets (PHFs) has been come up with, and there are still untapped territories. The TODIM (TOmada deDecisao Iterativa Multicrite´rio) method is a common decision-making method which is based on the prospect theory (PT). Unlike the other multiple criteria decision making (MCDM) methods, the TODIM method think over the bounded rationality of decision makers to choose the optimal alternative according to the decision maker’s psychological reality. In this essay, we introduce the Extended TODIM Based on Cumulative Prospect Theory (CPT) for probabilistic hesitant fuzzy multiple attributes group decision-making (MAGDM). In addition, the entropy is applied to calculate the weights between attributes. Finally, the developed method is used to solve the decision-making case study. To test the reasonability of this new method, we utilize a numerical case to compare the extended TODIM method with other methods.

Online tourist reviews are the real feeling of tourists after the journey, which have a strong reference value for potential tourists to make travel decisions. However, it is almost impossible for a potential tourist to look through the massive online reviews related to tourist attractions (TAs) so that he/she can make the most appropriate decision. To this end, this paper proposes a recommender system to rank the alternative TAs through online reviews based on aspect-level sentiment analysis and multi-criteria decision-making (MCDM) with intuitionistic and hesitant fuzzy information. In this methodology, the aspects that the experienced tourists concern are extracted from online reviews to construct a three-level evaluation system (including target layer, criteria layer and sub-criteria layer), which not only ensures the comprehensive evaluation of TAs as much as possible, but also reduces the complexity of the decision-making process. Then, the online reviews related to these sub-criteria are transformed into the corresponding intuitionistic and hesitant fuzzy performance scores through aspect-level sentiment analysis. Furthermore, in order to obtain the final ranking result that more in line with the expectations of the potential tourist, the preference information from the potential tourist and experienced tourists is integrated to determine the weights of criteria. Subsequently, the intuitionistic and hesitant fuzzy TOPSIS (IHF-TOPSIS) method is proposed to rank the alternative TAs. Finally, a case study is provided to verify the validity and applicability of the methodology.

The more attached a customer becomes toward a specific brand, the stronger the extent of customer loyalty he or she will present. However, studies on brand attachment (BA) have been limited to the perspectives of enterprises about the manner in which to consolidate customer loyalty while opinions and views of customers are absent. This study integrates the views of enterprises and those of customers to build a BA-based multi-criteria decision-making (MCDM) model and adopts consistent fuzzy linguistic preference relations (CFLPR) to conduct empirical research on three car brands, namely Lexus, Mercedes-Benz, and BMW, by analyzing differences in customers’ BA preference to the three brands and assessing management performance. Findings reveal that the customers of the two German brands, Mercedes-Benz and BMW, emphasize hedonic needs while customers of Lexus, the Japanese brand, stress on bonds of personal emotional factors. Apart from being able to measure the precise strength of customers’ BAs, this analytic model can also help enterprises to examine changes of factors concerning customers’ BA on a regular basis as well as serving as the foundation for evoking consumers’ identification about brand personality, consolidating brand loyalty, and developing marketing communications strategies.

Thermal energy is the energy from a substance in which molecules and atoms vibrate faster because of an increase in temperature. Thermal energy storage (TES) is an available energy resource for renewable energy platforms that enables them to meet sustainable technical requirements. The TES technique is divided into three categories; sensible TES, latent-heat TES, and thermo-chemical TES. The best of these techniques is selected in this research paper. Here the Interval-Valued Hesitant Pythagorean Fuzzy Set (IVPHFS) under the Normal Wiggly Mathematical Methodology is proposed and described for application to multi-criteria decision making (MCDM) technology. The MCDM methods, the Step-wise Weight Assessment Ratio Analysis (SWARA) method for determining weight values, and the Weighted Aggregated Sum Product Assessment (WASPAS) method for ranking alternative values are used employed here. The alternative values are selected based on the following criteria: capacity, efficiency, storage period, charging and discharging times, and cost

