A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Probabilistic linguistic term sets(PLTSs)are an effective tool for expressing subjective human cognition that offer advantages in the field ofmulti-attribute decision-making(MADM).However,studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers(DMs)in certain circumstances,such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete,thus affecting their role in the decision-making process.Belief function theory is a leading streamof thought in uncertainty processing that is suitable for dealing with the limitations of PLTS.Therefore,the purpose of this study is to extend PLTS to incorporate belief function theory.First,we provide the basic concepts of the extended PLTS(i.e.,belief-based PLTS)through case analyses.Second,the aggregation operator of belief-based PLTS is defined with the ordered weighted average(OWA)-based soft likelihood function,which is improved by considering the reliability of the information source.Third,to measure the magnitude of different belief-based PLTSs,the belief interval of singleton is calculated,and the comparison method of belief-based PLTS is constructed based on probabilities.On the basis of the preceding discussion,we further develop an emergency decision framework that includes several novel techniques,such as attribute weight determination and decision information aggregation.Finally,the usefulness of the framework is demonstrated through a case study,and its effectiveness is illustrated through a series of comparisons.

Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

Multi-attribute Decision Making Method Based on the Attribute Difference Degree and Its Application in Rice Breeding

[Objective]The aim was to establish a multi-attribute decision making method and introduce its application in rice breeding.[Method]Based on the defined closeness degree among attributes,the difference degrees among attributes were discussed.Furthermore,the weights of attributes were determined based on the difference degrees among the attributes.[Result]A multi-attribute decision making method based on difference degrees among attributes was established,the feasibility of applying it in rice breeding was also analyzed.[Conclusion]This study enriched the methods to determine attribute weights in multi-attribute decision making and provided the necessary theoretical support for selecting rice varieties scientifically and rationally.

Selecting proper sites for underground dam construction using Multi-Attribute Utility Theory in arid and semi-arid regions

Although the construction of underground dams is one of the best methods to conserve water resources in arid and semi-arid regions,applying efficient methods for the selection of suitable sites for subsurface dam construction remains a challenge.Due to the costly and time-consuming methods of site selection for underground dam construction,this study aimed to present a new method using geographic information systems techniques and decision-making processes.The exclusionary criteria including fault,slope,hypsometry,land use,soil,stream,geology,and chemical properties of groundwater were selected for site selection of dam construction and inappropriate regions were omitted by integration and scoring layers in ArcGIS based on the Boolean logic.Finally,appropriate sites were prioritized using the Multi-Attribute Utility Theory.According to the results of the utility coefficient,seven sites were selected as the region for underground dam construction based on all criteria and experts’opinions.The site of Nazarabad dam was the best location for underground dam construction with a utility coefficient of 0.7137 followed by sites of Akhavan with a utility coefficient of 0.4633 and Mirshamsi with a utility coefficient of 0.4083.This study proposed a new approach for the construction of the subsurface dam at the proper site and help managers and decision-makers achieve sustainable water resources with limited facilities and capital and avoid wasting national capital.

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

A Method of Job Scheduling on SMEs' Key Equipments Based on Hybrid Multi-attribute Decision Making

An analysis of the key factors affecting on the single production process job scheduling of the parts waiting for be- ing processed on the key equipments for SMEs (Small Manufacturing Enterprises) is given in this paper,which include interval number,real number and uncertain linguistic value.A kind of hybrid multi-attribute decision making method for the single pro- duction process job scheduling is presented in this paper,that the parts are firstly sorted about each factor,and then the total evalu- ative attributive value of each part is calculated with the method of weighted arithmetic average,and thus the part with the highest total evaluative attributive value is chosen for being processed firstly.The mathematic model corresponding to the method is set up in this paper.An example is studied in this paper,and the results of the example testify the correctness of this model.

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set(SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging(SNNPWA) operator, simplified neutrosophic number power weighted geometric(SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging(SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric(SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multiattribute group decision making(MAGDM) within the framework of SNSs is developed by the above aggregation operators.Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

Multi-attribute group decision making method under 2-dimension uncertain linguistic variables

A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.

Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Dynamic Multi-Attribute Decision-Making Method with Double Reference Points and Its Application

To better reflect the psychological behavior characteristics of loss aversion,this paper builds a double reference point decision making method for dynamic multi-attribute decision-making(DMADM)problem,taking bottom-line and target as reference pints.First,the gain/loss function is given,and the state is divided according to the relationship between the gain/loss value and the reference point.Second,the attitude function is constructed based on the results of state division to establish the utility function.Third,the comprehensive utility value is calculated as the basis for alternatives classification and ranking.Finally,the new method is used to evaluate the development level of smart cities.The results show that the new method can judge the degree to which the alternatives meet the requirements of the decision-maker.While the new method can effectively screen out the unsatisfactory alternatives,the ranking results of other alternatives are consistent with those of traditional methods.

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems:Survey and Challenges

Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal object,of which prospect theory and regret theory are two widely used tools.The hesitant fuzzy set(HFS)captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades.Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together,this paper reviews and examines advances in three-way behavioral decision making(TW-BDM)with hesitant fuzzy information systems(HFIS)from the perspective of the past,present,and future.First,we provide a brief historical account of the three topics and present basic formulations.Second,we summarize the latest development trends and examine a number of basic issues,such as one-sidedness of reference points and subjective randomness for result values,and then report the results of a comparative analysis of existing methods.Finally,we point out key challenges and future research directions.

A kinetic description of the impact of agent competence and psychological factors on investment decision-making

The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agents set their own investment strategies.The herding behavior is considered when analyzing the impact of an agent's psychological factors on investment decision-making.A nonlinear Boltzmann model containing herding behavior,agent competence and irrational behavior is employed to investigate investment decision-making.To characterize the agent's irrational behavior,we utilize a value function which includes current and ideal-investment decisions to describe the agent's irrational behavior.Employing the asymptotic procedure,we obtain the Fokker-Planck equation from the Boltzmann equation.Numerical results and the stationary solution of the obtained Fokker-Planck equation illustrate how herding behavior,agent competence,psychological factors,and irrational behavior affect investment decision-making,i.e.,herding behavior has both advantages and disadvantages for investment decision-making,and the agent's competence to invest helps the agent to increase income and to reduce loss.

Game Theory Model and Equilibrium Analysis of Peasant's Production Decision

Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government＇s positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants＇ income