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Livestock and poultry manure is usually recycled to the nearby cropland as it is rich in elements required for crop growth. It is necessary to measure the pollution risk caused by recycled manure. In this study, a risk assessment model based 2-tuple linguistic is constructed to evaluate the pollution risk. Firstly, based on pollution source factors and migration factors, the index system is established, which includes nominal indexes and quantitative indexes. The 2-tuple linguistic method converts two attribute indexes into one form. Meanwhile, the firework algorithm is adopted to make the weights of indicators objective. Then, livestock and poultry farms in Xinzhou District, Wuhan City, Hubei Province, are taken as the empirical objects to get the spatial distribution of farms' risk. Through the index ablation experiment and sensitivity analysis, it is found that the soil resistance factor, manure removal method and the river channel distance are the main influencing indexes. Targeted improvement of these three influencing indicators can reduce the pollution risk by manure. [ABSTRACT FROM AUTHOR]

Cholecystitis is a common disease with a high incidence, and attracts much attention. It not only harms human health, but also affects quality of work and life. Therefore, the choice of a suitable treatment is badly important for patients. In this paper, a novel selection model of treatments for cholecystitis based on hybrid multiple-criteria group decision-making (MCGDM), which is helpful to choose the most suitable treatment in the case of asymmetric information between doctors and patients. Subsequently, subjective and objective criteria are comprehensively taken into account in the index system of the selection model for cholecystitis, and combines 2-tuple linguistic with quantitative data analysis. Besides, the evaluation information obtained from the patient's conditions, the treatment and the hospital's medical status, etc., including real numbers, interval numbers, and linguistic labels with multi-granularity, is more complete and real. And the 2-tuple linguistic model is used to unify the non-homogeneous information, so the treatment selection is accurate and reliable. Simultaneously, for the unknown index and criteria weight, the improved entropy weight method and the BWM (best-worst-method) are utilized to figure out the index weight and criteria weight, respectively. Further, TODIM (an acronym in Portuguese for interactive and multi-criteria decision-making model) method based on the prospect theory is applied to solve the prioritization of cholecystitis treatments, and give full consideration to the decision maker of risk aversion. Eventually, an empirical study of treatment selection for cholecystitis is conducted. Sensitivity analysis and comparative analysis indicate that the proposed selection model of treatments for cholecystitis patients is reliable and effective.

Probabilistic linguistic term set can give different degrees of preference by assigning corresponding probabilities through linguistic set. This paper used probabilistic linguistic term set to obtain the hesitant and uncertain evaluation information of the experts. Aiming at the problem that the weights of indicators in traditional multi-criteria decision-making method did not consider the mutual influence relationships between indicators, it used probabilistic linguistic to analysis the net influence of the indexes and used 2-tuple linguistic to convert the PLTS' s score of the mutual influence relationships between indicators into precise values, then it obtained the weight of the indexes. Considering the different preferences and psychological behaviors of the decision makers, it used the improved TO DIM method of PLTS to evaluate candidate schemes. Finally, a case study of the liner companies' comprehensive competitiveness ranking shows that this method can illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on multi-attribute two-sided matching with 2-tuple preferences. A new framework consisting of paring process and feedback process is proposed to generate matching results (couples) in multiple stages. According to the assumption that matching couples should be satisfied with each other, the concept of expected matching ordinal (EMO) is defined and used for filtering unqualified couples in each stage. To derive optimal results, payoff matrices and preference ordinals are firstly obtained on the basis of the preferences given by two-sided players. The paring process formulates a bi-objective optimization model to generate primary matching couples based on the payoff matrices. Subsequently, the feedback process identifies targeted couples from them with the EMO constraint. This mechanism is performed to ensure that matching couples are all mutually satisfied. The novelty of our approach is that we manage matching decisions by balancing individual benefit and party's benefit. Finally, a practical example is given to illustrate the proposed approach and comparison analysis shows the advantages of our approach. Some related issues are further discussed. [ABSTRACT FROM AUTHOR]

Voice-driven adaptive cooperative systems have been widely used. However, the ambiguity of the voice-based task goals remains a challenge. How to integrate fuzzy task goals into adaptive cooperative systems to make decisions is a problem that should be resolved imperatively. We propose a fuzzy voice-driven self-adaptive cooperative framework and a corresponding decision method. Firstly, the system publishes tasks, submits tenders and makes decisions based on the market-based approach. Secondly, multi-attributes evaluation information is transformed into 2-tuple linguistic and the VIKOR method is used to rank the candidates. Finally, we take the heterogeneous robot self-adaptive cooperative system as an example to illustrate the decision-making steps of the proposed method, and the experimental results verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, the method based on 2-tuple linguistic is proposed to evaluate the adaptability of the emergency response plan. In this model, dynamic weights are introduced to empress different stages of the emergency. The variables are constructed to measure the correlation between the indexes in the method. Also, the indexes are constructed to evaluate the adaptability of the emergency response plan according to the characteristics of the emergency. For illustration and verification purposes, the case of sudden event from the Longjiang River cadmium pollution of Guangxi province in China is presented. Experimental results obtained demonstrate that the proposed 2-tuple linguistic methodology can improve the evaluation for the adaptability of emergency response plan. [ABSTRACT FROM AUTHOR]