Assessment of the lecturer’s research capacity plays an important role in improving their knowledge and determining each lecturer’s contribution to the universities. To assess the lecturers’ research capacity, many quantitative and qualitative criteria are needed in the evaluation process. Therefore, lecturer’s research capacity evaluation can be viewed as a multi-criteria decision-making (MCDM) problem in vague environment. In 1985, Chen proposed arithmetic operations to deal with the generalized fuzzy numbers. However, there were some shortcomings associated with Chen’s arithmetic operations. In 2013, Dat et al. proposed an improved arithmetical operation of generalized fuzzy numbers to overcome the shortcomings of Chen’s arithmetic operations. This study aims to propose an extension of generalized fuzzy multi-criteria decision-making to evaluate the lecturer’s research capacity. In the proposed approach, the improved arithmetical operation of generalized fuzzy numbers is used to aggregate weights of criteria and ratings of alternatives versus criteria. The membership functions of the weighted fuzzy decision matrix of lecturers are further developed based on linguistic expressions. Then, a simplified centroid-index ranking approach is applied to evaluate and rank the lecturer’s research capacity. Finally, a case study is used to illustrate the efficiency of the proposed MCDM approach.

Fuzzy addition is one of the operations widely used in the application of fuzzy systems. The analytical and closed form expressions of the fuzzy additions of the generalized fuzzy numbers and the interval type 2 fuzzy numbers (IT2FS) are developed. The generalized fuzzy numbers is a non-flat and subnormal fuzzy number with different left and right shape functions. Classical fuzzy operations based on the minimum t-norm could lead to uncontrollable fuzziness. Fuzzy addition based on generalized t-norm can better control ambiguity. In order to control the ambiguity of fuzzy addition, this paper is to develop a general type 1 fuzzy set and interval type 2 fuzzy set (IT2FS) additions based on t-norm. The closed forms of the generalized IT2FS additions based on some popular t-norms are formulated. The specific analytical and closed form expressions based on Archimedean t-norms: e.g. drastic, Łukasiewicz, product and the families of Schweizer-Sklar and Yager t-norms are derived. The IT2FS are widely used to characterize the natural words, e.g. the decision making linguistic judgments, the fuzzy real time control systems with linguistic rules. Furthermore, based on the analytical T1FS additions results, the application to the linguistic multiple criteria decision making aggregation of the IT2FS additions based on t-norms is introduced. A comparative MCDM numerical example is demonstrated for the verification of the developed closed form expressions.

In the field of information fusion and decision making, integral is very common and important for aggregating a large variety of information. The integral to be used is usually nonlinear due to the nonadditive measure determined by the real world. In this study, we put forward a new nonlinear integral, which is first expressed as an interval, containing the infimum and supremum of the integrand on the nonadditive measure. Furthermore, an attitudinal nonlinear integral is defined by introducing the subjective attitude of the decision maker based on the integral interval obtained. A multi-criteria decision-making (MCDM) method considering the interaction between attribute features is developed based on the proposed attitudinal nonlinear integral and a case study is provided to demonstrate the usefulness of the decision-making method. Inspired by the golden rule representation, we define the generalized golden rule representative value of the interval integral and use it to solve the problem in the case study to illustrate its usefulness.

The statistic of global laptop shipment showed that 161.6 million laptops were sold, 65.23% more than desktop-PCs, and almost the same quantity as tablets in 2017. So, laptop demand is quite high and needs to be researched on what kind of criteria (properties) are crucial. Since there are more than one criteria, this study focuses on multi-criteria decision-making (MCDM) methods in selecting laptops. This study aims to determine the interaction between criteria, and the criteria priorities in laptop selection problem that can be added/changing new features every day and to present the findings/results to the researcher/decision-makers. DEMATEL method is used for determining the interactions which are not observed in laptop literature, and fuzzy AHP is for criteria priorities. The price and brand image of a laptop have more interrelated action than the other main criteria. According to results, the brand image is determined as the most important criteria. Along with the brand image, other/peripheral properties and price criteria have totally two-thirds priority among six main criteria. The brand image along with the price had a dominant effect on other criteria according to the interaction matrices/diagrams. This study also shows that criteria priority results should be considered along with interaction matrices/diagrams that may produce such following information: speed, storage, monitor and other/peripheral properties criteria have overall effecting feature but not strongly, while brand image is a transition criterion along with having the highest priority, and the price criterion is obviously being affected by all criteria.

