Solution to multiple attribute group decision making problems with two decision makers

A kind of multiple attribute group decision making （MAGDM） problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.

Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

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.

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

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 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.

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 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.

Hybrid aggregation operator and its application to multiple attribute decision making problems

By combining the advantages of the additive weighted mean (AWM) operator and the ordered weighted averaging (OWA) operator, this paper first presents a hybrid operator for aggregating data information, and then proposes a hybrid aggregation (HA) operator-based method for multiple attribute decision making (MADM) problems. The theoretical analyses and the numerical results show that the HA operator generalizes both the AWM and OWA operators, and reflects the importance of both the given argument and the ordered position of the argument. Thus, the HA operator can reflect better real situations in practical applications. Finally, an illustrative example is given.

Multiple attribute decision making method based on trapezoid fuzzy linguistic variables

The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variables（TFLV）, is studied. The formula of the degree of possibility between two TFLVs is defined, and some of its characteristics are studied. Based on the degree of possibility of fuzzy linguistic variables, an approach to ranking the decision alternatives in multiple attribute decision making with TFLV is developed. The trapezoid fuzzy linguistic weighted averaging （TFLWA） operator method is utilized to aggregate the decision information, and then all the alternatives are ranked by comparing the degree of possibility of TFLV. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision results reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a practical example.

Multiple attribute decision making based on different types of linguistic information

Distance measures between exact linguistic variables and between uncertain linguistic variables are introduced respectively. Based on exact linguistic variables and uncertain linguistic variables, the concepts of positive linguistic ideal solution and negative linguistic ideal solution of attribute values are defined. To rank and select alternatives, based on the distance measures of two types of linguistic variables and the linguistic ideal solutions, a method for multiple attribute decision making with different types of linguistic information is proposed, by which all alternatives can be ranked. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision result reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a numerical example.

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.

Multi-attribute decision-making approach dealing with uncertain linguistic assessment information

An approach is presented to deal with a multi-attribute decision-making problem in which the attribute weights are unknown and the attribute values take the form of uncertain linguistic variables. First, a linguistic assessment standard is set up to deal with the uncertain linguistic attributes, and the operation laws of uncertain linguistic variables and the uncertain linguistic weighting average(ULWA)operator are introduced. Then a ranking formula of uncertain linguistic variables based on expectation-variance is proposed. As for the case without weight information, a goal program based on a warp function is constructed to determine the attribute weights, and the ULWA operator is utilized to aggregate the assessment information of uncertain linguistic variables, and the corresponding alternatives are ranked by a formula based on expectation-variance. Finally, a numerical example is given, and the results demonstrate that it is much easier and faster for the ranking method based on expectation-variance when compared to the existing methods.

Application of Interval Multi-attribute Decision-Making Method to Aeroengine Performance Ranking

In view of the uncertainty of the monitored performance parameters of aeroengines, the fluctuating scope of the monitored infurmation during a period is taken as interval numbers, and the interval multi-attribute decision-making method is employed to predict the performance of aeroengine, The synthetic weights of interval numbers are obtained by calculating deviation degree and possibility degree. As an example of application, 5 performance parameters monitored on 10 CF6 aeroengines of China Eastern Airlines Co., Ltd are adopted as decision attributes to verify the algorithm. The obtained synthetic ranking result shows the effectiveness and rationality of the proposed method in reflecting the performance stares of aeroengins.

New approach to multiple attribute decision making with interval numbers

In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin＇s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin＇s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Method for multiple attribute decision making based on incomplete linguistic judgment matrix

With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.