Consumers equipped with standby electric source will become electricity providers at particular moments in the future smart grid. From the perspective of smart grid risk management, this paper concludes the supply risk factors that may lead to the dissatisfaction of consumer demands for security, quality and benefit, which are further classified to supply risk elements. Then the mapping relations between supply risks and consumer demands is established. For the risk assessment problem involving consumer demands and power supply risk, a risk assessment model based on catastrophe theory and 2-tuple linguistic representation is proposed. Firstly, the experts' linguistic variables are converted to 2-tuples linguistics, and catastrophe theory expands operations from real numbers to linguistic variables. Secondly, combining the expert subjective weights in the form of linguistic, a compromised weighting method based on similarity and deviation is proposed. Subsequently, the ranking results are obtained according to the total catastrophe 2-tuple linguistic value of each supply risk element. The ranking results are helpful for power supply companies to identify important risks and develop risk aversion strategies. At last, the feasibility and effectiveness of the proposed method is proved by contrastive analysis. Therefore, the study could provide reference for future smart grid risk management. [ABSTRACT FROM AUTHOR]

Low-speed wind farm site selection is crucially important for investment returns. However, three great problems reducing the decision-making accuracy and restricting applications exist in the present multiple criteria decision analysis. Firstly, the uncertainty of information fails to be fully described, without considering its randomness. Secondly, during dimensionless treatment and normalizing, some information distortion and loss are caused when evaluating the differences among criteria values just from a mathematical standpoint. Thirdly, the managers are excluded from the decision-making process, which decreases the practicality and operability, and considerably restricts the application of the decision-making methods at the same time. In order to overcome these deficiencies, a cloud-based decision framework under pure 2-tuple linguistic environment is proposed for low-speed wind farm site selection in this paper. First, the criteria values are transformed into 2-tuple linguistic through dimensionless treatment and normalizing; then the extended golden section method is used to transform 2-tuple linguistic into cloud variable. Next, a pure cloud weighted arithmetic averaging operator is constructed to rank the alternatives. After that a case from China is presented to demonstrate the effectiveness. Finally, the comparison analysis and sensitive analysis are conducted, proving the correctness and advantages of the proposed decision framework. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators. [ABSTRACT FROM AUTHOR]

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM PUBLISHER]

For actual decision making problems, decision makers sometimes may have difficulty to provide all the preference information over alternatives through pairwise comparisons. In this paper, we focus on estimating missing elements for an incomplete uncertain 2-tuple linguistic preference relation. First, the additive consistency of an uncertain 2-tuple linguistic preference relation is defined. Based on the defined additive consistency, we define acceptable incomplete uncertain 2-tuple linguistic preference relation and propose two new algorithms, including an iterative algorithm and an optimization-based algorithm to estimate the missing elements for an uncertain 2-tuple linguistic preference relation. Finally, some numerical examples are presented to illustrate the applicability of the two algorithms.

Aiming at the problem of evaluation information was subjective and uncertain in product scheme selection process, and some shortcomings of existing research about product scheme selection, a new approach based on information axiom with 2-tuple linguistic was proposed. Firstly, the method converted the linguistic assessment information of each expert to 2-tuple linguistic, the group's 2-tuple linguistic decision matrix and the attribute weights vector of product schemes were calculated according to the 2-tuple linguistic aggregation operator,and the attribute combination weights vector was determined. Then the 2-tuple linguistic information content of product schemes were calculated based on information axiom and the best scheme was obtained with information content. The results in indicate that the proposed method can avoid the information loss in transferring and integrating the linguistic evaluation, combination weighting of attributes can fully reflect the subjective and objective, and the calculation is simple, accurate and effective in the product design scheme decision process, it has potentially practical value. [ABSTRACT FROM AUTHOR]

Theory Decision Making describes the steps that includes the development of this, the difficulties presented by adding multigranular linguistic information, numerical and linguistic information. In turn, explain how to adapt the model to avoid loss of information during the combinatorial to be undertaken in the aggregation process. Once contextualized the background, an example to which the application of theory to explain organizational case develops. This case is the adequacy of the installation of an ERP (Enterprise Resource Planning) in a company, where shall take into account the limitations, and based on these, the generation of factors that will figure out a solution. [ABSTRACT FROM AUTHOR]