The study proposes a novel, convenient and dimensionless model of multi-criteria decision-making (MCDM), hereby referred to as Grey Absolute Decision Analysis (GADA) method. The foundation of the GADA method rests upon the Absolute Grey Relational Analysis (Absolute GRA) model and the system that the method follows to produce GADA Indexes and GADA Weights. The GADA Weights represent the relative weights of decision alternatives under given criteria. The method can handle both positive (“higher the better”) and negative (“lower the better”) criteria simultaneously in its algorithm. The method can deal with problems involving uncertainty and incomplete data. Two practical cases have been presented in the study to demonstrate the feasibility of the method. Furthermore, the GADA Weights obtained for the cases show that these values are comparable to the relative weights obtained through the traditional methods like AHP and SAW thus signifying the feasibility of the method. However, the conventional methods do not consider the mutual association between the judgments of the members of decision-making group (experts’ opinions), a weakness that the proposed method overwhelms. Therefore, the overall ranking obtained from the proposed method is acceptable, especially under the uncertain environment where the nature of mutual association between the judgments is not precise. The key benefit of the method lies in its adaptability to different scales of measurement. Also, it can provide relative weights and rankings of experts, criterion and alternatives. These benefits make the GADA method significant among the class of MCDM methods.

Online customer reviews (OCRs) provide much information about products or service, but the mass of information increases the difficulty for customers to make decisions. Thus, we establish a multi-criteria decision making (MCDM) model to evaluate products or service. To analyze OCRs, the sentiment analysis (SA) is introduced to identify the sentiment orientation of reviews. Considering that the textual information in OCRs is linguistic information, probabilistic linguistic term sets (PLTSs) are applied to present the results of the SA. A process of extracting probabilistic linguistic information based on SA from OCRs is also presented. Then, for the MCDM problems with unknown criteria weights, we combine the PP (projection pursuit) method and the MULTIMOORA (multiplicative multi-objective optimization by ratio analysis) method, and develop an extended method (named as the PP-MULTIMOORA method). The projection pursuit (PP) method is developed to derive objective criteria weights and the MULTIMOORA method is to derive final rankings of products or service. Finally, we apply the proposed model to a case of evaluating doctors’ service quality and further conduct a comparative analysis to illustrate the effectiveness of our work.

As a multi-disciplinary process, planning of public transportation systems needs special attention from several groups of stakeholders such as passengers, transportation planners, system providers, and so on. Since each stakeholder has dissimilar viewpoints on the evaluation of the public transportation systems, they have contradictory goal and objectives. In this sense, multi-criteria decision-making (MCDM) provides an important procedural outline for the evaluation of public transportation alternatives. This paper presents an application of MCDM method to assess the public transportation alternatives designed for a public university in a large-sized metropolitan area. Two alternatives of MCDM methods, named Interval-Valued Intuitionistic Fuzzy Analytical Hierarchy Process & COmbinative Distance-based Assessment (IVIF-AHP & CODAS), are integrated in the evaluation process. The proposed method ensures consistent and reasonable results and provides suggestions for the forthcoming progresses of public transportation service quality. In order to validate robustness of the proposed method, sensitivity analyses are implemented. Also, at the end of the study, to prove the superiority of the proposed approach, a comparative analysis is employed.

Evidential reasoning (ER) approach is a representative method for analyzing uncertain multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problems. Its core is ER algorithm used to combine belief distributions on criteria, which is developed based on Dempster’s rule of combination and probability theory. The ER algorithm is nonlinear and more computationally complex than linear combination of belief distributions. To address the necessity of the ER algorithm in MCDM and MCGDM, it is compared with linear combination from three perspectives by simulation. The first is to examine differences between the aggregated assessments derived from the ER algorithm and linear combination. The second is to examine error rates of best alternatives derived from two combination ways. The third is to examine alternative ranking differences derived from two combination ways. To facilitate the comparison, difference between aggregated assessments is designed and score function of alternative is developed from the expected utilities of alternative. Simulation experiments show that differences between the aggregated assessments are influenced by the number of assessment grades, and error rates of best alternatives and alternative ranking differences are influenced by the numbers of criteria and alternatives.

We propose a novel method for hesitant fuzzy linguistic decision making by utilizing Dempster–Shafer (D–S) theory of evidence. First, we propose some novel operations of hesitant fuzzy linguistic term sets (HFLTSs) on the basis of closed operations on linguistic 2-tuples and distribution linguistic average aggregation (DLAA) operators. These novel operations not only avoid information loss and operational results exceeding the boundary of linguistic term sets, but also make the aggregation results interpretable. Then, we define the hesitant fuzzy linguistic Archimedean weighted arithmetic mean (HFLAWAM) and hesitant fuzzy linguistic Archimedean weighted geometric mean (HFLAWGM) operators of HFLTSs. These two proposed operators are able to overcome the shortcomings of the existing approaches to multicriteria decision making (MCDM) with HFLTSs. Then, to take into account the novel operations of HFLTSs and the MCDM under uncertainty, we propose the belief structure-HFLAWAM (BS-HFLAWAM) and belief structure-HFLAWGM (BS-HFLAWGM) operators of HFLTSs. After that, we create an approach to handle the hesitant fuzzy linguistic MCDM problems in light of proposed operators. Finally, we apply the created approach to a MCDM problem regarding political management of a country.

The evaluation of green supply chain management (GSCM) practices is a typical multi-criteria decision making (MCDM) problem. Considering widely existed uncertainty, evaluating GSCM practices in a fuzzy environment becomes a fuzzy MCDM issue. Traditional fuzzy MCDM approaches solve the issue usually through fusing the fuzzy assessments on different criteria for each alternative. In the process, the fuzzy uncertainty of every assessment has been given much attention; however, the non-exclusiveness between fuzzy linguistic variables is often ignored especially when combining the fuzzy assessments. In this paper, the non-exclusiveness between fuzzy assessments represented by linguistic variables is fully taken into consideration. A theory called D number theory, as an extension of Dempster–Shafer theory, is used to deal with this non-exclusiveness. Based on D number theory, a novel method is proposed to evaluate GSCM practices in the fuzzy environment. The main contribution and advantage of the proposed method is being able to simultaneously cope with fuzziness, ambiguity, and non-exclusiveness involved in the process of evaluating GSCM practices. A numerical example and related analysis are provided to show the effectiveness of the proposed method.

The probabilistic linguistic term sets (PLTSs) are very powerful in solving the multi-criteria decision-making (MCDM) problems. The previous comparison methods associated with PLTSs are finite and unreasonable. Hence, developing a more effective way to compare PLTSs and proposing a reasonable decision-making method to cope with MCDM problems are important work of this paper. Firstly, a new possibility degree is proposed and a visual comparison method is given to present the process of comparing PLTSs. Subsequently, a similarity measure for PLTSs is also proposed to make up for the lack of similarity measure. Combining the new comparison method with the similarity measure, the TOPSIS is extended to solve real-life problems under probabilistic linguistic environment. Finally, a numerical example considers the selection of public opinion monitoring systems and the comparative analyses are shown to illustrate the effectiveness of the proposed method.