Because of the difficulties and low efficiency of the failure diagnosis of complex equipment, an integrated model of FMEA and QFD based on grey two-tuple linguistic evaluation method is proposed to prioritize the failure modes. FMEA and QFD are two commonly used quality management tools with similarity and complementarity, the 2-tuple linguistic is used to improve the accuracy of the grey linguistic evaluation information. Besides, the entropy method is used in this integrated model to determine the risk assessment indicators ' weights. Finally, an example is used to illustrate the applicability of the integrated model. [ABSTRACT FROM AUTHOR]

Decision makers often express their evaluations on decision problems with multi-granular linguistic terms. This fact leads to the unification of the multi-granular linguistic terms into a single linguistic set in the literature. However, this unification process increases the complexity of computation and the subjectivity in the determination of transformation functions. To overcome this deficiency, this paper aims to develop a normalized numerical scaling method for determining the semantics of multi-granular linguistic terms in the same domain. We first introduce a class of numerical scaling functions to generate several balanced or unbalanced linguistic sets. Since these scaled linguistic sets have different domains, we then develop a normalized numerical scaling method to form them into the unique interval [0,1]. As a result of this development, two classes of normalized scaling functions are derived from the priori scale information and applications of piecewise linear interpolation and piecewise arc interpolation. Finally, an example is given to illustrate how the method works. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop an interactive approach for multiple attribute decision making with incomplete weight information under linguistic environment. Some of the concepts are defined, such as the distance between two 2-tuple linguistic variables, the expectation level of alternative, the achievement scale, the alternative comprehensive scale under linguistic environment. Based on these concepts, we establish some linear programming models, through which the decision maker interacts with the analyst. Furthermore, we establish a practical interactive approach for selecting the most desirable alternative(s). The interactive process can be realized by giving and revising the achievement scale and comprehensive scale of alternatives till the achievement scale and the comprehensive scale are achieved to the decision maker's request. Finally, an illustrative example is also given.

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method. [ABSTRACT FROM AUTHOR]

In order to successfully realize the stable and sustainable execution of supply chain for complex product, it is important to improve the performance evaluation mechanism for suppliers of complex product Owing to the complexity of performance evaluation for complex product suppliers and the fact that expert's grasping degree for evaluation attribute information is not adequate and different, a linguistic evaluation approach of supplier performance for complex product was proposed in this study via taking grey information into account Firstly, the evaluation information of experts was transformed into a combination of grey information and two-tuple linguistic, and the degree of greyness was applied to measure the grey part of linguistic evaluation information. Then the geometric means of grey-levels of linguistic evaluation information corresponding to each expert was computed to adjust experts' weights on each index, thus the expert s evaluating viewpoints were gathered to obtain the rating and weight for each index as a result of group evaluation. Based on that, weighted averaging operator was utilized to integrate the group evaluation information to get the comprehensive evaluation result for suppliers' performance, and the ranking of each supplier was gained through constructing quadratic function. Finally, this method was applied to evaluate the supplier performance in a large passenger aircraft project, and the information loss and distortion emerging in collecting and calculating linguistic evaluation information could be effectively avoided. Thus, the proposed approach was able to provide decision makers richer and more accurate information. [ABSTRACT FROM AUTHOR]

Abstract: We establish in this paper the optimization model of group consensus of 2-tuple linguistic preferential relations (LPRGCO Model), put forward three kinds of solutions to this model, and discover in it the convergence of group consensus. To detect the LPRGCO Model, we first build two kinds of optimal matrices as standards to measure the group consensus of 2-tuple linguistic preference relations (LPRs). And to analyze consensus deviations, we then adopt three types of measures, namely, the individual degree of consistency regarding alternative decision pairs, the deviational degree of the group consensus regarding alternative decision pairs, and the degree of group consensus regarding the original 2-tuple LPRs. On the basis of the previous analysis we not only construct an optimization model to probe into the deviation of the group consensus of 2-tuple LPRs by minimizing the weighted arithmetic average of deviation degrees of individual consistency, but also point out three feasible solutions to this optimization model: the optimal solution, satisfactory solutions, and non-inferior solutions. Accordingly, we discover different conditions in terms of the three solutions. And hence, we can from the aforementioned discussion draw a conclusion that the deviation of group consensus either decreases or stays invariant as the number of decision makers (DM) increases. To expatiate on the practical value of the model proposed, we will display in this paper numerical examples. [Copyright &y& Elsevier]

Abstract: With respect to 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate. [ABSTRACT FROM AUTHOR]

Considering the character of grey cluster decision-making and 2-tuple linguistic assessment, this paper proposes the method of 2-tuple linguistic assessment based on grey clustering. It can combine qualitative analysis and quantitative analysis well. In the end, an empirical study on commercial banking regulation based on this method is given to improve this method's validity. [ABSTRACT FROM AUTHOR]