The final values of alternatives usually are fuzzy numbers in most decision making problems under uncertain environment. These fuzzy numbers need to be defuzzified by a ranking method to assist in decision making. Chen proposed ranking fuzzy numbers with maximizing set and minimizing set as an improvement on Jain’s maximizing set method. Liou and Wang indicated that ranking of any two fuzzy numbers by Chen’s method may be altered when xmax, xmin and k are changed. To solve this problem, Liou and Wang proposed ranking fuzzy numbers with integral value. However, the problem of Chen’s method remains. This work proposes relative maximizing and minimizing sets to improve upon Chen’s method. Comparative examples are provided to demonstrate advantages of the proposed ranking method, and an experiment is conducted to show its robustness. The proposed ranking method is applied to a fuzzy multiple criteria decision making (MCDM) model to present its applicability. Ranking procedure can be clearly displayed to enhance execution efficiency of the suggested fuzzy MCDM model. A numerical example is used to display feasibility of the proposed model. Finally, an experiment is investigated to show that the proposed ranking method improves upon Chen’s method in consistently ranking the final fuzzy numbers in the suggested fuzzy MCDM model.

Multiple-criteria decision-making (MCDM) is an important branch of operations research which judges multiple criteria under decision-making environments. In the process of handling MCDM problems, because of the subjective judgment of human beings, it unavoidably involves a variety of uncertainties, like imprecision, fuzziness and incompleteness. The D numbers, as a reliable and effective expression of uncertain information, has a good performance to handle these types of uncertainties. However, there still are some spaces to be further researched. Therefore, a novel belief entropy-based method with regard to D numbers is proposed for MCDM problems. Finally, an application in the MCDM problem is illustrated to reveal the efficiency of the proposed method.

How to select the optimal supplier is an open and important issue in supply chain management, which can be considered as a multi-criteria decision-making (MCDM) problem. The assessment of experts plays a very important role in the process of supplier selection, while their subjective judgment could produce unpredictable uncertainty. However, existing methods cannot represent and deal with the uncertainty effectively. Dempster–Shafer evidence theory (D–S theory) is widely used in uncertainty modeling, decision-making and conflicts management due to its advantages of handling uncertain information. The VIKOR method has a great advantage to handle MCDM problems with non-commensurable and even conflicting criteria, and to obtain the compromised optimal solution. In this paper, the DS-VIKOR method is proposed for supplier selection problem, which expends the VIKOR method by D–S theory. In the proposed method, the basic probability assignment is used to denote the assessment of domain experts for alternatives, Deng entropy weight-based method is defined and applied to determine the weights of multi-criteria, and VIKOR method is used to get the final ranking results. A numerical example for supplier selection is conducted to analyze and demonstrate the practicality and effectiveness of the proposed DS-VIKOR method.

Bipolar fuzzy set theory, an extension of fuzzy set theory, deals with incomplete and vague information. The purpose of this research paper is to develop new methodologies in handling multi-criteria decision-making (MCDM) problems where the subjective data given by a decision maker are expressed with bipolar fuzzy information. Every alternative has a rating consists of two parts: positive and negative. The positive part represents the benefit (or satisfaction degree) and the negative part represents the cost (or dissatisfaction degree) of the alternative on the corresponding criterion. In this paper, we present bipolar fuzzy TOPSIS (BF-TOPSIS) method and bipolar fuzzy ELECTRE I (BF-ELECTRE I) method for solving MCDM problems that are equipped with bipolar fuzzy information. We illustrate our proposed methods with examples. We design algorithms of BF-TOPSIS method and BF-ELECTRE I method. We also give comparison of BF-TOPSIS method and BF-ELECTRE I method.

This paper primarily focuses on multi-criteria decision-making (MCDM) based on picture 2-tuple linguistic information. Since the picture 2-tuple linguistic set is structured by a linguistic 2-tuple and a picture fuzzy set, we first point out the inappropriateness of existing operations relating to picture fuzzy numbers and picture 2-tuple linguistic numbers. For the purpose of improving these misleading computations, we further propose novel operational laws for picture 2-tuple linguistic numbers from a correct version. Counterexamples, which are in one-to-one correspondence with the listed counterintuitive cases, are furnished to illustrate the limitations of existing operations and prove the feasibility of our newly presented operations. Moreover, by applying the novel operations, we put forward some modified aggregation operators which are further employed to a handling method for the MCDM problem with a picture 2-tuple linguistic matrix. Finally, two comparative and illustrative examples are furnished to verify the applicability and advantages of the proposed method.

Supplier selection is a common and important problem, which is usually modeled in a multi-criterion decision-making framework. In this framework, multiple criteria need to be determined and an expert team needs to be constructed. Generally, different criteria and experts always hold different weights. Due to the complexity of the practical problems, sometimes lots of fuzzy and uncertain information exists inevitably and the weights are tough to determine accurately. Interval number is a simple but effective method to handle the uncertainty. However, most current papers transform an interval number to a crisp number to make decisions, which causes loss of information more or less. To address this issue, a new evidential method based on interval data fusion is proposed in this paper. Dempster–Shafer evidence theory is a widely used method in a supplier selection problem due to its powerful ability in handling uncertainty. In our method, the criteria and decision makers are weighted in the form of interval numbers to generate interval basic probability probabilities, which represent the supporting degree to an event in Dempster–Shafer evidence theory. The obtained interval basic probabilities assignments are fused to make a final decision. Due to the properties of interval data, our method has its own specific advantages, like losing less information, providing different strategies for decision making and so on. The new method is proposed aiming at solving multi-criterion decision-making problems in which the reliability of decision makers or weights of criteria are described in the form of fuzzy data like linguistic terms or interval data. A numerical example of supplier selection is used to illustrate our method. Also, the results and comparison show the correctness and effectiveness of the new interval data fusing evidential method.

The hesitant fuzzy linguistic term set (HFLTS) has gained great success as it can be used to represent several linguistic terms or comparative linguistic expressions together with some context-free grammars. This new approach has enabled the analysis and computing of linguistic expressions with uncertainties and opened the door for the possibility to develop more comprehensive and powerful decision theories and methods based on linguistic knowledge. Lots of new approaches and proposals for decision-making problems have been proposed to overcome the limitations of previous linguistic decision-making approaches. Now and in the future, decision-making methodologies and algorithms with hesitant fuzzy linguistic models would be a quite promising research line representing a high-quality breakthrough in this topic. To facilitate the study on HFLTS theory, this paper makes a state-of-the-art survey on HFLTSs based on the 134 selected papers from Web of Sciences published from January 2012 to October 2017. We justify the motivation, definitions, operations, comparison methods and measures of HFLTSs. We also summarize the different extensions of HFLTSs. The studies on multiple criteria decision making (MCDM) with HFLTSs in terms of aggregation operators and MCDM methods are clearly reviewed. We also conduce some overviews on decision making with hesitant fuzzy linguistic preference relations. The applications, research challenges and future directions are also given.

The supplier selection plays an important role in supplier chain management. How to evaluate the performance of suppliers is still an open issue. Multi-criteria decision-making (MCDM), due to its ability of solving multi-source information problem, has become a quite effective tool. Currently, the analytic network process (ANP) and Entropy weight are employed to solved MCDM problems. However, these techniques ignore the one-sidedness of the single weighting method and cannot deal with the uncertainties of input data. In this paper, a new evidential ANP methodology based on game theory is proposed to efficiently address supplier management under uncertain environment. First, ANP and entropy weight are employed to obtain the subjective and objective weights of criteria. Second, based on decision-making trial and evaluation laboratory (DEMATEL) and game theory, the comprehensive weight of ANP and entropy weight can be determined. Game theory is employed to combine the merits of subjective weight and objective weight, and DEMATEL is adopted to adjust the weight of criteria to make the result more reasonable. Finally, evidence theory is adopted to deal with the uncertainties of input data and get the supplier selection result. A case study is given to demonstrate the proposed modeling process. By comparing with the existing methods, we demonstrate that the proposed model has many advantages and it shows the efficiency and rationality in supplier selection problem.

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.

Because gross domestic product is a deficient measure of well-being, designing well-being indicators has become a new international trend for informing government policies to better citizens’ lives. To facilitate achieving this goal, governments must establish sustainable, sufficient material living conditions and quality of life and attempt to understand citizens’ real needs. Given that analyzing well-being involves imprecise information, a fuzzy multiple criteria decision-making (MCDM) model is conducive to addressing the complex interrelationships among all indicators. Therefore, this paper proposes a hybrid fuzzy MCDM model that could facilitate strategizing for better life development. With aspiration levels based on the well-being indicators of the Organization for Economic Cooperation and Development, the proposed model combines the fuzzy DEMATEL technique, fuzzy DEMATEL-based analytic network process, and modified fuzzy VIKOR methods to process the interrelationships among all indicators and select the most pressing factors requiring improvement and development. A case study was used to demonstrate the effectiveness of the proposed fuzzy model. The empirical results attested that the proposed fuzzy model is superior to the traditional fuzzy model, identifying that for Taiwan, the “air pollution” criterion in the “environment” dimension is the most pressing issue to be addressed.

Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively.

There have always been problems associated with managing vague or imprecise information, and therefore, various tools have recently been investigated to handle this uncertainty. In this study, hesitant intuitionistic fuzzy sets are introduced to resolve situations where decision-makers hesitate in selecting between several intuitionistic fuzzy values when assessing alternatives. Furthermore, new operations, based on the Archimedean t-norms and t-conorms, are developed and corresponding properties and the ranking method of HIFNs are also investigated. Additionally, the hesitant intuitionistic fuzzy weighted averaging operator and the hesitant intuitionistic fuzzy power weighted averaging operator based on the Archimedean t-norms and t-conorms are proposed to aggregate decision-makers’ information in multi-criteria decision-making (MCDM) problems, and an approach to MCDM problems that employ hesitant intuitionistic fuzzy information is constructed based on the proposed aggregation operators. Lastly, an example of selecting project is investigated to verify the applicability and validity of the proposed approach and the study is supported by comparative analyses.

Simplified neutrosophic sets (SNSs) can effectively solve the uncertainty problems, especially those involving the indeterminate and inconsistent information. Considering the advantages of SNSs, a new approach for multi-criteria decision-making (MCDM) problems is developed under the simplified neutrosophic environment. First, the prioritized weighted average operator and prioritized weighted geometric operator for simplified neutrosophic numbers (SNNs) are defined, and the related theorems are also proved. Then two novel effective cross-entropy measures for SNSs are proposed, and their properties are proved as well. Furthermore, based on the proposed prioritized aggregation operators and cross-entropy measures, the ranking methods for SNSs are established in order to solve MCDM problems. Finally, a practical MCDM example for coping with supplier selection of an automotive company is used to demonstrate the effectiveness of the developed methods. Moreover, the same example-based comparison analysis of between the proposed methods and other existing methods is carried out.

The aim of this paper is to develop an approach to solve the multiple criteria decision making (MCDM) problems under the hesitant fuzzy environment, in which the criteria values take the form of the hesitant fuzzy elements (HFEs) and the information about criteria weights are correlative. Based on the λ-fuzzy measure, we firstly get the weight vector of the criteria. Secondly, we propose the linear assignment method to acquire the optimal preference ranking of the alternatives according to a set of criteria-wise rankings and a set of criteria importance within the context of HFEs on the basis of the Hesitant Euclidean distance. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Financial performance evaluation is a very crucial process for industries in current highly competitive environment. Therefore, designing an accurate and appropriate performance evaluation framework is beneficial for insiders and also shareholders of a company. To evaluate financial performance, we need to consider some financial indicators that reflect the competitiveness of a company. There are many financial indicators and criteria that are vague and can be regarded as a fuzzy multiple criteria decision-making (MCDM) problem. In this paper, we developed a new financial performance evaluation framework to rank the companies in Iranian petrochemical industry based on fuzzy MCDM approach. To achieve this aim, firstly, the main criteria are identified by comprehensive literature review and experts’ opinion. Then, a hierarchical financial performance evaluation model is structured using main financial criteria and their sub-criteria. We used fuzzy analytic hierarchy process to determine the weights of the criteria. Then companies are ranked using fuzzy AHP and fuzzy TOPSIS comparatively. The results indicate that the obtained ranks of the companies by these methods are almost the same with respect to their own sectors.